Quant - Mixed 2 (Use Paper) Flashcards
There are 5 women and 4 men. How many different teams of 2 women and 2 men are possible?
Count the women pairs and men pairs separately, then multiply for the total.
Women: 5 * 4 / 2 = 10
Men: 4 * 3 / 2 = 6
10 * 6 = 60
There are 9 candidates for 4 positions on a committee. How many different committees are possible?
126
out of 9, pick 4
4 slots on top, then divide by 4!, because the order doesn’t matter.
6 athletes are competing for gold, silver and bronze medals, plus 1 honorable mention. How many different ways can the awards be distributed?
This time, the order matters, so we don’t divide by “4!”
4 Slots (for gold, silver, bronze, honorable mention) –> 6*5*4*3 = 30*12 = 360
What is the sum of the odd integers from 5 to 25, inclusive?
“inclusive” means including 5 and 25.
Sum = Number of values (N) * Average Value
= N * (First + Last) / 2
N = (Last - First) / Increment + 1
= (25 - 5) / 2 + 1 = 20/2 + 1 = 11
Sum = 11 * (5+25) / 2 = 11 * 15 = 10*15 + 15 = 165
Mary spent a total of $10,000 on supplies, taxes, and rent last year. How much did she spend on rent?
(1) The amount spent on rent was 50 percent of the amount spent on taxes and supplies.
(2) The amount spent on supplies was 1/3 of the amount spent on taxes and rent
A- (1) Alone
DON’T CALCULATE!
Rephrase: 10,000 = S + T + R, R = ?
If we have 2 more unique equations, or 1 equation that has the combo “S + T”, it’s sufficient!
(1) R = .5(T + S) –> 2R = S + T –> Can substitute S + T into the equation, and solve for R.
(2) S = 1/3 (T + R). This time, we can’t isolate “S+T”. Insufficient.
If the product of the two digits of the positive integer N is 12, what is N?
(1) N > 40
(2) N is an odd integer
B: (2) Alone
Rephrase: what are the possibilities for N?
4*3 = 12, 2*6 = 12
So, N could be 43, 34, 26, or 62
1) Could be 43 or 62 –> Insufficient
2) Can only be 43 –> Sufficient
The number of pens that Joe and Mary had were in a 2:3 ratio. After Mary gave Joe 6 pens, Mary had 3 pens for every 7 that Joe had. After this gift, Joe had how many more pens than Mary?
8
Start with unknown multiplier: Joe / Mary = 2x / 3x
Then, we add 6 to Joe, and subtract 6 from Mary, to create an equation with the new ratio.
Make sure to put the ratio in the correct order: The new ratio is 7/3
Cross-multiply and solve for x.
Make sure to answer the question asked!
Plug in x –> (2x + 6) / (3x - 6) = 14 / 6 –> 14 - 6 = 8
A boat was sold at a loss of 40% of the purchase price. Another boat was sold at a profit of 20% of the purchase price. If each boat was sold for $30,000, what was the total profit or loss combined?
Let C = Cost ; calculate separately
Loss: 30,000 = (100% - 40%) * C
30,000 = .6C = 3/5 C
Divide by 3/5 –> Multiply by 5/3 –> C = 50,000 –> Loss = 20,000
Profit: 30,000 = (100% + 20%) * C = 1.2C = 6/5 C
C = 25,000 –> Profit = 5000
Combined, 20,000 - 5,000 = $15,000 Loss
Find the ratio of boxes loaded– night crew : day crew
3/4 the speed, 4/5 as many workers
3/4 * 4/5 = 3/5 = night crew : day crew.
Read carefully! Question asks what fraction of the TOTAL is the day crew
5 / (3+5) = 5/8
Shirts were sold for $20 more than the cost. They were sold at a profit of 40% of the purchase price. The total revenue from shirt sales was $2800. How many shirts were sold?
40
C = Cost or Purchase Price S = Sales Price
20 = 40% * C
20 = 2/5 * C
C = 50
S = 50 + 20 = 70
Revenue = Sales Price * Number sold –> R = SN –> N = R/S
2800 / 70 = 40
If n is a positive integer and the product of all the integers from 1 to n, inclusive, is a multiple of 2^8, what is the least possible value of n?
10
“The product of all integers from 1 to n” translates to n! (n factorial)
We need to find the lowest factorial that includes 8 total 2’s as factors.
