Problem Solving

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?[/b]

scraby07 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?[/b]

Hi Scraby!

First, please always post the answer choices, since they play a large role in many GMAT strategies. On this question, for example, backsolving (working backwards from the choices) is almost certainly the quickest way to get the answer.

Let's approach it via both algebra and backsolving (we'll have to make up some answers!).

First, algebra:

From the first sentence, we know that J = 1.4P. Since it's almost always easier to do math with fractions than decimals, let's rewrite that as:

J = (7/5)P

From the second sentence, we know that:

(1.1)(J - 45) = P + 45

or, swapping to fractions:

(11/10)(J-45) = P + 45

Since we've been asked to solve for J, let's isolate P and sub in:

J = (7/5)P
(5/7)J = P


(11/10)(J-45) = (5/7)J + 45
(11/10)J - (11/10)45 = (5/7)J + 45

Collecting like terms:

(11/10)J - (5/7)J = 45 + (11/10)45

getting a common denominator:

(77/70)J - (50/70)J = 45 + (11/10)45

(27/70)J = 45 + (11/10)45

finally, multiplying both sides by (70/27):

(70/27)(27/70)J = (45 + (11/10)45)*(70/27)
J = 45(70/27) + (11/10)(70/27)45
J = 5*70/3 + (77/27)*45
J = 350/3 + 385/3
J = 735/3 = 245

Now I think we can all agree there's no way to do that in under 2 minutes, even if you can cut out a few steps!

Backsolving, however, is much much faster. Let's say the choices are:

a) 150
b) 175
c) 200
d) 245
e) 300

When we backsolve, we generally start with (b) or (d); as long as you can figure out if that choice is too big or too small, you'll never have to check more than 2 answers before you're done. We also always apply logic before diving in. Here, we need a pretty big number for that swing of 45 stamps to have a relatively small impact, so let's start with (d).

Now we assume that Jennifer started with 245 stamps. We know that's 40% more than Peter, so:

245 = (7/5)P
(5/7)245 = p
5*35 = P
175 = P

Then we take 45 away from Jennifer and give them to Peter. The totals are now:

J = 200
P = 220

The stem says that Peter should now have 10% more stamps than Jennifer. is 220 10% more than 200? Yes indeed! Therefore, 245 is the correct answer... choose (D)!