In the last five years, the country of Norland has reduced b

Question

In the last five years, the country of Norland has halved its exports to the country of Estavia and tripled its exports to other countries. Now, only  p% % of its exports go to Estavia.

What percent of Norland’s exports went to Estavia five years ago?

(A)  \frac{600p}{5p + 100} %
(B)  \frac{600p}{5p - 100} %
(C)  \frac{300p}{5p + 100} %
(D)  \frac{600p}{6p + 100} %
(E)  \frac{100p}{5p + 100} %

AdarshSambare · Answer

Let total exports 5 years ago = 100.
Let exports to Estavia = x, so others = 100 − x.
After 5 years:
Estavia = x/2
Others = 3(100 − x)
New total = x/2 + 3(100 − x) = 300 − 5x/2
Given (x/2) / (300 − 5x/2) = p/100
Solve:
x/2 = (p/100)(300 − 5x/2)
50x = p(300 − 5x/2)
100x = 600p − 5px
100x + 5px = 600p
x(100 + 5p) = 600p
x = 600p / (100 + 5p) 
 Answer: Option A

kevincan · Answer

You could also go backwards!

chetan2u · Answer

Questions speaking about percentage can be tackled by taking total as 100.
Let the export to Estavia be 20% or 20 units, and to remaining be 80 units.
Export to Estavia if halved becomes 10 units ...
Export to remaining if tripled becomes 80*3 or 240 units ...
So p% becomes 10/250 * 100 or 4%.
Look for option that gives you answer as 20 when p is substituted as 4.

(A)  \frac{600p}{5p + 100} %
 \frac{600*4}{5*4 + 100} %
 \frac{2400}{120} % or 20%
That is what we were looking for..

kevincan · Answer

Suppose that now, the value of Norland’s exports is 100.
 
P go to Estavia and 100 - p go elsewhere .

Then five years ago, exports to Estavia were 2p and those to other countries were 1/3(100 - p)

Thus the ratio of exports to Estavia to those elsewhere was 6p to 100 - p

So the ratio of exports to Estavia to total exports was 6p to 100 + 5p

Therefore the percentage of Norland’s exports that went to Estavia was 600p/(100+5p) percent

In the last five years, the country of Norland has reduced b

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In the last five years, the country of Norland has reduced b

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards