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Pat bought 5 pounds of apples. How many pounds of pears could he have bought for same amount of money? 1) 1 pound of pears cost $0.5 more that 1 pound of apples 2) 1 pound of pears cost 1.5 times as much as 1 pound of apples

B should be it

st. 1
cost of 1 pound of apples= $x
cost of 1 pound pears= $x+0.5
5 pounds of apples for $5x
and 5x/x+0.5 pounds of pears for $5x INSUFF

st. 2
1 pound of pears= $1.5x
so 5x/1.5x pounds of pears for $5x= 5/1.5 approx= 3 pounds of pears
SUFF

Pat bought 5 pounds of apples. How many pounds of pears could he have bought for same amount of money?

(1) 1 pound of pears cost $0.5 more that 1 pound of apples.

If 1 pound of pears cost $1 and 1 pound of apples cost $0.5, then the cost of 5 pounds of apples is 5*0.5=$2.5. For $2.5 we can buy 2.5/1=2.5 pounds of pears. If 1 pound of pears cost $1.5 and 1 pound of apples cost $1, then the cost of 5 pounds of apples is 5*1=$5. For $5 we can buy 5/1.5=10/3 pounds of pears.

Not sufficient.

(2) 1 pound of pears cost 1.5 times as much as 1 pound of apples. The cost of 5 pounds of apples is $5a (where a is the cost of 1 pound of apples). For $5a we can buy 5a/(1.5a)=5/1.5 pounds of pears. Sufficient.

Re: Pat bought 5 pounds of apples. How many pounds of pears [#permalink]

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10 Aug 2013, 13:17

Bunuel wrote:

fozzzy wrote:

I didn't understand statement 2

Pat bought 5 pounds of apples. How many pounds of pears could he have bought for same amount of money?

(1) 1 pound of pears cost $0.5 more that 1 pound of apples.

If 1 pound of pears cost $1 and 1 pound of apples cost $0.5, then the cost of 5 pounds of apples is 5*0.5=$2.5. For $2.5 we can buy 2.5/1=2.5 pounds of pears. If 1 pound of pears cost $1.5 and 1 pound of apples cost $1, then the cost of 5 pounds of apples is 5*1=$5. For $5 we can buy 5/1.5=10/3 pounds of pears.

Not sufficient.

(2) 1 pound of pears cost 1.5 times as much as 1 pound of apples. The cost of 5 pounds of apples is $5a (where a is the cost of 1 pound of apples). For $5a we can buy 5a/(1.5a)=5/1.5 pounds of pears. Sufficient.

Answer: B.

Hope it's clear.

Hello Bunuel,

Can you please correct my approach of solving this question.

Statement 1:

5 pound of apple cost x 1 pound of apple cost x/5

1 pound of pear would have cost x/5 + 0.5$. Since x is unknown . Hence not sufficient

Statement 2:

1 pound of pear cost 3/2(x/5).

Here, now i thought that since x is still unknown its not sufficient.

Combining both also doesnt give value for x. Hence my answer was E which is incorrect,

Can you please solve this question using my approach. If its correct thanks!

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01 Nov 2014, 12:19

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Re: Pat bought 5 pounds of apples. How many pounds of pears [#permalink]

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26 Feb 2015, 15:00

Seen quite a number of DS problem of this type, when they give you ratio then most probably you can figure it out the values, (2) 3x = 2y. But if they simply give you data like (1) x = y + 0.5 then there are high chances you can't figure it out the answer.

While ankurjohar's question is over 1.5 years old, I'll still answer it because that approach COULD have worked, but the work was incomplete...

Based on that user's initial steps....

$X = cost of 5 pounds of apples $X/5 = cost of 1 pound of apples

Fact 2 tells us that 1 pound of pears costs 1.5 times the cost of 1 pound of apples.

With some Algebra, we have...

(X/5) = cost of 1 pound of apples (3/2)(X/5) = cost of 1 pound of pears 3X/10 = cost of 1 pound of pears

At this point, ankurjohar assumed that this was insufficient, but there's still more work to do....

We now have a ratio that relates what $X will buy you in this situation:

$X buys you 5 pounds of apples

Since $(3/10)(X) buys you 1 pound of pears, $X will buy you 10/3 pounds of pears, so we CAN answer the question with this information. Fact 2 is SUFFICIENT.

Re: Pat bought 5 pounds of apples. How many pounds of pears [#permalink]

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15 Aug 2015, 07:53

Hi

Please, is my reasoning correct?

st2: 1 pound of pears buys 1.5 pounds of apples (so to say you can change back your pears and receive apples instead). Hence 5 pounds of pears will buy 5*1.5 pounds of apples equals 7.5 pounds of apples
_________________

Yes, the ratio that you've calculated IS correct and you can use that ratio to eventually answer the given question (although you did not do any of that work in your explanation).

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Pat bought 5 pounds of apples. How many pounds of pears could he have bought for same amount of money?

(1) 1 pound of pears cost $0.5 more that 1 pound of apples (2) 1 pound of pears cost 1.5 times as much as 1 pound of apples

When you modify the original condition and the question, it is frequently given on GMAT Math, which is "2 by 2" que like the table below.

Attachment:

GCDS r019h Pat bought 5 pounds of apples (20160115).jpg [ 21.67 KiB | Viewed 4931 times ]

On the tables, n=? is derived from 5a=np. Generally, when one con indicates number and the other con indicates ratio, it is most likely that ratio is an answer. As for this question, in 1) number and 2) ratio, substitute p=1.5a in 2) to 5a=np and it becomes 5a=n(1.5a). Then delete a on the both equations -> 5=1.5n, n=5/1.5, which is unique and sufficient. Therefore the answer is B.

Once we modify the original condition and the question according to the variable approach method 1, we can solve approximately 30% of DS questions.
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