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18 Oct 2022, 01:30
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
42% (02:12) correct
58%
(02:19)
wrong
based on 73
sessions
History
Date
Time
Result
Not Attempted Yet
b is a multiple of 7. Is ab a multiple of 1,638 ? (a and b are positive integers)
(1) a is divisible by 39
(2) Every factor of 42 is a factor of a
(1) a is divisible by 39
(2) Every factor of 42 is a factor of a
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
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Data Sufficiency Forum
18 Oct 2022, 01:57
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Bunuel
b=7k. Is ab = 1638t? ( k and t are integers)
(1) a is divisible by 39
a=39y, so ab=7k*39y=273ky.
If ky=6*1 or 12*2, then answer is yes.
If ky=2*5 or 2*1, then no.
Insufficient
(2) Every factor of 42 is a factor of a
a=42y, so ab=7k*42y=294ky.
If ky=39*1 or 39*2, then answer is yes.
If ky=2*5 or 2*1, then no.
Insufficient
Combined
We can say is multiple of LCM(42,39) or 546 => a=546y
so ab=7k*546y.
If ky=3*1 or 9*2, that is multiple of 3, then answer is yes.
If ky=2*5 or 2*1, then no.
Insufficient
E
18 Oct 2022, 08:23
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Bunuel
Solution:
Pre Analysis:
- Given b is a multiple of 7 which means we can write \(b=7k\) where k is a positive integer
- We are asked if ab is a multiple of 1638 or not. This means we are asked if \(ab=1638p\) where p is a positive integer
\(⇒7k\times b=1638p\)
\(⇒b=\frac{1638p}{7k}\)
\(⇒b=234 \frac{p}{k}\) - For p to be a positive integer, p has to be a multiple of k
- Thus, we are asked if p is a multiple of k or not
Statement 1: a is divisible by 39
- According to this statement, \(a=39q\) where q is a positive integer
- And we can write \(ab=1638p⇒39q\times 7k=1638p⇒qk=6p\)
- From the above expression, we cannot be sure if p is a multiple of k or not
- Thus, statement 1 alone is not sufficient and we can eliminate options A and D
Statement 2: Every factor of 42 is a factor of a
- According to this statement, a is a multiple of 42 or \(a=42r\) where r is a positive integer
- And we can write \(ab=1638p⇒42r\times 7k=1638p⇒42rk=234p\)
- From the above expression, we cannot be sure if p is a multiple of k or not
- Thus, statement 2 alone is also not sufficient and we can eliminate option B
Combining:
- Upin combining, we get that a=LCM(39,42)s where s is a positive integer
- Or \(a=546s\)
- \(ab=1638p⇒546s\times 7k=1638p⇒546sk=234p\)
- Still not sufficient
Hence the right answer is Option E
