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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. # The quantities S and T are positive and are related by the e  Question banks Downloads My Bookmarks Reviews Important topics
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The quantities S and T are positive and are related by the e [#permalink]
Expert's post 00:00

Question Stats: 52% (01:03) correct 47% (01:14) wrong based on 69 sessions

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

A $$25$$%

B $$33 \frac{1}{3}$$%

C $$50$$%

D $$66 \frac{2}{3}$$%

E $$75$$%
[Reveal] Spoiler: OA

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Re: The quantities S and T are positive and are related by the e [#permalink]
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Expert's post
Explanation

Plugging numbers for S, T, and k:

S = 4, k = 8, T = 2 → $$4=\frac{8}{2}$$.

Now observe what happens when S is increased by 50%:
50% of 4 is 2, so 4 + 2 = 6

S = 6, k = 8 (constant), T = ? → $$S =\frac{k}{T}$$ → $$6= \frac{8}{?}$$ → $$?= \frac{8}{6}$$ or 1.333
T decreased from 2 to 1.333, or 0.666.....

Compute the percent change:

Percent change = decrease ÷ original number × 100 → 0.666.... ÷ 2 × 100 → 33.333....

Hence option B is correct.
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Re: The quantities S and T are positive and are related by the e [#permalink]
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Expert's post
Carcass 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 T decreases by what percent?

A) 25%

B) 33 and $$\frac{1}{3}%$$

C) 50%

D) 66 and $$\frac{2}{3}$$%

E) 75%

Another approach it to first find some values that satisfy the condition that S = K/T
How about S = 2, K = 2 and T = 1 (since 2 = 2/1)

Now what happens to T if we increase S by 50%?

Well, if we increase 2 (the value of T) by 50%, we get S = 3
K is constant, so K = 2 (still)
What must T equal?

Take S = K/T and plug in the new value of S to get 3 = 2/T (and now solve for T)
To do so, multiply both sides by T to get: 3T = 2
Now divide both sides by 3 to get: T = 2/3

So, the value of T has DECREASED from 1 to 2/3
This represents a 33 1/3% decrease

Cheers,
Brent
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Re: The quantities S and T are positive and are related by the e [#permalink]
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Anytime I see a percent change problem without actual numbers I ask myself, which variable can I make 100?

I care about T most of all so I can make that 100
Then S can be any number so I'll make that something easily increased by 50% so S=2
K must be 200.

2= $$\frac{200}{100}$$

If S is increased by 50% then it becomes 3. K can't change so you're left with

3=$$\frac{200}{T}$$

Solve for T you end up with $$\frac{200}{3}$$or 66.6. It started at 100 ended up at 66.6 so it decreased by 33.3% Answer choice B.
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Re: The quantities S and T are positive and are related by the e [#permalink]
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Carcass wrote:

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

A $$25$$%

B $$33 \frac{1}{3}$$%

C $$50$$%

D $$66 \frac{2}{3}$$%

E $$75$$%

Basically cross multiply s*t = k

then we should get 3/2 * s * 2/3 *t = k

this way it becomes s * t = k

Since we need 2/3 * t it means we reduced it by 1/3.

So answer choice B Re: The quantities S and T are positive and are related by the e   [#permalink] 23 Nov 2018, 18:04
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