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Jennifer has 40% more stamps than Peter. However, if she gives 45 of

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Jennifer has 40% more stamps than Peter. However, if she gives 45 of  [#permalink]

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New post 16 May 2018, 04:46
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

57% (02:53) correct 43% (03:18) wrong based on 79 sessions

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Re: Jennifer has 40% more stamps than Peter. However, if she gives 45 of  [#permalink]

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New post 16 May 2018, 06:03
Bunuel 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


If Peter, P = x
Jeniffer, J = 1.4x

After giving 45% of her stamps,

Jeniffer = 1.4x-45
Peter = x+45

Now Peter = 1.1 Jeniffer

i.e. x+45 = 1.1*(1.4x-45)

i.w. x+45 = 1.54x - 49.5

i.e. 0.54x = 94.5

i.e. x = 175

So Jeniffer in beginning = 1.4x = 245

Answer: Option E
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Re: Jennifer has 40% more stamps than Peter. However, if she gives 45 of  [#permalink]

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New post 17 May 2018, 18:00
Bunuel 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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Jennifer has 40% more stamps than Peter. However, if she gives 45 of  [#permalink]

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New post 17 May 2018, 19:19
Bunuel 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

Using answer choices is quick. Steps:
1) Start: J has 40% more than P. (J = 1.4P)
2) P, start #? Find from #1
3) Then J, end: (J - 45)
4) And P, end: (P + 45)
5) At the end, does P have 10% more = 1.1J?

One more step. To begin, J = 1.4P. There is a factor of 7, which often is not a "nice" number.
Convert: \(1.4=\frac{14}{10}=\frac{7}{5}\)
Start: \(J=\frac{7}{5}P\) which means that \(P=\frac{5}{7}J\)

To find a benchmark, start with (C)
J, start: 200
P, start: \(\frac{5}{7}J\)
P, start: \(\frac{5}{7}*(200)\)
STOP. 200 is not divisible by 7
J's original # of stamps must be divisible by 7

Eliminate C and D Not divisible by 7. Other options? Quick math: (A) 140 = (7 * 20).
(B) 175 = (7 * 25). (E) 245 = (7 * 35) Keep all

Lower and upper limits are A and E. Test one of them. C was no help

Try (A) 140
J, start: 140
P start: \(P=(\frac{5}{7}*J)=(\frac{5}{7}*140)=100=P\)
P start: 100
J, final: (140 - 45) = 95
P, final: (100 + 45) = 145

Does P now have "10% more than J" = \(1.1J\)?
\(\frac{P}{J}=\frac{145}{95}\approx\frac{150}{100}\approx{\frac{3}{2}}=1.5\)
REJECT

\(P\approx1.5J\) is much greater than \(P=1.1J\)

J's original # must be greater so that (J - 45) has a smaller impact. Increase J's base by a lot

E) 245
P, start: \(\frac{5}{7}J=P\)
P, start: \(\frac{5}{7}*(200)=175\)
J, final: (245 - 45) = 200
P, final: (175 + 45) = 220

Is P now equal to 1.1 J?
\(\frac{P}{J}=\frac{220}{200}=\frac{11}{10}=1.1\)

That's a match.

Answer E
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Re: Jennifer has 40% more stamps than Peter. However, if she gives 45 of  [#permalink]

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New post 17 Sep 2018, 02:54
since j = 7/5 p
p = 5/7 j
so options has to be multiple of 7 so 2 options are rejected check rest 3 options
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Re: Jennifer has 40% more stamps than Peter. However, if she gives 45 of   [#permalink] 17 Sep 2018, 02:54
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