Missed Quant

Question 1

A farm has chickens, cows and sheep. There are three times the number of chickens and cows than sheep. If there are more cows than chickens or sheep, and together, cows and chickens have a total of 100 feet and heads, how many sheep live at the farm?

A. 5
B. 8
C. 10
D. 14
E. 17

Answer 1

Before approaching this question. We should invest 15 seconds to think about the best approach.

We are told that cows and chicken have 100 feet and heads total.

Chicken= 3 heads and feet
Cows= 5 heads and feet

We are also told that chicken+cows=3sheep

We know that chicken has to be multiple of 5’s and chickens are less than cows. So our options could be be 5 chicken, 17 cows, or 10 chickens and 14 cows. we know that the number of sheep must be divisible by 3, so it must be that there are 10 chickens and 14 cows. this means that there are 8 sheep.

Question 2

If all of the six faces of a concrete block are rectangular, what is the volume of the block?

(1) Each of the four lateral faces of the block has an area of 200 square inches.
(2) The top of the block is square and has an area of 400 square inches.

Answer 2

to figure out this problem, we must realize that to find the volume of a cube/rectangle, we need to know lengthwidthheight.

1) there are many options can result in each lateral face having 200sq^in. for example 2010 or 405.. furthermore, we don’t know the top portion of the surface.
2) the top is a square with an area of 400, this means that each side is 20*20. however, we don’t know the dimensions of the four sides of the figure.

When combining both answer choices, we can see that the dimensions have to be 202010 because the area of the sides have to be 200. We know that the top is 20 by 20. So to plug in the number, the know the other length must be 10.

As such, the answer choice is C.

Question 3

If a and b are integers, is a + b + 3 an odd integer?

(1) ab is an odd integer.
(2) a − b is an even integer.

Answer 3

Remember for this question, we need to understand that odd+odd=even, even+even=even, and odd+even=odd

(1) this means that a & b are both odd integers, because if one value was even then the whole value would be an even integer. this answer choice is S.

(2) a-b is an even integer
this means that 4-2=even
or 3-1=2 even

Let’s check our answer choices 4+2+3=9, odd
3+1+3=7 odd. Thus, this is S
Answer choice is D

Question 4

Last year, a certain company began producing soup A and sold all of the soup A that it produced. To make all of the soup A produced last year, raw ingredients were cooked until their weight was 30% less than their original weight, then a total of 28 kilograms of herbs and spices were added just before soup A was packaged in cans. Did the company sell more than 4,800 cans of soup A last year?

(1) Each can of soup A sold last year contained 0.45 kilograms.
(2) Last year, the total weight of the raw ingredients for soup A, before cooking and excluding the herbs and spices added after cooking, was greater than 3,000 kilograms.

Answer 4

I orignally picked answer C.

We want to know if the company sold more than 4,800 cans of soup A last year. For that we would need to know

1) capacity of each can
2) weight of all raw ingredients

from the information provided, we can set up an equation .7x+28 = final weight of can

1) tells us the capacity, but does not tell us the weight that goes into each can. NS, eliminate A&D

2) this says that x>3,000. Let ‘s plug this into our equation. 3000*.7=2100
2100+28=2128 KG, but we don’t know the capacity of each can. Eliminate

(1)+(2) we know that each can of soupd is .45kg, so
4800*.45 (or 9/20) = 2,160.

As (2) says that it can be be >2,160 or <2,160, the answer is E.

Question 5

At a restaurant, a group of friends ordered four main dishes and three side dishes at a total cost of $91. The prices of the seven items, in dollars, were all different integers, and every main dish cost more than every side dish. What was the price, in dollars, of the most expensive side dish?

(1) the most expensive main dish cost $16
(2) the lease expensive side dish cost $10

Answer 5

I was baited into choosing answer C

(1) we can see that this is S. The only possible outcome is noted below

16+15+14+13+12+11+10=91

(2) same as the statement above. the only outcome is
16+15+14+13+12+11+10=91.

