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69% (02:13) correct
31%
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If the LCM of two numbers a and b is 1104 and their HCF is 4, which of the following MUST be true?
I. a * b = 4416
II. a and b are both divisible by 8
III. a : b = 48 : 23
A. I only
B. II only
C. I and III only
D. II and III only
E. I, II, and III
I. a * b = 4416
II. a and b are both divisible by 8
III. a : b = 48 : 23
A. I only
B. II only
C. I and III only
D. II and III only
E. I, II, and III
10 Apr 2014, 02:05
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ricsingh
If the LCM of two numbers a and b is 1104 and their HCF is 4, which of the following MUST be true?
I. a * b = 4416
II. a and b are both divisible by 8
III. a : b = 48 : 23
A. I only
B. II only
C. I and III only
D. II and III only
E. I, II, and III
I. a * b = 4416
II. a and b are both divisible by 8
III. a : b = 48 : 23
A. I only
B. II only
C. I and III only
D. II and III only
E. I, II, and III
One of the most important properties of LCM (the least common multiple) and GCD (the greatest common divisor) is: for any positive integers \(x\) and \(y\), \(x*y=GCD(x,y)*LCM(x,y)\), so ab = 1104*4 = 4416. Hence option I is in fact true.
Since the greatest common divisor of the two numbers is 4, then at least one number is NOT divisible by 8. Hence II must not be true.
As for III: one number can be 4 and another 1,104, their ratio is not 48:23, thus III must not be true.
Answer: A.
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farful
Joined: 09 Sep 2013
Last visit: 24 Nov 2020
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Location: United States
Schools: Tepper '16 (M)
GMAT 1: 730 Q52 V37
09 Apr 2014, 10:48
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On first sight, this question might look difficult, but if you read through the choices, it's fairly easy.
Look at a. Yeah, who knows. Skip!
Look at b. This answer choice doesn't make any sense. If "x:y = 48:23" is a true statement, there's nothing preventing "x:y = 23:48" from being a true statement either. Thus it's false.
At this point, the answer is "a only" because everything else includes b.
c makes no sense either because we are already given that HCF is 4... if c was true, the HCF would b 8 (or a multiple of 8)
Look at a. Yeah, who knows. Skip!
Look at b. This answer choice doesn't make any sense. If "x:y = 48:23" is a true statement, there's nothing preventing "x:y = 23:48" from being a true statement either. Thus it's false.
At this point, the answer is "a only" because everything else includes b.
c makes no sense either because we are already given that HCF is 4... if c was true, the HCF would b 8 (or a multiple of 8)
