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# If a and b are two positive numbers, what is the product

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e-GMAT Representative
Joined: 04 Jan 2015
Posts: 1209
If a and b are two positive numbers, what is the product [#permalink]

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Updated on: 07 Mar 2018, 05:35
00:00

Difficulty:

15% (low)

Question Stats:

82% (00:31) correct 18% (01:01) wrong based on 56 sessions

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e-GMAT Question:

If a and b are two positive numbers, what is the product of a and b?

1) The LCM of a and b is 16
2) The GCD of a and b is 4

A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D) EACH statement ALONE is sufficient.
E) Statements (1) and (2) TOGETHER are NOT sufficient.

This is

Question 1 of The e-GMAT Number Properties Marathon

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Question 2 of the Marathon

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Originally posted by EgmatQuantExpert on 27 Feb 2018, 10:01.
Last edited by EgmatQuantExpert on 07 Mar 2018, 05:35, edited 3 times in total.
PS Forum Moderator
Joined: 25 Feb 2013
Posts: 1108
Location: India
GPA: 3.82
Re: If a and b are two positive numbers, what is the product [#permalink]

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27 Feb 2018, 11:07
EgmatQuantExpert wrote:

Question:

If a and b are two positive numbers, what is the product of a and b?

1) The LCM of a and b is 16
2) The GCD of a and b is 4

A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D) EACH statement ALONE is sufficient.
E) Statements (1) and (2) TOGETHER are NOT sufficient.

Statement 1: if a=1 & b=16, then LCM=16 & a*b=16. but is a=2 & b=16, then LCM =16 but a*b=2*16=32. Insufficient

Statement 2: if a=b=4, then HCF=4 & a*b=4*4=16 but if a=4 & b=8, GCD=4 but a*b=32. Insufficient

Combining 1 & 2: Product of two numbers = LCM*GCD. Sufficient

OPtion C
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Joined: 04 Jan 2015
Posts: 1209
Re: If a and b are two positive numbers, what is the product [#permalink]

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28 Feb 2018, 00:06
Expert's post
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Solution:

Step 1: Analyse Statement 1:
The LCM of$$a$$ and $$b$$ is $$16$$.
• Both a and b can have more than 1 combination for their LCM to be $$16$$.
• For example, all the following combinations will have $$LCM (a, b) = 16$$.

From the table, it is evident that there are more than 1 possible combinations of $$a$$ and $$b$$ where their LCM is $$16$$. Hence, their product is also not unique.
Since this statement doesn’t give a unique answer, it is alone not sufficient to answer our question.
Statement 1 alone is NOT sufficient to answer the question.
Hence, we can eliminate answer choices A and D.
Step 2: Analyse Statement 2:
The HCF of $$a$$ and $$b$$ is $$4$$.
• Both a and b can have more than 1 combination for their GCD to be $$4$$.
• For example, all the following combinations will have $$GCD (a, b) = 4$$.

From the table, it is evident that there are more than 1 possible combinations of a and b where their GCD is 4, and hence, their product is also not unique.
Since this statement doesn’t give a unique answer, it is alone not sufficient to answer our question.
Step 3: Combine both Statements:
• From the first Statement we got: $$LCM (a, b)$$ = $$16$$
• From the second Statement we got:$$GCD (a, b)$$ = $$4$$
Per our conceptual knowledge, we can say that the product of two numbers is the product of their LCM and GCD.
• Hence, $$a * b$$= $$LCM (a, b) * GCD (a, b)$$
• Or, $$a*b$$ = $$16*4$$ = $$64$$
By combining both statements we got a unique answer.
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Re: If a and b are two positive numbers, what is the product [#permalink]

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11 May 2018, 11:45
It is recommended to remember the following points:
1) Product of numbers cannot be determined by their LCM only.
2) Product of numbers cannot be determined by their GCD only.

3) Product of numbers = product of LCM & GCD.

Now this question can be done in mind as soon as reading the question stem.
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Re: If a and b are two positive numbers, what is the product   [#permalink] 11 May 2018, 11:45
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