As such, the answer is D.

Question 6

If an ≠ 0 and n is a positive integer, is n odd?

(1) a^n + a^(n + 1) < 0
(2) a is an integer

Answer 6

this is difficult problem, i choose answer choice E

(1) if factor out this problem, we get a^n(1+a)<0.
looking at the two sets, we know that the two things being multiplied must have opposite signs.
if n=even then the left is positive and -1<a></a>

Question 7

A palindrome is a number that reads the same forward and backward, such as 121. How many odd, 4-digit numbers are palindromes?

A. 40
B. 45
C. 50
D. 90
E. 2500

Answer 7

remember to read the quesiton carefully as it asks for ODD numbers only.
_ _ _ _

If we are only considering odd numbers, then the last blank space up there would only have 5 possibilities (1,3,5,7,9). Furthemore, the first blank would have to equal the last blank to be considered a palindrome.

Next, the two middle blanks can be any single digit, so we have 10 options. We know that they two inner blanks must match each other as well.

Piecing together the logic, we have 5101*1, because we have 5 digits to choose from for the first blank and we have 10 digits to chose from for the second blank. Thus, the answer is C, 50.

Question 8

If a and b are positive integers, what is the remainder when ab is divided by 40?

(1) b is 60% greater than a.
(2) Each of a^2b and ab^2 is divisible by 40.

Answer 8

I got this question incorrect, because I was indimindate by the problem.

(1) states that B=8/5(A).
We can further simplify this if we see 5B=8A
From (1), we can see that A must be a multiple of 5 and B must be a multiple of 8. Therefore, ab will always produce a remainder of 0.

(2) NS, plug in numbers to see.

Question 9

Which of the following integers is NOT a divisor of x if x = (21)(3^7) – (112)?

A 7
B 11
C 15
D 17
E 35

Answer 9

I approached this problem correctly, as I broke down the numbers into their prime factorization.
x=(73)(3^7)-(2^47)

We can start by factoring out the 7
7((3^8-2^4)), we can expanding by seeing a difference of two squares

7(3^4+2^2)(3^4-2^2), we can further expand and we can see that we eventually get
{7857*11}
We can get all factors in the options except for 17.

Question 10

In a room filled with 7 people, 4 people have exactly 1 sibling in the room and 3 people have exactly 2 siblings in the room. If two individuals are selected from the room at random, what is the probability that those two individuals are NOT siblings?

A. 5/21
B. 3/7
C. 4/7
D. 5/7
E. 16/21

Answer 10

{A,B,C,D,E,F,G} ===> represents the people in the room
with the information from the passage, we can see that

4 people in the room has one sibling, we can assume that
{A,B} and {C,D} are a sibling pair.

3 people have exactly 2 siblings in the room
{EF}, {EG}, and {GF} are a sibling pair noted above.

We can see that 7 choose 2, there are 21 possibles ways to choose from the group.
the probability that any 2 individuals in the group are NOT siblings are 1-5/21=16/21.

Question 11

In a group of 68 students, each student is registered for at least one of three classes – History, Math and English. Twenty-five students are registered for History, twenty-five students are registered for Math, and thirty-four students are registered for English. If only three students are registered for all three classes, how many students are registered for exactly two classes?

A. 13
B. 10
C. 9
D. 8
E. 7

Answer 11

three venn diagram equation is
sum of students = sum of A+sum of B+sum of C-people in both - 2(people doing all 3)

68=25+25+34-2(3)-x
x=10

Question 12

What is the distance between x and y on the number line?

(1) |x| – |y| = 5
(2) |x| + |y| = 11

Answer 12

(1) we can plug in actual values to test
assume that x=6 and y=1 abs value equals 5
however, x=6 and y=-1, means that the abs value distance is 7. NS

(2) plug in numbers, assume x=5 and y=6 equals 11.
however, x=5 and y=-6 results in different absolute value results.

combined there are still not sufficient.

