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23 Sep 2022, 06:15
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
71% (01:42) correct
29%
(01:36)
wrong
based on 68
sessions
History
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Not Attempted Yet
If a is a multiple of 7, is ab a multiple of 21 ? (a and b are positive integers.)
(1) Every factor of 65 is also a factor of b.
(2) b is divisible by 51.
(1) Every factor of 65 is also a factor of b.
(2) b is divisible by 51.
25 Sep 2022, 11:23
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Given
a consists of at least 7 as one of its prime factors (we don't know at this stage if there are other primes in a)
Question
is ab a multiple of 21 ?
Inference - Does the product of a and b divisible by both 7 and 3.
We already know that the product will be divisible by 7, so we need to find out if either a or b has a 3 in it.
Statement 1
(1) Every factor of 65 is also a factor of b.
Inference : b consists of both 5 and 13. We don't know if b or a has a 3 in it.
If either of them has a 3, the product (ab) will be divisible by 21. Otherwise, the product is not divisible by 21.
Hence this statement is not sufficient.
Statement 2
(2) b is divisible by 51.
Inference : If b is divisible by 51, its also divisible by a factor of 51. As 3 is a factor of 51, b is divisible by 3.
In other words, b has a 3 in it.
This statement is sufficient to answer the question - is ab a multiple of 21
Option B
a consists of at least 7 as one of its prime factors (we don't know at this stage if there are other primes in a)
Question
is ab a multiple of 21 ?
Inference - Does the product of a and b divisible by both 7 and 3.
We already know that the product will be divisible by 7, so we need to find out if either a or b has a 3 in it.
Statement 1
(1) Every factor of 65 is also a factor of b.
Inference : b consists of both 5 and 13. We don't know if b or a has a 3 in it.
If either of them has a 3, the product (ab) will be divisible by 21. Otherwise, the product is not divisible by 21.
Hence this statement is not sufficient.
Statement 2
(2) b is divisible by 51.
Inference : If b is divisible by 51, its also divisible by a factor of 51. As 3 is a factor of 51, b is divisible by 3.
In other words, b has a 3 in it.
This statement is sufficient to answer the question - is ab a multiple of 21
Option B
26 Sep 2022, 01:08
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Bunuel
Solution:
Pre-Analysis:
- a and b are positive integers such that a is a multiple of 7
- We are asked if ab is a multiple of 21 or not
- Two ways can know this:
- If we know that a is a multiple of 21 itself or
- If we get to know that b is a multiple of 3
Statement 1: Every factor of 65 is also a factor of b
- Factors of 65 = Factors of b = 1, 5, 13 and 65
- b might have some other factors like 3 which we don't know
- Thus, statement 1 alone is not sufficient and we can eliminate options A and D
Statement 2: b is divisible by 51.
- If b is divisible by 51, then we can be sure that b is a multiple of 3
- Thus, statement 2 alone is sufficient
Hence the right answer is Option B
