Question: 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 T decreases by what percent?

1. 25%
2. 33 ¹/₃%
3. 50%
4. 66 ²/₃%
5. 75%

“The quantities S and T are positive and are related by the equation” - is a topic of the GMAT Quantitative reasoning section of GMAT. To solve GMAT Problem Solving questions a student must have knowledge about a good number of qualitative skills. GMAT Quant section consists of 31 questions in total. The GMAT quant topics in the problem-solving part require calculative mathematical problems that should be solved with proper mathematical knowledge.

Solutions and Explanation

Approach Solution : 1

The simplest way to solve this issue will be to plug in values. Numerous figures could be used. Because 10 = 20/2, you could use S = 10, k = 20, and T = 2.

S is now increased by 50%, giving you 15. Find the new T using this:

> S = k/T
> 15 = 20/T
> 15T = 20
> T = 20/15 = 4/3

T thus increases from 2 to 4/3. Determine the percentage reduction:

> Percent change equals Difference/Original, which is 100%.
> Change in percentage = 2/3 / 2 100% = 1/3 100% = 33 ⅓ %

Correct Answer: (B)

Approach Solution : 2

Keep in mind that ST = k if S = k/T. S has a multiplier of 1.5 because its value increases by 50%. We can now let m equal the multiplier of T to form the following equation:

(1.5S)(mT) = k
1.5m(ST) = k
1.5m(k) = k
1.5m = 1
m = 1/1.5 = 2/3

We can see that the value of T must drop by 1/3, or 33⅓ %, in order to preserve the predetermined relationship between S and T because m, the multiplier of T, is 2/3.

Correct Answer: (B)

Approach Solution : 3

Allow S to be 4 and T to be 3. As can be seen, ST = k = 12.
As a result, 6T = k = 12 and we see that T must equal 2 if S increases by 50%.
The percent change of the value of T, from 3 to 2, is given by the percent change equation (New - Old)/Old x 100:
(2 - 3)/3 x 100 = -⅓ x 100 = -33.3%, or a 33.3% decline.

Correct Answer: (B)

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