Question 13

A rectangular wall is covered entirely with two kinds of decorative tiles: regular and jumbo. 1/3 of the tiles are jumbo tiles, which have a length three times that of regular tiles and have the same ratio of length to width as the regular tiles. If regular tiles cover 80 square feet of the wall, and no tiles overlap, what is the area of the entire wall?

A. 160
B. 240
C. 360
D. 440
E. 560

Answer 13

Alternatively, use a neat shortcut. If 1/3 of the tiles are jumbo, then 2/3 are regular. In that case, for every two regular tiles, there is one jumbo tile. One jumbo tile has an area 9Lw and two normal tiles have an area 2Lw, so the tiles will be placed in “sets” of 9Lw + 2Lw = 11Lw. The correct answer, then, must be a multiple of 11, and only answer (D) is a multiple of 11.

Question 14

Bob just filled his car’s gas tank with 20 gallons of gasohol, a mixture consisting of 5% ethanol and 95% gasoline. If his car runs best on a mixture consisting of 10% ethanol and 90% gasoline, how many gallons of ethanol must he add into the gas tank for his car to achieve optimum performance?

A. 9/10
B. 1
C. 10/9
D. 20/19
E. 2

Answer 14

We know that that there is currently
1 gallon E
19 gallon G in his tank right now.

Since we want E=10%, we can set up an equation

(1+x)/(20+x)=1/10, if we solve then we can get the correct answer

C.

Question 15

If 8x > 4 + 6x, what is the value of the integer x?

(1) 6 – 5x > -13
(2) 3 – 2x < -x + 4 < 7.2 – 2x

Answer 15

Remember that x must be an integer
from the stem we get x>2

(1) we can solve and we get x<19/5
this is sufficient, we can conclude that x=3

(2) = we can break this into two inequalities

3 – 2x < –x + 4
3 – 4 < x
–1 < x

–x + 4 < 7.2 – 2x
x < 7.2 – 4
x < 3.2

So, we end up with –1 < x < 3.2. Since we know from the information given in the question that x > 2, we can conclude that 2 < x < 3.2. The only integer between 2 and 3.2 is 3. Therefore, x = 3.

Question 16

If x is a positive integer and 4x–3=y4x–3=y, which of the following CANNOT be a value of y ?

A. 1

B. 7

C. 13

D. 61

E. 253

Answer 16

B

Question 17

If p, r, and s are consecutive integers in ascending order and x is the average (arithmetic mean) of the three integers, what is the value of x ?

(1) Twice x is equal to the sum of p, r, and s.
(2) The sum of p, r, and s is zero.

Answer 17

I originally seletcted as my answer because I did not understand (1).

However, we can see that since p,r,s are consecutive integers then it must be true that
r=x… the median = mean.

Furthermore, we can see that 2x=(x-1)+(x)+(x+1), simpfiy and we get 2x=3x.. the only answer that would satisfy that is 0. thus S.

Answer is D.

Question 18

The total price of 5 pounds of regular coffee and 3 pounds of decaffeinated coffee was $21.50. What was the price of the 5 pounds of regular coffee?

(1) If the price of the 5 pounds of regular coffee had been reduced 10 percent and the price of the 3 pounds of decaffeinated coffee had been reduced 20 percent, the total price would have been $18.45.
(2) T he price of the 5 pounds of regular coffee was $3.50 more than the price of the 3 pounds of decaffeinated coffee.

Answer 18

I orginally picked ans B.

the answer should be D, because option (1) presents us with new information which we can use to solve the problem

Question 19

Jack picked 76 apples. Of these, he sold 4y apples to Juanita and 3t apples to Sylvia. If he kept the remaining apples, how many apples did he keep? (t and y are positive integers.)

