Word Problems Flashcards
- During 2005, a company produced an average of 2,000 products per month. How many products will the company need to produce from 2006 through 2008 in order to increase its monthly average for the period from 2005 through 2008 by 200% over its 2005 average?
(A) 148,000 (B) 172,000 (C) 200,000 (D) 264,000 (E) 288,000
200% more than 2,000 is 6,000 products per month.
Now, in order the monthly average, from 2005 through 2008, to be 6,000 products per month, the company should produce total of 6,000*48 products in these four years (48 months).
Since in 2005, the company produced total of 2,00012 products, then from 2006 through 2008, the company should produce 6,00048-2,00012=2,00012(34-1)=2,0001211=264,000.
Answer: D.
- An investor purchased 100 shares of stock X at 6 1/8 dollars per share and sold them all a year later at 24 dollars per share. If the investor paid a 2 percent brokerage fee on both the total purchase price and the total selling price, which of the following is closest to the investor’s percent gain on this investment?
(A) 92% (B) 240% (C) 280% (D) 300% (E) 380%
Why many are going wrong is not taking it step wise.
Let us Work on CP and SP separately
CP — 6 1/8 + 2% of 6 1/8=1.0249/8~50/8=6.25
SP — 24-2%of 24=0.9824 should be between 23 and 24, say 23.5
Profit =23.5-6.25=17.25
Profit %=10017.25/6.25=1001725/(625)=(254)(2569)/(2525)=469=276~280%
- A theater with 600 seats sells tickets at $1.20, $1.80, or $2.40 per seat. On Wednesday evening, 1/3 of the tickets sold were at $1.80 per seat and the total receipts from the sale of 600 tickets was $1,020. How many of the tickets sold were at $2.40 per seat?
A. 150 B. 160 C. 200 D. 250 E. 300
Given: 600 tickets were sold
One third of those tickets were at $1.80 per seat
1/3 of 600 = 200
So, 200 tickets sold for $1.80 per seat
And the remaining 400 tickets were sold for either $1.20 each of $2.40 each
Let x = the NUMBER of tickets sold for $2.40
So, 400 - x = the NUMBER of tickets sold for $1.20
The total receipts from the sale of 600 tickets was $1,020
In other words: (receipts from the $1.20 tickets) + (receipts from the $1.80 tickets) + (receipts from the $2.40 tickets) = $1,020
(200)($1.80) = $360
So, $360 = the total receipts from the $1.80 tickets
Likewise, (400 - x)($1.20) = the total receipts from the $1.20 tickets
And (x)($2.40) = the total receipts from the $2.40 tickets
Substitute values into our “word equation” to get: (400 - x)($1.20) + $360 + (x)($2.40) = $1020
Expand to get: 480 - 1.20x + 360 + 2.40x = 1020
Simplify to get: 840 + 1.20x = 1020
Subtract 840 from both sides: 1.20x = 180
Solve: x = 180/1.20 = 150
Answer: A
Method 2:
Total Tickets at $1.80 = 1/3 * 600 = 200
Total cost for 200 tickets at $1.80 = $360
Remaining count of tickets sold at $1.20 & $2.40 = 400
Let total count of tickets sold at $1.20= x
total count of tickets sold at $2.40= 400-x
Total cost for tickets sold at $1.20 = 1.20x
Total cost for tickets sold at $2.40 = 2.40(400-x)
As per question: 1.20x + 360 + 2.40 (400-x) = 1020
Solving for x, x = 250
Tickets at $2.40 = 400-250 = 150
- The average (arithmetic mean) of the 5 houses on a certain street is $60,000. If the price of the least expensive house is $55,000, which of the following could NOT be the price of the most expensive house?
A. $82,000 B. $78,000 C. $72,000 D. $65,000 E. $62,500
Chentu
If you are looking for the least value of the most expensive, take all the others to be maximum possible.
Now the least expensive is 55000, then the other four can be equal and will be (60000*5-55000)/4=245000/4=61250 each
But say all were different, then we would have taken consecutive values for the 4 most expensive
- In 1985 a company sold a brand of shoes to retailers for a fixed price per pair. In 1986 the number of pairs of the shoes that the company sold to retailers decreased by 20 percent, while the price per pair increased by 20 percent. If the company’s revenue from the sale of the shoes in 1986 was $3.0 million, what was the approximate revenue from the sale of the shoes in 1985 ?
(A) $2.4 million (B) $2.9 million (C) $3.0 million (D) $3.1 million (E) $3.6 million
We can let the number of pairs of shoes sold in 1985 = n and the price per pair = p.
Thus, the revenue in 1985 is np and we can create the following equation for the revenue in 1986:
(0. 8n)(1.2p) = 3,000,000
0. 96np = 3,000,000
np = 3,125,000, which is roughly 3.1 million.
Answer: D
- Alice’s take-home pay last year was the same each month, and she saved the same fraction of her take-home pay each month. The total amount of money that she had saved at the end of the year was 3 times the amount of that portion of her monthly take-home pay that she did NOT save. If all the money that she saved last year was from her take-home pay, what fraction of her take-home pay did she save each month?
A. 1/2 B. 1/3 C. 1/4 D. 1/5 E. 1/6
Here’s another algebraic approach.
Let M = Alice’s monthly take home pay
Let f = the fraction we’ll use to calculate monthly savings
The means that fM = the amount of $ Alice saves each month.
And this means that her annual savings = 12fM
Important: If f = the fraction used to calculate monthly savings, then 1-f = the fraction used to calculate amount not saved
The means that (1-f)M = the amount of $ Alice does not save each month.
