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

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by BTGmoderatorDC » Thu Oct 25, 2018 4:59 pm

Timer

00:00

Answers

A

B

C

D

E

Stats

Difficulty—

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

OA C

Source: e-GMAT
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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Thu Oct 25, 2018 10:42 pm
BTGmoderatorDC wrote: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

OA C

Source: e-GMAT
Note that the product of two numbers equals the product of their LCM and GCD. Thus, we need both the statements.

The correct answer: C

Hope this helps!

-Jay
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by Byjus » Thu Oct 25, 2018 11:31 pm
Hi,

This question tests the basic rule of L.C.M and H.C.F

Rule:

If "x" and "y" are two numbers, then

Product of two numbers = Product of their L.C.M and H.C.F

i.e.,

(x*y) = (L.C.M(x,y) * H.C.F(x,y)).

Given in this question,

Two numbers are "a" and "b".

Statement I insufficient:

The LCM of a and b is 16

If a = 4 and b = 16, then LCM is 16 but the product of ab is 64

If a = 2 and b = 16, then LCM is 16 but the product of ab is 32.

So not sufficient.

Statement II insufficient:

The GCD of a and b is 4

If a = 4 and b = 16, then GCD is 4 but the product of ab is 64

If a = 4 and b = 8, then GCD is 4 but the product of ab is 32.

So not sufficient.

Together it is sufficient.

According to the rule,

Product of two numbers = Product of their L.C.M and H.C.F

So, Product of two numbers = 16*4 = 64

So the answer is C.
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by Brent@GMATPrepNow » Fri Oct 26, 2018 6:25 am
BTGmoderatorDC wrote: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
Target question: What is the value of ab?

Statement 1: The LCM of a and b is 16
Let's TEST some values.
There are several values of a and b that satisfy statement 1. Here are two:
Case a: a = 1 and b = 16 (the LCM of 1 and 16 is 16). In this case, the answer to the target question is ab = (1)(16) = 16
Case b: a = 2 and b = 16 (the LCM of 2 and 16 is 16). In this case, the answer to the target question is ab = (2)(16) = 32
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The GCD of a and b is 4
Let's TEST some more values.
Case a: a = 4 and b = 4 (the GCD of 4 and 4 is 16). In this case, the answer to the target question is ab = (4)(4) = 16
Case b: a = 4 and b = 12 (the GCD of 4 and 12 is 16). In this case, the answer to the target question is ab = (4)(12) = 48
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
--------ASIDE----------------------
There's a nice rule that says:
(greatest common divisor of x and y)(least common multiple of x and y) = xy
Example: x = 10 and y = 15
Greatest common divisor of 10 and 15 = 5
Least common multiple of 10 and 15 = 30
Notice that these values satisfy the above rule, since (5)(30) = (10)(15)
--------BACK TO THE QUESTION! ----------------------

Statement 1 tells us that the LCM of a and b is 16
Statement 2 tells us that the GCD of a and b is 4
So, the product ab = (16)(4) = 64
So, the answer to the target question is ab = 64
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by deloitte247 » Fri Oct 26, 2018 1:27 pm
Product of numbers =product of L.C.M * product of GCD/H.C.F
$$Statement\ 1=LCM\ of\ a\ and\ b\ =16$$
$$Given\ that\ L.C.M\ of\ a\ and\ b=16$$
1 and 16; product will be 16
2 and 16; product will be 32
4 and 16; product will be 64
This product doesn't give a unique answer hence it is INSUFFICIENT
$$statement2\ =\ GCD\ a\ and\ \ b\ =4$$
a and b could be =
4 and 8 ; product will be 32
4 and 12 ; product will be 48
4 and 16 ; product will be 64
There are more that 1 possible combination and statement doesn't give a unique answer hence statement 2 is INSUFFICIENT.
statement 1 and 2 together
product of numbers =LCM *GCD
=16*4
=64
Both statements together are SUFFICIENT
$$answer=option\ C$$
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