(1) y ≥ 15 and t = 2
(2) y = 17

Answer 19

Incorrect math led me to choose A. Howver, the answer is C.

Question 20

If each side of parallelogram P has length 1, what is the area of P ?

(1) One angle of P measures 45 degrees.
(2) The altitude of P is √2/2

Answer 20

need to google response.

I orginally picked B,

answer is D>

Question 21

Jones has worked at Firm X twice as many years as Green, and Green has worked at Firm X four years longer than Smith. How many years has Green worked at Firm X ?

(1) Jones has worked at Firm X 9 years longer than Smith.
(2) Green has worked at Firm X 5 years less than Jones.

Answer 21

I orginally selected answer choice B.

However, if we look closely, (1) is S as well.
the answer should be D.

Question 22

A dance troupe has a total of 50 dancers split into 2 groups. The costumes worn by Group A cost $80 each, and those worn by Group B cost $90 each. If the total cost of all the costumes is $4,270, what is the total cost of the costumes worn by Group B ?

(A) $1,840
(B) $2,070
(C) $2,135
(D) $2,160
(E) $2,430

Answer 22

# in Group B = x
# in Group A= 50-x

90(x)+80(50-x)=4270 ====> tells how many dancers there are in group B. Solve and plug in

ANswer E.

Question 23

Three-fourths of the area of a rectangular lawn 30 feet wide by 40 feet long is to be enclosed by a rectangular fence. If the enclosure has full width and reduced length rather than full length and reduced width, how much less fence will be needed?

A. 5/2
B. 5
C. 10
D. 15
E. 20

Answer 23

Ans is B.

google to find explaination

Question 24

A paint mixture was formed by mixing exactly 3 colors of paint. By volume, the mixture was x% blue paint, y% green paint, and z% red paint. If exactly 1 gallon of blue paint and 3 gallons of red paint were used, how many gallons of green paint were used?

(1) x = y
(2) z = 60

Answer 24

if we really think about this problem, it we don’t really need to use our math skills here. Let’s break it down

x% blue = 1 gallon used
y% green = ? gallon used
z% red = 3 gallons used

(1) x=y if we know that x&y are the same then 1 gallon of green must also be used, S.
(2) if we know that z=60%, we can find out how much 1 gallon is a % of the total. As such, we can further figure out the total gallon used for y.

Question 25

Is the sum of the prices of the 3 books that Shana bought less than $48 ?

(1) The price of the most expensive of the 3 books that Shana bought is less than $17.
(2) The price of the least expensive of the 3 books that Shana bought is exactly $3 less than the price of the second most expensive book.

Answer 25

Remeber, the problem doesn’t say that the prices have to be integers.

(1) this means that the 3 books could be $16.993, which is >48. or 315=45, which is <48
(2) ns

combined, we can see that 17*2=34, and the price of the third book has to be a little less than 14. Doing the math the price of the 3 books will never be greater than 48 .

Question 26

Jill has applied for a job with each of two different companies. What is the probability that she will get job offers from both companies?

1) The probability that she will get a job offer from neither company is 0.3
2) The probability that she will get a job offer from exactly one of the two companies is 0.5

Answer 26

Remember that 
P1 = jobs from both
P2= jobs from only the first company
P3= jobs from only the second company
P4= jobs from neither 

We can see that 1-P4-P2 will tell us P1.
As such answer is C and is .2.

Question 27

If xy ≠ 0 and x2y2−xy=6x2y2−xy=6, which of the following could be y in terms of x?

I. 1/(2x)
II. -2/x
III. 3/x

(A) I only
(B) II only
(C) I and II
(D) I and III
(E) II and III

Answer 27

ran out of time on this one.. couldn’t get an answer.

answer is E… need to remember that we need to have flexible thinking and not linear soooo

x^2+xb+c is quadratic

Question 28

Tanks A and B are each in the shape of a right circular cylinder. The interior of Tank A has a height of 10 meters and a circumference of 8 meters, and the interior of tank B has a height of 8 meters and a circumference of 10 meters. The capacity of tank A is what percent of the capacity of tank B?

