The weight of pears Pat could have bought for the same amount of money depends on the ratio of prices. For instance, if pears cost 1/2 as much as apples, then Pat could have bought twice as many pounds of Pears(10 pounds)
Rephrase: What is the ratio of the price of 1 pound of apples to the price of 1 pound of pears?
Statement 1:
This makes ratio impossible to determine. the ratio of prices could be $0.50/$1.00 or $1.00/$1.50. Since we cannot answer our rephrase, this statement is INSUFFICIENT.
We can also think about this logically. if apples cost $0.01 and pears cost $0.51, then we can buy about 50 times as many pounds of apples as pears with the same amount of money. On the other hand, if apples cost $0.50 and pears $1, we can buy just twice as many pounds of apples.
Statement 2:
This directly answers hour rephrase. ratio of prices of apples to pears is 2/3 (or pears to apples is 3/2). So this statement is SUFFICIENT.
If this were a problem solving and we wanted to solve, we could use the knowledge that total spent is price-per-pound x pounds, and that total spent is the same for both fruits, to draw the equation:
apple-price-per-pound * 5 pounds = pear-price-per-pound * x pounds
Replace pear-price-per-pound with (3/2)(apple-price-per-pound) and you will see that the prices cancel each other out to give you:
5 = (3/2) * x where x is the number of pounds of pears.
The answer is B
Pears
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Given: Pat bought 5 pounds of apples.Sak32 wrote:Pat bought 5 pounds of apples. How many pounds of pears could Pat have bought for the same amount of money?
1) One pound of pears costs 0.50$ more than one pound of apples.
2) One pound of pears costs 3/2 times as much as one pound of apples.
Target question: How many pounds of pears could Pat have bought for the same amount of money?
This is a good candidate for rephrasing the target question.
Let A = the price per pound of apples
Let P = the price per pound of pears
If Pat bought 5 pounds of apples, then 5A = the total amount that Pat spent
Pat then wants to spend her 5A dollars on pears
So, 5A/P = the number of pounds of pears Pat can buy with the 5A dollars
REPHRASED target question: What is the value of 5A/P?
Aside: Here's a video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100
Statement 1: One pound of pears costs 0.50$ more than one pound of apples.
In other words, P = A + 0.5
Does this help us determine the value of 5A/P?
No.
Take 5A/P and replace P with A + 0.5 to get: 5A/P = 5A/(A + 0.5)
Since there's no way to determine the value of 5A/(A + 0.5) (aka 5A/P), we cannot answer the REPHRASED target question with certainty.
So, statement 1 is NOT SUFFICIENT
Statement 2: One pound of pears costs 3/2 times as much as one pound of apples.
In other words, P = (3/2)A or we can write P = 1.5A
Does this help us determine the value of 5A/P?
Yes!!
Take 5A/P and replace P with 1.5A to get: 5A/P = 5A/1.5A = 5/1.5 = 3 1/3
Since we can answer the REPHRASED target question with certainty, statement 2 is SUFFICIENT
Answer: B
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We are given that Pat bought 5 pounds of apples for some amount of money, and we are asked to determine the number of pounds of pears she could have bought for the same amount of money.Sak32 wrote:Pat bought 5 pounds of apples. How many pounds of pears could Pat have bought for the same amount of money?
1) One pound of pears costs 0.50$ more than one pound of apples.
2) One pound of pears costs 3/2 times as much as one pound of apples.
Statement One Alone:
One pound of pears costs $0.50 more than one pound of apples.
If we let a = the cost (in dollars) of a pound of apples, then a + 0.5 = the cost (in dollars) of a pound of pears. We can also let x = the number of pounds of pears that cost exactly the same as 5 pounds of apples.
Since the overall cost for 5 pounds of apples needs to be the same as for x pounds of pears, we can create the following equation:
5a = x(a + 0.5)
x = 5a/(a + 0.5)
Since we cannot determine a value for x, statement one alone is not sufficient.
Statement Two Alone:
One pound of pears costs 3/2 times as much as one pound of apples.
Once again, we can let a = the cost (in dollars) of a pound of apples. It must then be true that 1.5a = the cost (in dollars) of a pound of pears. We also can let x = the number of pounds of pears that cost exactly the same as 5 pounds of apples.
Since the overall cost for 5 pounds of apples needs to be the same as for x pounds of pears, we can create the following equation:
5a = x(1.5a)
x = 5a/(1.5a)
x = 5/1.5
x = 10/3 = 3.33 lbs
Statement two alone is sufficient.
Answer: B
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