Now we’re ready to write an equation.
The total amount of money that she had saved at the end of the year was 3 times the amount of that portion of her monthly take home pay that she did not save.
We get: 12fM = 3(1-f)M
Now solve for f
Expand to get: 12fM = 3M - 3fM
Simplify: 15fM = 3M
Divide both sides by 15M to get: f = 3M/15M = 1/5
Answer: D
- A subway train made eleven stops on its route. If an average (arithmetic mean) of 30 passengers boarded at each of the first nine stops and at each stop, beginning with the second, 5 fewer passengers boarded than at the previous stop, how many passengers boarded the train at its first stop?
A. 60 B. 50 C. 30 D. 20 E. 10
GMAT Insight
Total passengers boarded at 9 stations = 9*30 = 270
If passengers at 9th station = x
then passengers at 8th station = x+5
i. e. x+(x+5)+(x+10)+(x+15)+(x+20)+(x+25)+(x+30)+(x+35)+(x+40) = 270
i. e. 9x + 180 = 270
i. e. x = 10
i.e. Passanger at 2nd station = x+40 = 10+40 = 50
Answer: Option B
Scotty
Since at each stop, beginning with the second, 5 fewer passengers boarded the train than at the previous stop, the number of passengers boarding the train at each of the first nine stops forms an evenly-spaced set. Therefore, the 5th stop must have the median, or the average, number of passengers, which is 30. So, the 4th stop has 35, the third has 40, the second has 45, and finally, the first stop has 50 passengers.
Answer: B
- A dealer sold a total of 60 of the three appliances listed in the table above for a total of $4,200. If the dealer sold twice as many food processors as mixers, what was the ratio of the number of blenders sold to the number of food processors sold?
A. 3/2 B. 4/3 C. 6/7 D. 5/12 E. 1/3
Creepy Brent
The dealer sold twice as many food processors as mixers.
Let M = the number of mixers has sold
So, 2M = the number of the food processors sold
The dealer sold a total of 60 of the three appliance
M + 2M = 3M
So, 3M represents the total number of mixers and food processors sold.
Since 60 appliances were sold in total, 60 - 3M = the number of blenders sold
The dealer sold everything for a total of $4,200
We get: (30)(M) + (120)(2M) + (50)(60 - 3M) = 4,200
Simplify: 30M + 240M + 3000 - 150M = 4200
Simplify: 130M + 3000 = 4200
Subtract 3000 from both sides: 120M = 1200
Divide both sides by 120 to get: M = 10
So, the dealer sold 10 mixers
This means the dealer sold 20 food processors
And the dealer sold 30 food processors
Ratio of blenders sold to food processors sold = 30/20 = 3/2
Answer: A
- Dick and Jane each saved $3,000 in 1989. In 1990 Dick saved 8 percent more than in 1989, and together he and Jane saved a total of $5,000. Approximately what percent less did Jane save in 1990 than in 1989?
A. 8% B. 25% C. 41% D. 59% E. 70%
BrentGMATPrepNow
In 1990, Dick saved 8 percent more than in 1989
So, Dick’s savings in 1990 = 1.08($3000)
= $3240
In 1990, Dick and Jane saved a total of $5,000.
So, Jane’s savings = $5,000 - $3240
= $1760
Approximately what percent less did Jane save in 1990 than in 1989?
In 1989, Jane saved $3000
$3000 - $1760 = $1240
ASIDE: We COULD convert $1240/$3000 to a percent, but that’s no fun!
A faster approach is to use the answer choices to our advantage (ALWAYS check the answer choices before performing any calculations)
Notice that $1500/$3000 = 1/2 = 50%
So, $1240/$3000 must be a little less than 50%
Check the answer choices . . . . only C works
Answer: C
- Ms. Adams sold two properties, X and Y, for $30,000 each. She sold property X for 20 % more than she paid for it and sold property Y for 20% less than she paid for it. If expenses are disregarded , what was her total net gain or loss, if any, on the two properties ?
(A) Loss of $1,250 (B) Loss of $2,500 (C) Gain of $1,250 (D) Gain of $2,500 (E) Neither a net gain nor a net loss
There is a property to solve such questions with Common Selling Price and Common %gain and loss. such cases always result in a loss and…
Total %Loss = (Common Gain% or Loss%/10)^2
Hence Here Loss% = (20/10)^2 = 4%
which means he recovered only 96% of his investment which amount to a total revenue = 30000 + 30000 = 60000
i.e. 96% of cost = 60000
therefore, 4% of cost (Loss) = $2500
ALTERNATE
COST PRICE = SELLING PRICE - PROFIT
i. e. COST PRICE of X = 30,000 - (20/100)* COST
i. e. 1.2 Cost of X = 30000
i. e. Cost of X = 30000/1.2 = 25000
Similarly,
COST PRICE = SELLING PRICE + LOSS
i. e. Cost of Y = 30,000 + (20/100)* COST
i. e. 0.8 Cost of Y = 30000
i. e. Cost of Y = 30000/0.8 = 37500
Total Cost of X and Y = 25000 + 37500 = 62500
Total Revenue = 62500 - 60000 = 2500
It discusses how and why we get this formula:
When two items are sold at the same selling price, one at a profit of x% and the other at a loss of x%, there is an overall loss. The loss% = (x^2/100)%
So the loss % here is (20^2/100)% = 4%
Now just approximate. The Cost price will be higher than the selling price and overall selling price is 2*30,000 = $60,000
4% of selling price (60,000) is 2400 so 4% of cost price will be slightly higher.
Answer must be (B)
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