If positive integer P is a multiple of 22 and positive integer Q is a

Question

If positive integer P is a multiple of 22 and positive integer Q is a multiple of 55, is PQ a multiple of 70?

(1) Q is a multiple of 49

(2) P is a multiple of 4

GMATinsight · Answer

Answer: Option A

Please check the video and image attached below for an explanation

https://www.youtube.com/watch?v=ugKI9bWf9tM

yashikaaggarwal · Answer

IMO A,

P=22x and Q=55y
Is PQ = 70z

Solution= PQ = 2*5*7*z
2*11*5*11*x*y = 2*5*7*z
To satisfy the constraint. Either P or Q must have 7 or its multiple in them.

Statement 1: Q = 49a
Therefore. Q has 7 as among its multiple satisfying constraints. (Sufficient)

Statement 2: P = 4b
7 is not mentioned among the factors. 
(Insufficient)

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RaghavKhanna · Answer

P = 22n = 2 * 11 * n
Q = 55m = 5 * 11 * m

To check: PQ = 70s = 2 * 5 * 7 * s

Statement 1:
Q also contains 7^2 
=> PQ contains 2 * 5 * 7
=> PQ is a multiple of 70.
=> Statement 1 is sufficient

Statement 2:
P contains 2^2,but we have no information about power of 7

=> Statement 2 is insufficient.

Answer: A

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rajatchopra1994 · Answer

Explanation:
P is a multiple of 22 = 2x11xA
Q is a multiple of 55, = 5x11xB
Find: is PQ a multiple of 70?, For we need 2x5x7.

Statement 1: Q is multiple of 49; means 7x7.
So, PQ will have 2,5,7 as multiple. Yes it will be also multiple of 70
Sufficient.

Statement 2: P is multiple of 4; means 2x2 
So, but we need 7 to make PQ multiple of 70
Not Sufficient.

IMO-A

sambitspm · Answer

Kindly see the attachment.

Concept - Number Properties and HCF (Highest Common Factor)

IMO A

suchita2409 · Answer

IMO A.

P=2*11*X
Q=5*11*Y
Question basically asks PQ is divisible by 7
Stmt 1
 helps us answer the question directly.

Stmt 2 
Insuff 
 It only says pq is divisible by 4 nothing about 7.

A it is!

ScottTargetTestPrep · Answer

Question Stem Analysis:

We need to determine whether PQ is a multiple of 70 = 2 * 5 * 7. We are told that P is a multiple of 22, which means PQ contains a factor of 2. We are also told that Q is a multiple of 55, which means PQ contains a factor of 5. If we can determine that PQ also contains a factor of 7, we can conclude that PQ is a multiple of 70.

Statement One Alone:

\Rightarrow  Q is a multiple of 49

Thus, Q contains a factor of 7, which in turn means that PQ contains a factor of 7. Since PQ contains a factor of 2, 5, and 7, PQ is a multiple of 70. Statement one alone is sufficient.

Eliminate answer choices B, C, and E.

Statement Two Alone:

\Rightarrow  P is a multiple of 4

While we know that P is a multiple of 4, we cannot determine whether P also contains a factor of 7. If P = 44 and Q = 55, then PQ is not a multiple of 70. On the other hand, if P = 308 and Q = 55, then PQ is a multiple of 70. Since there are more than one possible answers to the question, statement two alone is not sufficient.

Answer: A

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