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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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Updated on: 27 Feb 2013, 06:13
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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, 19:25. Last edited by Bunuel on 27 Feb 2013, 06:13, edited 1 time in total. Edited the question and added the OA. Most Helpful Expert Reply Math Expert Joined: 02 Sep 2009 Posts: 51073 Re: Pat bought 5 pounds of apples. How many pounds of pears [#permalink] Show Tags 27 Feb 2013, 06:44 6 6 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.

Hope it's clear.
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Re: gmatprep DS- apples and pears  [#permalink]

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30 Oct 2007, 19:41
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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 General Discussion Manager Joined: 22 Dec 2011 Posts: 233 Pat bought 5 pounds of apples. How many pounds of [#permalink] Show Tags 14 Nov 2012, 05:36 3 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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14 Nov 2012, 09:48
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! _________________ Ankit Check my Tutoring Site -> Brush My Quant GMAT Quant Tutor How to start GMAT preparations? How to Improve Quant Score? Gmatclub Topic Tags Check out my GMAT debrief How to Solve : Statistics || Reflection of a line || Remainder Problems || Inequalities Director Joined: 29 Nov 2012 Posts: 759 Re: Pat bought 5 pounds of apples. How many pounds of pears [#permalink] Show Tags 27 Feb 2013, 03:05 I didn't understand statement 2 Intern Joined: 27 Jul 2010 Posts: 12 Re: Pat bought 5 pounds of apples. How many pounds of pears [#permalink] Show Tags 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.

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! EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 13058 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: Pat bought 5 pounds of apples. How many pounds of [#permalink] Show Tags 04 Jan 2015, 12:26 4 3 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: GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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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.
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Re: Pat bought 5 pounds of apples. How many pounds of pears  [#permalink]

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26 Feb 2015, 20:15
4
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.

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

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14 Jan 2016, 10:32
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 _________________ When you’re up, your friends know who you are. When you’re down, you know who your friends are. Share some Kudos, if my posts help you. Thank you ! 800Score ONLY QUANT CAT1 51, CAT2 50, CAT3 50 GMAT PREP 670 MGMAT CAT 630 KAPLAN CAT 660 Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6616 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Pat bought 5 pounds of apples. How many pounds of pears [#permalink] Show Tags 14 Jan 2016, 17:31 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 [ 21.67 KiB | Viewed 17561 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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y pounds of peers -------> 1.5x $Solving we have: 5x/1/3x/2---->10/3---> 3 1/3 pounds of peers. Sufficient. Hence B. _________________ Thanks & Regards, Anaira Mitch Intern Joined: 10 Nov 2016 Posts: 3 Re: Pat bought 5 pounds of apples. How many pounds of pears [#permalink] Show Tags 04 May 2017, 01:42 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 Intern Joined: 19 Aug 2016 Posts: 2 Re: Pat bought 5 pounds of apples. How many pounds of pears [#permalink] Show Tags 06 Jul 2017, 15:53 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 CEO Joined: 11 Sep 2015 Posts: 3228 Location: Canada Re: Pat bought 5 pounds of apples. How many pounds of pears [#permalink] Show Tags 26 Jul 2018, 13:24 Top Contributor 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

Cheers,
Brent

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Re: Pat bought 5 pounds of apples. How many pounds of pears &nbs [#permalink] 26 Jul 2018, 13:24

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