What is the area of the yellow shaded region?
What strategy can we use, if an area is hard to calculate directly?
Calculate the area of the entire region, then subtract the unshaded part.
Area of square = 16
For circle, D = 4, so r = 2
Area of circle = πr2 = π(22) = 4π
16 - 4π
Machine type A does a job in 8 hours, while machine type B does a job in 12 hours. If 2 machines of type A are used, how many machines of type B are needed to complete the job in 90 minutes?
Calculate the Work separately for A and B:
A: N = 2, R = 1/8, T = 90 minutes = 3/2 hours
W = NRT = 2 * 1/8 * 3/2 = 3/8
So, work remaining for type B is 1 - (3/8) = 5/8
B: 5/8 = N * 1/12 * 3/2
5/8 = N * 1/8 –> N = 5
DS: What is the remainder when the positive integer x is divided by 4?
(How can we translate the following statements? What is the pattern?)
(1) When x is divided by 8, the remainder is 1
(2) When x is divided by 6, the remainder is 5
A –> (1) Alone
(1) –> 1 more than a multiple of 8
1, 9, 17, 25, 33….
All are also 1 more than a multiple of 4 –> Sufficient
(2) 5 more than a multiple of 6 –> 5, 11, 17, 24…
5/4 – > remainder 1
11/4 —> remainder 3
Insufficient.
DS: What is the remainder when the positive integer x is divided by 8?
(How can we translate the following statements? What is the pattern?)
(1) When x is divided by 8, the remainder is less than 5
(2) When x is divided by 4, the remainder is 2
C: Together
(1) Clearly insufficient alone: R (remainder) can be 1, 2, 3, or 4
(2) 2 more than a multiple of 4
Pattern is 2, 6, 10, 14,
Remainders when above numbers are divided by 8: 2, 6, 2, 6
2 possibilities –> Insufficient
Together, statement (1) eliminates 6, so the reminder must be 2 –> Sufficient
An integer between 1 and 66 is chosen at random. What is the probability that n(n+1) will be divisible by 6?
Pattern will repeat every 6 numbers, up to 66.
“Divisible by 6” means “has both 2 and 3 as factors”
Easiest way is to create a chart:
4/6 = 2/3
Mary drives at a speed of 66 feet/second. How many miles away is she from her home, if it will take her 3 hours to reach home? (Given 1 mile = 5280 feet)
A) 25
B) 80
C) 135
D) 210
E) 300
c) 135
RT = D ; T = 3 –> 3R = D
Need to convert from feet/second to miles/hour. Set it up so units cross out on top and bottom, to avoid mistakes. (see image below)
If we notice the answer chioces are quite far apart, we can approximate, instead of calculating exactly!
3600/5280 is approximately 2/3 –> 2/3 * 66 = 44 mi/hr. (3600/5280 simplifies to 15/22 –> you can verify this as practice, but if we can approximate and save time that’s great)
3R = D –> 44*3 = 132 –> C
Is the probability greater than 50% that a student randomly selected will be a female with brown hair?
(1) 1/2 of the students are female
(2) 1/2 of the students have brown hair
D - Each Alone
If the question asked for the probability VALUE, we couldn’t find it.
But since it asks for YES / NO, we can definitively say NO for each statement.
The BOTH box on matrix (or green “Intersection” on Venn Diagram) can’t be greater than the total female or total brown hair!
Is the probability less than 40% that a student randomly selected will be a female with brown hair?
(1) 1/2 of the students are female
(2) 1/3 of the students have brown hair
B - (2) Alone
Could convert fractions to percents for easier comparison: 1/2 = 50%, 1/3 is about 33%.
(1) Maximum for Both is 50%. Could be YES or NO. Insufficient
(2) The maximum for Both is 1/3 –> Must be YES –> Sufficient.
The Both box on matrix can’t be greater than the Total for brown hair!
Of 400 athletes, 160 neither ran nor jumped, and 120 jumped. For every athlete that did both, 3 only ran. What percentage of athletes both ran and jumped?
We want “Both”. So define x as “Both”.
Then, 3x goes in “only ran”.
400 - 120 = 280 in “Not J” box
Solve for x: 3x + 160 = 280 –> 3x = 120 –> x = 40
40 / 400 = 10%