(A) 75%
(B) 80%
(C) 100%
(D) 120%
(E) 125%

Answer 28

For the question we are looking for a ratio, is it possible to use ratios only to find ratios. The formula for the volume of a cylinder is V=π∗r2∗hV=π∗r2∗h. Focus on the variables in the formula, we only need to compare their radius squared and height. The ratio of radii is 8:10. The ratio of heights is 10:8. Then the ratio of the volumes is (810)2∗108=8/10=80

Question 29

For a party, three solid cheese balls with diameters of 2 inches, 4 inches, and 6 inches, respectively, were combined to form a single cheese ball. What was the approximate diameter, in inches, of the new cheese ball? (The volume of a sphere is 43πr343πr3, where r is the radius.)

(A) 12

(B) 16

(C) 16−−√3163

(D) 38√3383

(E) 236−−√3

Answer 29

for this problem, we can add the volumes to find the volume of new object (all of them combined). then work backwards to find radius of new object. As such, the answer to this one is E. Can google for full problem and explanation.

Question 30

A certain experimental mathematics program was tried out in 2 classes in each of 32 elementary schools and involved 37 teachers. Each of the classes had 1 teacher and each of the teachers taught at least 1, but not more than 3, of the classes. If the number of teachers who taught 3 classes is n, then the least and greatest possible values of n, respectively, are

A) 0 and 13
B) 0 and 14
C) 1 and 10
D) 1 and 9
E) 2 and 8

Answer 30

Answer is A:

64-37=27

27 to distribute to the remainder
27/2=13.5

13 is the max number of teachers who will receive 3 classes. A is the only one with 13 as an option.

Question 31

The interior of a rectangular carton is designed by a certain manufacturer to have a volume of x cubic feet and a ratio of length to width to height of 3:2:2. In terms of x, which of the following equals the height of the carton, in feet?

A. x√3x3

B. 2x3−−−√32x33

C. 3x2−−−√33x23

D. 23∗x√323∗x3

E. 32∗x√3

https://gmatclub.com/forum/the-interior-of-a-rectangular-carton-is-designed-by-a-certain-110002.html

Answer 31

the ratio is LHW
3k:2k:2k
x=12k^3

k=x12−−√3k=x123 ..
height is 2k as ratios are 3k:2k:2k
so 2k=2x12−−√32k=2x123..
=> 2k=8√3x12−−√32k=83x123..
2k=8x12−−−√32k=8x123..
height=2k=2x3−−−√3height=2k=2x33..
hope this is what you were looking

Question 32

A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 68 percent of the distribution lies within one standard deviation d of the mean, what percent of the distribution is less than m + d ?

(A) 16%
(B) 32%
(C) 48%
(D) 84%
(E) 92%

Answer 32

68% of the distirbution lies within m-d and m+d. we know that the mean is equal to 50% of the distribution.

we know that m+d will be 34%.

so 50%+34% = 84%, ANSWER D.

Question 33

Club X has more than 10 but fewer than 40 members. Sometimes the members sit at tables with 3 members at one table and 4 members at each of the other tables, and sometimes they sit at tables with 3 members at one table and 5 members at each of the other tables. If they sit at tables with 6 members at each table except one and fewer than 6 members at that one table, how many members will be at the table that has fewer than 6 members?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

Answer 33

Remainder type question.. answer choice is E

Question 34

A researcher plans to identify each participant in a certain medical experiment with a code consisting of either a single letter or a pair of distinct letters written in alphabetical order. What is the least number of letters that can be used if there are 12 participants, and each participant is to receive a different code?

A. 4
B. 5
C. 6
D. 7
E. 8

Answer 34

the reason why I got this question wrong is that I didn’t realize the wording of “pair of distinct letters”
that means we cannot use the letter pair “AA or BB”

If I knew that then I would have choose the answer choice B!

