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

Question

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

GMATinsight · Answer

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

JeffTargetTestPrep · Answer

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

generis · Answer

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

manjot123 · Answer

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

NTA · Answer

How could you calculate 94.5/0.54 mentally or without a calculator?  JeffTargetTestPrep

minustark · Answer

Lets say, Peter has x stamps and so, Jennifer has 1.4 *x stamps. When, 1.4 *x - 45, then (x + 45) is 110% of 1.4 *x - 45. So, x + 45 = 1.1 (1.4 x -45) , or, 1.54 x - 49.5 , 0. 54 x = 94.5 , x = 1050/6 = 175.
Jennifer had 175 + 70 = 245 stamps.
E is the answer.

adewale223 · Answer

Multiply both numerator and denominator by 100.

It will give you 9450/54. Then divide.

Posted from my mobile device

bumpbot · Answer

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

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