Problem Solving

Hi Rastis,

This question is based on a math 'truism' that's often associated with Rate questions. The answer you chose is actually the answer to a DIFFERENT question.

We're told that S = K/T. Algebraically, that's the same as....

(S)(T) = K

We're told that S and T are both positive and that K is a constant. We're given a hypothetical situation to consider: IF S increases by 50%, by what PERCENT does T decrease....

By increasing S by 50%, we'd have....

(3/2)(S)

...but since K is a CONSTANT, we have to 'offset' that (3/2) with its inverse (in this case, 2/3), which would give us...

(3/2)(S)(2/3)(T) = K
(3/2)(2/3)(S)(T) = K
(6/6)(S)(T) = K
(1)(S)(T) = K
(S)(T) = K

Since T is now 2/3 of its original value, T has DECREASED by 1/3 (or 33 1/3%).

Answer D is the answer to the question "what fraction of T remains?"

GMAT assassins aren't born, they're made,
Rich

Chetan - I was about to say the exact same thing! It's very common on the GMAT for students to do correct math, but then answer the wrong question. Mixing up percent of v. percent change is a really common mistake.

With percent questions, I always have my students write either "% OF" or "% CHANGE" (depending on which the question is asking for) at the top of their paper before they start solving. That can help prevent the mixup.

Rastis wrote: ↑

Mon Jan 11, 2016 6:56 am

The quantities S and T are positive and are related by the equation S = K/T, where K is a constant. If the value of S increases by 50 percent, then the value of of T decreases by what percent?

a) 25%

b) 33 1/3%

c) 50%

d) 66 2/3%

e) 75%

Solution:

Notice that S = k/T means ST = k. Since the value of S increases by 50 percent, S has a multiplier of 1.5. Now we can let m = the multiplier of T and create the equation:

(1.5S)(mT) = k

1.5m(ST) = k

1.5m(k) = k

1.5m = 1

m = 1/1.5 = 2/3

Since m, the multiplier of T, is 2/3, we see that the value of T must decrease by 1/3 or 33 ⅓% to maintain the given relationship between S and T.

Alternate Solution:

Let’s let S = 4 and T = 3. We see that ST = k = 12. Now, if S increases by 50%, its new value is 6, and so 6T = k = 12, and we see that T must now equal 2.

Using the percent change equation (New - Old)/Old x 100, the percent change of T is:

(2 - 3)/3 x 100 = -⅓ x 100 = -33.3%, or a 33.3% decrease.

Answer: B