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22 Apr 2022, 01:30
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C
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Difficulty:
15%
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Question Stats:
89% (01:19) correct
11%
(01:12)
wrong
based on 36
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If x and y are positive integers and x is a multiple of 3, is xy divisible by 48?
(1) x is divisible by 8
(2) y is divisible by 8
(1) x is divisible by 8
(2) y is divisible by 8
24 Apr 2022, 21:46
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Pre-thinking
48 = 3 * 2^4
If xy contains, as factors, at least one 3 and four 2's, xy is divisible by 48.
(1) Only
x contains at least one 3 and three 2's.
no info about y.
xy contains at least one 3 and three 2's.
Insufficient.
(2) Only
x contains at least one 3.
y contains at least three 2's.
xy contains at least one 3 and three 2's.
Insufficient
(1)(2) Together
x contains at least one 3 and three 2's.
y contains at least three 2's.
xy contains at least one 3 and six 2's.
Sufficient
(YES to the question "is xy divisible by 48").
The answer is thus (C).
48 = 3 * 2^4
If xy contains, as factors, at least one 3 and four 2's, xy is divisible by 48.
(1) Only
x contains at least one 3 and three 2's.
no info about y.
xy contains at least one 3 and three 2's.
Insufficient.
(2) Only
x contains at least one 3.
y contains at least three 2's.
xy contains at least one 3 and three 2's.
Insufficient
(1)(2) Together
x contains at least one 3 and three 2's.
y contains at least three 2's.
xy contains at least one 3 and six 2's.
Sufficient
(YES to the question "is xy divisible by 48").
The answer is thus (C).
25 Apr 2022, 03:45
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Step 1: Analyse Question Stem
x and y are positive integers. x is also a multiple of 3.
We have to find out if the product xy is a multiple of 48.
48 = \(2^4\) * 3.
Therefore, if the product xy should be divisible by 48, it should contain a \( 2^4\) * 3 in it.
Step 2: Analyse Statements Independently (And eliminate options) – AD / BCE
Statement 1: x is divisible by 8
From the question data, x is a multiple of 3. Therefore, the product xy will definitely contain \(2^3\) * 3; however depending on the value of y, it may or may not contain the additional 2.
There is no information about y in Statement 1.
The data in statement 1 is insufficient to find out if xy is divisible by 48.
Statement 1 alone is insufficient. Answer options A and D can be eliminated.
Statement 2: y is divisible by 8
From the question data, x is a multiple of 3. Therefore, the product xy will definitely contain \(2^3\) * 3; however, again, we do not know if the additional 2 is present or not, since statement 2 does not provide any information about x.
The data in statement 2 is insufficient to find out if xy is divisible by 48.
Statement 2 alone is insufficient. Answer option B can be eliminated.
Step 3: Analyse Statements by combining
From statement 1: x is divisible by \(2^3\) * 3
From statement 2: y is divisible by \(2^3\)
Therefore, the product of xy must have at least \(2^6\) *3; hence the product will be divisible by 48.
The combination of statements is sufficient to answer that the product xy is divisible by 48.
Statements 1 and 2 together are sufficient. Answer option E can be eliminated.
The correct answer option is C.
x and y are positive integers. x is also a multiple of 3.
We have to find out if the product xy is a multiple of 48.
48 = \(2^4\) * 3.
Therefore, if the product xy should be divisible by 48, it should contain a \( 2^4\) * 3 in it.
Step 2: Analyse Statements Independently (And eliminate options) – AD / BCE
Statement 1: x is divisible by 8
From the question data, x is a multiple of 3. Therefore, the product xy will definitely contain \(2^3\) * 3; however depending on the value of y, it may or may not contain the additional 2.
There is no information about y in Statement 1.
The data in statement 1 is insufficient to find out if xy is divisible by 48.
Statement 1 alone is insufficient. Answer options A and D can be eliminated.
Statement 2: y is divisible by 8
From the question data, x is a multiple of 3. Therefore, the product xy will definitely contain \(2^3\) * 3; however, again, we do not know if the additional 2 is present or not, since statement 2 does not provide any information about x.
The data in statement 2 is insufficient to find out if xy is divisible by 48.
Statement 2 alone is insufficient. Answer option B can be eliminated.
Step 3: Analyse Statements by combining
From statement 1: x is divisible by \(2^3\) * 3
From statement 2: y is divisible by \(2^3\)
Therefore, the product of xy must have at least \(2^6\) *3; hence the product will be divisible by 48.
The combination of statements is sufficient to answer that the product xy is divisible by 48.
Statements 1 and 2 together are sufficient. Answer option E can be eliminated.
The correct answer option is C.
