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05 Feb 2019, 23:59
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E
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Difficulty:
95%
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Question Stats:
35% (02:17) correct
65%
(01:59)
wrong
based on 381
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If a price was increased by \(x\%\) and then decreased by \(y\%\), where x and y are both non-zero, is the new price higher than the original?
(1) \(x \gt y\)
(2) \(x = 1.2y\)
M16-12
(1) \(x \gt y\)
(2) \(x = 1.2y\)
M16-12
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12 May 2025, 07:38
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Official Solution:
If a price was increased by \(x\%\) and then decreased by \(y\%\), where x and y are both non-zero, is the new price higher than the original?
Let \(P\) represent the original price.
(1) \(x > y\).
If \(x\) is significantly larger than \(y\), the new price is higher than the original. However, if \(x\) is only slightly larger, the new price is lower. For example, if \(x = 20\) and \(y = 19\), the new price is \(P*1.20*0.81 < P\).
(2) \(x = 1.2y\)
Similar reasoning applies here. If \(y\) is large, the new price is smaller (if \(y = 100\), the new price is 0). If \(y\) is small, the new price is higher than the original (if \(y = 10\), the new price is \(P*1.12*0.9 = P*1.008 > P\)).
(1)+(2) Combining Statement 1 with Statement 2 provides no additional information. For example, if \(P = 100\), \(x = 120\), and \(y = 100\), the new price becomes 0, which is lower than the original price of 100. However, if \(P = 100\), \(x = 12\), and \(y = 10\), the new price becomes \(100 * 1.12 * 0.9 = 100 * 1.008\), which is higher than the original price of 100. Therefore, the given information is not sufficient to determine whether the new price is higher or lower than the original price.
Answer: E
If a price was increased by \(x\%\) and then decreased by \(y\%\), where x and y are both non-zero, is the new price higher than the original?
Let \(P\) represent the original price.
(1) \(x > y\).
If \(x\) is significantly larger than \(y\), the new price is higher than the original. However, if \(x\) is only slightly larger, the new price is lower. For example, if \(x = 20\) and \(y = 19\), the new price is \(P*1.20*0.81 < P\).
(2) \(x = 1.2y\)
Similar reasoning applies here. If \(y\) is large, the new price is smaller (if \(y = 100\), the new price is 0). If \(y\) is small, the new price is higher than the original (if \(y = 10\), the new price is \(P*1.12*0.9 = P*1.008 > P\)).
(1)+(2) Combining Statement 1 with Statement 2 provides no additional information. For example, if \(P = 100\), \(x = 120\), and \(y = 100\), the new price becomes 0, which is lower than the original price of 100. However, if \(P = 100\), \(x = 12\), and \(y = 10\), the new price becomes \(100 * 1.12 * 0.9 = 100 * 1.008\), which is higher than the original price of 100. Therefore, the given information is not sufficient to determine whether the new price is higher or lower than the original price.
Answer: E
General Discussion
06 Feb 2019, 11:41
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Bunuel
The answer is not going to be B, as even statement II is also not sufficient..
Statement I is contained within statement II, so let us straight way check statement II..
Now x=1.2y..
The final price is
\(a(1+\frac{1.2y}{100})(1-\frac{y}{100})=a(1+\frac{1.2y}{100}-\frac{y}{100} +\frac{1.2y^2}{10000}=a(10000+2y-1.2y^2)/10000\)..
Now is this greater than initial a
If you take initial price as 100 and y a small %, say 10%..x=1.2y=12%..
So final price is 100*(1+0.12)(1-0.1)=100*(1.12)*0.9=112*0.9=100.8 , so greater than 100..
But let us take y slightly bigger % say 50% and x=1.2*50%=60%
So final price is 100*(1+0.6)(1-0.5)=100*1.6*0.5=160*0.5=80, which is less than 100..
So different answers..
E
Always be careful while solving % problems when everything is in variables.
