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Jennifer has 40% more stamps than Peter. However,

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Jennifer has 40% more stamps than Peter. However, [#permalink] New post 27 Jul 2017, 10:50
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Jennifer has 40% more stamps than Peter. However, if she gives 45 of her stamps to Peter, then Peter will have 10 % more stamps than Jennifer. How many stamps did Jennifer begin with?

(A) 140

(B) 175

(C) 200

(D) 220

(E) 245
[Reveal] Spoiler: OA

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Re: Jennifer has 40% more stamps than Peter. However, [#permalink] New post 19 Sep 2017, 08:29
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If we call Peter's stamps X, we know that at the beginning Jennifer has 1.4X stamps, i.e. 40% more than Peter. In order to find Peter's stamps X, we have divide Jennifer's stamps by 1.4. Thus, I used this to exclude some of the answers, i.e. those who are not divisible by 1.4 since stamps are integers. Thus, I remained with two possible answers A and E. If we check A, we get that X = 100 while 1.4X = 140 but after the exchange X = 145 while 1.4X = 95 so that X is not 10% higher than 1.4X. Thus, the answer is E.
We can check that it is the right answer since X = 175 and 1.4X = 245 and after the exchange 1.4X = 200 while X = 220 which is exactly 10 percent higher than X.
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Re: Jennifer has 40% more stamps than Peter. However, [#permalink] New post 17 May 2018, 15:30
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Carcass wrote:


Jennifer has 40% more stamps than Peter. However, if she gives 45 of her stamps to Peter, then Peter will have 10 % more stamps than Jennifer. How many stamps did Jennifer begin with?

(A) 140

(B) 175

(C) 200

(D) 220

(E) 245


We can let Peter’s stamps = p and Jennifer’s stamps = 1.4p. If Peter is given 45 stamps from Jennifer, he will have (p + 45) stamps, and Jennifer will have (1.4p - 45) stamps.

We can create the equation:

1.1(1.4p - 45) = p + 45

1.54p - 49.5 = p + 45

0.54p = 94.5

p = 175

So Jennifer initially had 175 x 1.4 = 245 stamps.

Answer: E
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Re: Jennifer has 40% more stamps than Peter. However, [#permalink] New post 09 Jan 2019, 12:01
thanks
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Re: Jennifer has 40% more stamps than Peter. However, [#permalink] New post 14 May 2019, 09:11
Peter (X+45)-Jennifer(1.4X-45)=10% of Jennifer (1.4X-45)
So, X=175.
Jennifer=1.4*175=245.
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Re: Jennifer has 40% more stamps than Peter. However, [#permalink] New post 14 May 2019, 12:59
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Quote:
Jennifer has 40% more stamps than Peter. However, if she gives 45 of her stamps to Peter, then Peter will have 10 % more stamps than Jennifer. How many stamps did Jennifer begin with?

(A) 140

(B) 175

(C) 200

(D) 220

(E) 245


If struggling with the algebraic approach, note that in any GRE problem seeking one specific numeric value with the choices in ascending or descending numeric value and the phrase "how many" present, it is likely that a backsolving approach can be successful. Since the other explanations in this thread have more than adequately explained the algebraic method, let's take a look at the backsolving alternative.

List the choices for the problem as seen below.

Jennifer Stamps Beginning
a) 140
b) 175
c) 200
d) 220
e) 245

Then, eliminate any logically impossible choices by considering the steps of the problem. Since the first step of the problem states that Jennifer's number of stamps is 40% more than Peter to begin we know that to find Peter's number of stamps we must divide Jennifer's stamps by 1.4 or 7/5, which logically means that the correct choice must be divisible by 5 and 7 to result in whole number stamp values. Therefore, confidently eliminate choices C & D which are not divisible by 7. This leave choices A, B, and E, so take the middle remaining choice B and work through the constraints of the problem using columns as follows:

Jennifer's Stamps Beginning | Peter Stamps Beginning | J Stamps - 45 | P Stamps +45 | Does P Have 10% More?
||||||||b) 175 ||||||||||||||| 175 ÷ 1.4 = 125 ||| 175 - 45 = 130 | 125 + 45 = 170 || No (Too Many)

Because choice B is too low of a start for Jennifer and only choice E remains a logical possibility during the exam you should immediately select E. However, let's look at the column set up for the choice to confirm that it is indeed correct.

Jennifer's Stamps Beginning | Peter Stamps Beginning | J Stamps - 45 | P Stamps +45 | Does P Have 10% More?
|||||||||e) 245 |||||||||||||| 245 ÷ 1.4 = 175 |||| 245 - 45 = 200 | 175 + 45 = 220 |||| Yes!
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Last edited by MyGuruStefan on 14 May 2019, 17:33, edited 1 time in total.
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Re: Jennifer has 40% more stamps than Peter. However, [#permalink] New post 14 May 2019, 15:50
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Amazing explanation.

I have exhausted the kudos for you Sir, though.

regards
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Re: Jennifer has 40% more stamps than Peter. However, [#permalink] New post 14 May 2019, 17:38
Expert's post
Re: Jennifer has 40% more stamps than Peter. However,   [#permalink] 14 May 2019, 17:38
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