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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
54% (02:45) correct
46%
(02:42)
wrong
based on 197
sessions
History
Date
Time
Result
Not Attempted Yet
What is the smallest five digit number that is divisible by 16, 24, 36 and 54.
A. 10320
B. 10080
C. 10032
D. 10368
E. None of the above
A. 10320
B. 10080
C. 10032
D. 10368
E. None of the above
19 Nov 2010, 10:58
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nades09
What's the source of this question? It seems remarkably un-GMATesque, since you need to do a lot of crunching to come up with the right answer; especially given the inclusion of choice E, which makes backsolving almost impossible.
That said, let's do some crunching. When you see big numbers and factors or multiples, your first instinct should be to break things down into primes.
Let's break down our component numbers and create the lowest common multiple:
16 = 2*2*2*2
so, our LCM must have 2^4 in it
24 = 2*2*2*3
we already have lots of 2s, so we just need to bring in the 3. Our work in progress is now:
2^4 * 3
36 = 4*9 = 2*2*3*3
we already have lots of 2s and one 3, so we need to bring in one more 3. Our current LCM:
2^4 * 3^2
54 = 2*27 = 2*3*3*3
we need to add 1 more 3, giving us a final LCM of:
2^4 * 3^3
The question asks what's the smallest 5 digit number that's a multiple of our LCM. Here's where the question gets unfair, since there's no elegant (i.e. short and sweet) solution - brute force is now required, something that almost never happens on the GMAT.
Well, our number is 16*27 = 432
432 * 20 = 8640... that's a good starting point, let's work up from there:
8640 + 432 = 9072 + 432 = 9504 + 432 = 9936 + 432 = 10368... choose D.
So, not only is this a poorly constructed question, but (assuming that you copied it correctly) the answer provided is also wrong!
19 Nov 2010, 11:50
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Thanks!
That is how I derived the answer, except instead of adding the LCM, I just factorised each option to select the one that contains 2^4 and 3^2. The question is from 4Gmat question set.
That is how I derived the answer, except instead of adding the LCM, I just factorised each option to select the one that contains 2^4 and 3^2. The question is from 4Gmat question set.
