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

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

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New post Updated on: 13 Aug 2018, 01:56
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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.

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Originally posted by EgmatQuantExpert on 27 Feb 2018, 10:01.
Last edited by EgmatQuantExpert on 13 Aug 2018, 01:56, edited 4 times in total.
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Re: If a and b are two positive numbers, what is the product  [#permalink]

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New post 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

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Re: If a and b are two positive numbers, what is the product  [#permalink]

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New post 28 Feb 2018, 00:06

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 \(LCM (a, b) = 16\).
Image
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 \(GCD (a, b) = 4\).
Image
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.
Correct Answer: Option C
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Re: If a and b are two positive numbers, what is the product  [#permalink]

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New post 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 &nbs [#permalink] 11 May 2018, 11:45
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