GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 20 Oct 2018, 12:27

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2069
If a and b are two positive numbers, what is the product  [#permalink]

### Show Tags

Updated on: 13 Aug 2018, 01:56
00:00

Difficulty:

5% (low)

Question Stats:

82% (00:44) correct 18% (01:00) wrong based on 121 sessions

### HideShow timer Statistics

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

Go to

Question 2 of the Marathon

_________________

Number Properties | Algebra |Quant Workshop

Success Stories
Guillermo's Success Story | Carrie's Success Story

Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets

| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

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.
PS Forum Moderator
Joined: 25 Feb 2013
Posts: 1216
Location: India
GPA: 3.82
Re: If a and b are two positive numbers, what is the product  [#permalink]

### Show Tags

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
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2069
Re: If a and b are two positive numbers, what is the product  [#permalink]

### Show Tags

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 $$LCM (a, b) = 16$$.

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.
_________________

Number Properties | Algebra |Quant Workshop

Success Stories
Guillermo's Success Story | Carrie's Success Story

Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets

| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Senior DS Moderator
Joined: 27 Oct 2017
Posts: 910
Location: India
GPA: 3.64
WE: Business Development (Energy and Utilities)
Re: If a and b are two positive numbers, what is the product  [#permalink]

### Show Tags

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.
_________________
Re: If a and b are two positive numbers, what is the product &nbs [#permalink] 11 May 2018, 11:45
Display posts from previous: Sort by