Question 35

If [x] denotes the least integer greater than or equal to x, is [x] = 0?

(1) -1< x< 1
(2) x < 0

Answer 35

The key to this question is to understand the prompt. The prompt states that {x} will round up any number to the nearest greatest integer. For example, -.5 would round up to 0. the question is asking will {x} round to 0?
that means will x lie between -1 and 0.

answer is C.

Question 36

Image
In the figure above, points A, B, C, D, and E lie on a line. A is on both circles, B is the center of the smaller circle, C is the center of the larger circle, D is on the smaller circle, and E is on the larger circle. What is the area of the region inside the larger circle and outside the smaller circle?

(1) AB = 3 and BC = 2
(2) CD = 1 and DE = 4

https://gmatclub.com/forum/in-the-figure-above-points-a-b-c-d-and-e-lie-on-a-line-a-is-on-144125.html

Answer 36

1) is sufficent
2) I did not think this statement was sufficent at first, but if we look closely, we can see that we know the diameter of the larger circle. we also can figure the diameter of the smaller circle bc we know that AC is 5 and we know the distance of CD is 1. so we if we know both diameters in then we can find the area of the two.

answer D.

Question 37

In planning for a trip, Joan estimated both the distance of the trip, in miles, and her average speed, in miles per hour. She accurately divided her estimated distance by her estimated average speed to obtain an estimate for the time, in hours, that the trip would take. Was her estimate within 0.5 hour of the actual time that the trip took?

(1) Joan’s estimate for the distance was within 5 miles of the actual distance.
(2) Joan’s estimate for her average speed was within 10 miles per hour of her actual average speed.

Answer 37

We should think about this question logically before doing anything else. If we look at the statements, both of the statements are saying that the estimates are within a given range, but we don’t actually have the actual distance of her actual speed.

This means that her distance could be 10k miles or her speed could be the speed of light. Given the that her estimate is only off by the amounts in the statement then her estimate would be close. But we don’t know the distance so that means we can’t confirm. Answer choice E.

Question 38

y = ax - 5
y = x + 6
y = 3x + b
In the xy-plane, the straight-line graphs of the three equations above each contain the point (p,r). If a and b are constants, what is the value of b?

(1) a = 2
(2) r = 17

Answer 38

the key concept to understand here is that they all intersect at one point.

1) if we know the intersection point of two of the three equation then we can figure out the intersection point of the third.
2) if we know the y value of the intersection point (p,r), then we can back into the intersection point in statement 2. As such, we can find the intersection point of all thre lines.

Thus, answer is D.

Question 39

https://gmatclub.com/forum/if-n-and-k-are-positive-integers-is-n-k-1-2-2n-144724.html

If n and k are positive integers, is n+k−−−−−√>2n√n+k>2n ?

(1) k > 3n
(2) n + k > 3n

Answer 39

FIRST STEP: we should always try to simply the equation within the prompt. When doing so, we get n+k>4n? Or we get k>3n?

1) satisfies this statement
2) NS, because it can or cannot satisfy the statement.

Answer is A.

Question 40

In a certain business, production index p is directly proportional to efficiency index e, which is in turn directly proportional to investment i. What is p if i = 70?

(1) e = 0.5 whenever i = 60
(2) p = 2.0 whenever i = 50

Answer 40

if something is directly proportional then we know that if “p” shifts by a certain amount then i will also shift by a corresponding amount as well.

1) NS, because it gives us the proportional value of e to i only.
2) Sufficient, because it directly gives us the proportion of p to i

Question 41

If n is a positive integer, what is the tens digit of n ?

(1) The hundreds digit of 10n is 6.
(2) The tens digit of n + 1 is 7.

Answer 41

1) Notice what happens when we multiply any positive integer by 10:
34 x 10 = 340
60 x 10 = 600
128 x 10 = 1280
54629 x 10 = 546290
The tens digit in the original number becomes the hundreds digit in the new number.

