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Pat bought 5 pounds of apples. How many pounds of pears

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

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New post Updated on: 27 Feb 2013, 07:13
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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

Originally posted by r019h on 30 Oct 2007, 20:25.
Last edited by Bunuel on 27 Feb 2013, 07:13, edited 1 time in total.
Edited the question and added the OA.
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Re: Pat bought 5 pounds of apples. How many pounds of pears  [#permalink]

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New post 27 Feb 2013, 07:44
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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.
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Re: gmatprep DS- apples and pears  [#permalink]

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New post 30 Oct 2007, 20:41
5
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trivikram wrote:
r019h wrote:
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
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Pat bought 5 pounds of apples. How many pounds of  [#permalink]

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New post 14 Nov 2012, 06:36
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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

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

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New post 14 Nov 2012, 10:48
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

We need a relationship between price of pears and that of apples to solve the question.

STAT1
1p = 0.5 + 1a
But this relationship is not sufficient to answer because
price of 5 pounds of apples = 5p = 5*0.5 + 5a but we cannot tell for sure about the exact pounds of apples we can buy

STAT2
1p = 1.5*1a
This relationship is sufficient because
price of 5 pounds of apples = 5p = 5*1.5 *1a= 7.5a
so we know for sure that we can buy 7.5 pounds of apples with the same money.
So, Answer will be B

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

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New post 27 Feb 2013, 04:05
I didn't understand statement 2
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Re: Pat bought 5 pounds of apples. How many pounds of pears  [#permalink]

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New post 10 Aug 2013, 14:17
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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Re: Pat bought 5 pounds of apples. How many pounds of  [#permalink]

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New post 04 Jan 2015, 13:26
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Hi All,

In these types of DS questions, if you're sure if a pattern exists or not, you can prove it by TESTing VALUES and being thorough. Here's how:

We're told that Pat bought 5 pounds of apples. We're asked how many pounds of pears could have been purchased with the same amount of money.

**Note: I'm going to assume that both the cost per pound of apples and the cost per pound of pears remains constant.**

Fact 1: 1 pound of pears costs $0.5 more than 1 pound of apples.

IF....
A pound of apples cost $1, then a pound of pears costs $1.50
5 pounds of apples = $5
$5 = $1.50(X pounds of pears)
X = 3 1/3 pounds of pears

IF...
A pound of applies costs $.50, then a pound of pears costs $1
5 pounds of applies = $2.50
$2.50 = $1(X pounds of pears)
X = 2.5 pounds of pears
The answer changes based on the starting price of a pound of applies.
Fact 1 is INSUFFICIENT

Fact 2: 1 pound of pears costs 1.5 times as much as 1 pound of apples

IF...
A pound of applies costs $1, then a pound of pears costs $1.50
5 pounds of applies = $5
$5 = $1.50(X pounds of pears)
X = 3 1/3 pounds of pears

A pound of applies costs $2, then a pound of pears costs $3
5 pounds of applies = $10
$10 = $3(X pounds of pears)
X = 3 1/3 pounds of pears

A pound of applies costs $0.50, then a pound of pears costs $0.75
5 pounds of apples = $2.50
$2.50 = $0.75(X pounds of pears)
X = 3 1/3 pounds of pears

In EVERY situation, we end up with the SAME number of pounds of pears.
Fact 2 is SUFFICIENT

Final Answer:

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

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New post 26 Feb 2015, 16:00
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.
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Re: Pat bought 5 pounds of apples. How many pounds of pears  [#permalink]

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New post 26 Feb 2015, 21:15
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Hi All,

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.

Final Answer:

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

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New post 26 Feb 2015, 21:26
it is typical when difference in values of one item is not sufficient to count total number of items, but their ratio is sufficient

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

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New post 15 Aug 2015, 08:53
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
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Re: Pat bought 5 pounds of apples. How many pounds of pears  [#permalink]

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New post 15 Aug 2015, 10:33
Hi shasadou,

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).

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

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New post 14 Jan 2016, 11:32
r019h wrote:
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


................A........P
Pounds.......5.........P
Price.........x.........y

(1) \(y=x+0,5\), \(5x=p(x+0,5)\), you cannot get rid of x, hence not sufficient
(2) \(y=1,5x\) --> \(5x=p*1,5x\) -> \(p=10/3\)

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

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New post 14 Jan 2016, 18:31
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
GCDS r019h Pat bought 5 pounds of apples (20160115).jpg [ 21.67 KiB | Viewed 16568 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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Re: Pat bought 5 pounds of apples. How many pounds of pears  [#permalink]

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New post 28 Jan 2017, 16:29
A is insufficient because the amount of peers will change depending on the cost of apples.

B establishes a relationship:
5 pounds of apples -----> x $
y pounds of peers -------> 1.5x $

Solving we have: 5x/1/3x/2---->10/3---> 3 1/3 pounds of peers.
Sufficient.

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

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New post 28 Jan 2017, 16:30
A is insufficient ecause the amount of peers will change depending of the cost of apples.

B establishes a relationship:
5 pounds of apples -----> x $
y pounds of peers -------> 1.5x $

Solving we have: 5x/1/3x/2---->10/3---> 3 1/3 pounds of peers.
Sufficient.
Hence B.
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Re: Pat bought 5 pounds of apples. How many pounds of pears  [#permalink]

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New post 04 May 2017, 02:42
nitestr wrote:
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.


Super tip! was about to say the same :-D
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Re: Pat bought 5 pounds of apples. How many pounds of pears  [#permalink]

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New post 06 Jul 2017, 16:53
Stem -> 5*a = x*p

1 -> p = a+.5;
NS; as we cant solve for x without value of a

2 -> p = 1.5a
SF; substituting back, a cancels out, and we can solve for x
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Re: Pat bought 5 pounds of apples. How many pounds of pears  [#permalink]

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New post 26 Jul 2018, 14:24
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r019h wrote:
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


Given: Pat bought 5 pounds 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: Below, you'll find a video with tips on rephrasing the target question

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

Cheers,
Brent

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