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
5-Day Free Trial
5-day free, full-access trial TTP
Available with Beat the GMAT members only code
MORE DETAILS
If a and b are two positive numbers, what is the product of
This topic has expert replies
-
BTGmoderatorDC
- Moderator
- Posts: 7187
- Joined: Thu Sep 07, 2017 4:43 pm
- Followed by:23 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
GMAT/MBA Expert
-
Jay@ManhattanReview
- GMAT Instructor
- Posts: 3008
- Joined: Mon Aug 22, 2016 6:19 am
- Location: Grand Central / New York
- Thanked: 470 times
- Followed by:34 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
Note that the product of two numbers equals the product of their LCM and GCD. Thus, we need both the statements.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
The correct answer: C
Hope this helps!
-Jay
_________________
Manhattan Review GMAT Prep
Locations: Hyderabad | Kukatpally | Bangalore | Anna Nagar | and many more...
Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
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.
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.
GMAT/MBA Expert
-
Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
Target question: What is the value of ab?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
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
-
deloitte247
- Legendary Member
- Posts: 2214
- Joined: Fri Mar 02, 2018 2:22 pm
- Followed by:5 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
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
$$answer=option\ C$$
$$Statement\ 1=LCM\ of\ a\ and\ b\ =16$$
$$Given\ that\ L.C.M\ of\ a\ and\ b=16$$
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
$$answer=option\ C$$