So, if we’re told that the hundreds digit of 10n is 6, then we know that the tens digit in n must be 6
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

2) we can try some numbers here to prove this statement. Assume that n=70.. 70+1 does not sufficient but, 69+1 does satisfy the statement. Therefore, this is NS.

Answer: A

Question 42

At his regular hourly rate, Don had estimated the labor cost of a repair job as $336 and he was paid that amount. However, the job took 4 hours longer than he had estimated and, consequently, he earned $2 per hour less than his regular hourly rate. What was the time Don had estimated for the job, in hours?

(A) 28
(B) 24
(C) 16
(D) 14
(E) 12

Answer 42

I think the easiest method for this question is the plug and chug method. We know that 336/x is his hourly rate.

we know that 336/(x+4) is his new hourly rate.
In addition, his new hourly rate is 2 less than his normal rate

Let’s try choice B
336/24=14
336/28=12
This is our answer

Question 43

On a recent trip, Cindy drove her car 290 miles, rounded to the nearest 10 miles, and used 12 gallons of gasoline, rounded to the nearest gallon. The actual number of miles per gallon that Cindy’s car got on this trip must have been between

A. 290/12.5 and 290/11.5
B. 295/12 and 285/11.5
C. 285/12 and 295/12
D. 285/12.5 and 295/11.5
E. 295/12.5 and 285/11.5

Answer 43

we know that Cindy must have driven between
285-295
11.5-12.5

WE WANT TO KNOW THE FULL RANGE OF POSSIBILITIES SO THAT’S WHY WE TRY AND MIN/MAX THE RATIOS
In addition, if we want to minimize a ratio then we take the smallest numerator divided by the largest deminonator

if we want to maximize a ration then we take the largest num/smallest demon.

Thus, the answer is D.

Question 44

https://gmatclub.com/forum/which-of-the-following-inequalities-is-an-algebraic-expressi-144267.html

Which of the following inequalities is an algebraic expression for the shaded part of the number line above?

(A) |x| <= 3
(B) |x| <= 5
(C) |x - 2| <= 3
(D) |x - 1| <= 4
(E) |x +1| <= 4

Answer 44

Remember, when solving for inequalities, we have to solve for the positive and negative values of the set.

E) x+1 <= 4, simplifies to x<=3
AND
-x-1<=4, simplifies to x <=-5.

E is our answer

Question 45

In the first week of the Year, Nancy saved $1. In each of the next 51 weeks, she saved $1 more than she had saved in the previous week. What was the total amount that Nancy saved during the 52 weeks?

A. $1,326
B. $1,352
C. $1,378
D. $2,652
E. $2,756

Answer 45

The total amount of money will be 1 + 2 + 3 + 4 + … + 52 (in the 52nd week, she will save $52)

Sum of first n consecutive positive integers = n(n+1)/2
Sum = 5253/2 = 2653
The product will end with 8 since 63 = 18 so answer must be (C).

Question 46

Among a group of 2,500 people, 35 percent invest in municipal bonds, 18 percent invest in oil stocks, and 7 percent invest in both municipal bonds and oil stocks. If 1 person is to be randomly selected from the 2,500 people, what is the probability that the person selected will be one who invests in municipal bonds but NOT in oil stocks?

(A) 9/50
(B) 7/25
(C) 7/20
(D) 21/50
(E) 27/50

Answer 46

.35-.07= % of people that invests solely in muni bonds

28% * 2,500= 700

700/2500 = 7/25
Answer is B

Question 47

If x is to be chosen at random from the set {1, 2, 3, 4} and y is to be chosen at random from the set {5, 6, 7}, what is the probability that xy will be even?

(A) 1/6
(B) 1/3
(C) 1/2
(D) 2/3
(E) 5/6

Answer 47

Ans: D

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