Percent change

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Rastis: Master | Next Rank: 500 Posts; Posts: 183; Joined: Wed Sep 21, 2011 7:06 amFollowed by: 2 members; Location: Washington, DC; Thanked: 6 times; GMAT Score:500

by Rastis » 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%

I think the answer is D but according to the practice test I took the answer is B. Help please!

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DavidG@VeritasPrep: Legendary Member; Posts: 2663; Joined: Wed Jan 14, 2015 8:25 amFollowed by: 128 members; Location: Boston, MA; Thanked: 1153 times; GMAT Score:770

by DavidG@VeritasPrep » Mon Jan 11, 2016 7:18 am

Rastis wrote: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%

I think the answer is D but according to the practice test I took the answer is B. Help please!

Pick some starting values. Say S = 2, K = 6, and T = 3.

If S increases by 50% the new value of S is 3. (50% of 2 = 1; 2 + 1 = 3)
K is constant, so now we have 3= 6/T
Solving, we see T is now 2.

If the old value of T was 3, and the new value is 2, then T decreased by [(3-2)/3] = 1/3 = 33%

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by [email protected] » Mon Jan 11, 2016 10:12 am

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?"

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chetan.sharma: Senior | Next Rank: 100 Posts; Posts: 46; Joined: Sun Dec 27, 2015 7:03 amFollowed by: 1 member; Thanked: 8 times

by chetan.sharma » Mon Jan 11, 2016 10:35 pm

Rastis wrote: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%

I think the answer is D but according to the practice test I took the answer is B. Help please!

Hi,
where you must be going wrong is that you are talking about the new number being what % of old number, that is. 66 2/3%...
But what we have to find is decrease..
decrease will be initial-final= t-(66 2/3)% of t
= 33 1/3 % ...

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ceilidh.erickson: GMAT Instructor; Posts: 2095; Joined: Tue Dec 04, 2012 3:22 pmFollowed by: 247 members; Thanked: 1443 times

by ceilidh.erickson » Wed Jan 13, 2016 1:40 pm

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.

Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8155; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

Re: Percent change

by Scott@TargetTestPrep » Tue Sep 15, 2020 4:34 am

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

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