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Percentage of a Number compared with Fraction of a Number
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09 Oct 2016, 05:33
09 Oct 2016, 05:33
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Question Stats:
48% (00:38) correct
51% (00:35) wrong based on 153 sessions
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Quantity A |
Quantity B |
30 percent of x |
(4/13) of x |
- A : Quantity A is greater
- B : Quantity B is greater
- C : Both quantities are equal
- D : Answer Cannot be determined
Re: Percentage of a Number compared with Fraction of a Number
[#permalink]
09 Oct 2016, 05:45
09 Oct 2016, 05:45
3
Expert Reply
yasir9909 wrote:
Quantity A |
Quantity B |
30 percent of x |
(4/13) of x |
- A : Quantity A is greater
- B : Quantity B is greater
- C : Both quantities are equal
- D : Answer Cannot be determined
Now rewriting 30 percent of x as \(\frac{30}{100}x\)=\(\frac{3}{10}x\)=\(0.3x\).
Re writing Quantity B can be rewritten as \(0.3076x\).
Now x is a positive number say 5. Then Quantity B is greater than Quantity A.
If x = 0. Then Quantity A is equal to Quantity B.
If x is a negative number say -5. Then Quantity A is greater than Quantity B.
Hence Option D is the correct.
Re: Percentage of a Number compared with Fraction of a Number
[#permalink]
09 Oct 2016, 06:37
09 Oct 2016, 06:37
Since no information has been given about x so it could be integer,decimal,rational,irrational number or even 0.So we have three cases to test values of Quantity A & B
Case 1: if x>0 => let x = 2
=> Quantity A < Quantity B
Case 2: if x=0 => let x = 2
=> Quantity A = Quantity B
Case 3: if x<0 => let x = -2
=> Quantity A > Quantity B
Therefore answer is D and answer cannot be determined from given information
Case 1: if x>0 => let x = 2
Quantity A |
Quantity B |
0.3*2=0.6 |
0.3077*2~0.6164 |
=> Quantity A < Quantity B
Case 2: if x=0 => let x = 2
Quantity A |
Quantity B |
0.3*0=0.6 |
0.3077*0=0 |
=> Quantity A = Quantity B
Case 3: if x<0 => let x = -2
Quantity A |
Quantity B |
-0.3*2=-0.6 |
-0.3077*2~-0.6164 |
=> Quantity A > Quantity B
Therefore answer is D and answer cannot be determined from given information
