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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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

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

Answer: B

Cheers,
Brent
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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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Even without assuming smart numbers we can solve it.
S=K/T
s is increased by 50% so S = 150
150=K/T
150T=K
T=K/150 = 0.0066 * 100 = 0.66
Earlier T was 1, now 0.66, Percentage difference: 1-0.66 = 0.34

Sometimes I just get confused between percentage difference/decrease and percentage change. Any hint to identify?
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Percent decrease or increase IS a % change
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Thanks @carcass. Is there any percentage difference also? In which we add and subtract?

Posted from my mobile device
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Seee our math book for % theory, please

https://greprepclub.com/forum/gre-quant ... 18388.html
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The other way to solve this is to realise that we need to find percentage change of 'T' and we can say that since S=k/T then T(old)=k/s.

Now S increases by 50% so that means 150/100*S= 3S/2. So now 3S/2=k/T so T(new)= k/3s/2= 2k/3s.

Therefore %∆= 2k/3s–k/s / k/s *100=> –33.33% or 33 1/3 % i.e. B.

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