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Updated on: 21 Mar 2013, 04:46
Originally posted by johnwesley on 20 Mar 2013, 13:55.
Last edited by Bunuel on 21 Mar 2013, 04:46, edited 1 time in total.
Last edited by Bunuel on 21 Mar 2013, 04:46, edited 1 time in total.
Edited the question and the tags.
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D
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If the product of the integers a, b, c and d is 546 and if 1 < a < b < c < d, what is the value of b+c?
A. 273
B. 185
C. 21
D. 10
E. 4
A. 273
B. 185
C. 21
D. 10
E. 4
"If the product of the integers a, b, c and d is 546 and if 1 < a < b < c < d, what is the value of b+c?"
Factors of 546:
546 | 2
273 | 3
91 | 13
7 | 7
1 | 1
If 1 < a < b < c < d, the only possible way is:
d=13
c=7
b=3
a=2
Therefore: b+c = 3 + 7 = 10
Answer D
Factors of 546:
546 | 2
273 | 3
91 | 13
7 | 7
1 | 1
If 1 < a < b < c < d, the only possible way is:
d=13
c=7
b=3
a=2
Therefore: b+c = 3 + 7 = 10
Answer D
21 Mar 2013, 04:48
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johnwesley
Make prime factorization of 546: 546=2*3*7*13.
Now, since given that 1 < a < b < c < d, then a=2, b=3, c=7 and d=13 --> b+c=3+7=10.
Answer: D.
21 Mar 2013, 09:14
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Alright, so we know that the product of a,b,c and d is 546 and 1<a<b<c<d so the first thing we need to do is to break down 546 into a product of prime factors :
546 divided by 2 yields 273
273 divided by 3 yields 91
91 divided by 7 yields 13
Which means that \(546 = 2*3*7*13\).
So if we consider a = 2, b = 3, c = 7 and d = 13 (in respect to the second condition : 1<a<b<c<d), we have : b+c = 3 + 7 = 10 which is answer choice D.
Hope that helped
546 divided by 2 yields 273
273 divided by 3 yields 91
91 divided by 7 yields 13
Which means that \(546 = 2*3*7*13\).
So if we consider a = 2, b = 3, c = 7 and d = 13 (in respect to the second condition : 1<a<b<c<d), we have : b+c = 3 + 7 = 10 which is answer choice D.
Hope that helped
