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

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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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

Kindly see the attachment.

Concept - Number Properties and HCF (Highest Common Factor)

IMO A

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!

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