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11 Oct 2021, 04:13
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\(\frac{9}{20}^{th}\) of water from Jar X is poured to jar Y. After this, does jar Y contain more water than jar X ?
(1) After pouring the water, the amount of water in Jar Y increased by more than \(\frac{2}{3}^{rds}\)
(2) After pouring the water, the amount of water in Jar Y increased by less than \(\frac{4}{5}^{ths}\)
(1) After pouring the water, the amount of water in Jar Y increased by more than \(\frac{2}{3}^{rds}\)
(2) After pouring the water, the amount of water in Jar Y increased by less than \(\frac{4}{5}^{ths}\)
11 Oct 2021, 04:13
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Official Solution:
\(\frac{9}{20}^{th}\) of water from Jar X is poured to jar Y. After this, does jar Y contain more water than jar X ?
Say the amount of water in Jar X is \(x\) units and the amount of water in Jar Y is \(y\) units.
The question asks: is \(x - \frac{9}{20}*x < y + \frac{9}{20}*x\)?, which simplifies into is \(x < 10y\) ?.
(1) After pouring the water, the amount of water in Jar Y increased by more than \(\frac{2}{3}^{rds}\)
\(\frac{9}{20}*x > \frac{2}{3}*y\);
\(x > \frac{40}{27}*y\)
So, \(x\) can be less than \(10y\) as well as more than \(10y\). Not sufficient.
(2) After pouring the water, the amount of water in Jar Y increased by less than \(\frac{4}{5}^{ths}\)
\(\frac{9}{20}*x < \frac{4}{5}*y\);
\(x < \frac{16}{9}*y\)
\(x < \frac{16}{9}*y\) gives an YES answer to the question whether \(x < 10y\). Sufficient.
Answer: B
\(\frac{9}{20}^{th}\) of water from Jar X is poured to jar Y. After this, does jar Y contain more water than jar X ?
Say the amount of water in Jar X is \(x\) units and the amount of water in Jar Y is \(y\) units.
The question asks: is \(x - \frac{9}{20}*x < y + \frac{9}{20}*x\)?, which simplifies into is \(x < 10y\) ?.
(1) After pouring the water, the amount of water in Jar Y increased by more than \(\frac{2}{3}^{rds}\)
\(\frac{9}{20}*x > \frac{2}{3}*y\);
\(x > \frac{40}{27}*y\)
So, \(x\) can be less than \(10y\) as well as more than \(10y\). Not sufficient.
(2) After pouring the water, the amount of water in Jar Y increased by less than \(\frac{4}{5}^{ths}\)
\(\frac{9}{20}*x < \frac{4}{5}*y\);
\(x < \frac{16}{9}*y\)
\(x < \frac{16}{9}*y\) gives an YES answer to the question whether \(x < 10y\). Sufficient.
Answer: B
