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# If the product of the integers a, b, c and d is 546 and if 1

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Manager
Joined: 24 Jan 2013
Posts: 65
If the product of the integers a, b, c and d is 546 and if 1  [#permalink]

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Updated on: 21 Mar 2013, 04:46
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Question Stats:

79% (01:45) correct 21% (02:23) wrong based on 155 sessions

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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

"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

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.
Edited the question and the tags.
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Joined: 02 Sep 2009
Posts: 58453
Re: If the product of the integers a, b, c and d is 546 and if 1  [#permalink]

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21 Mar 2013, 04:48
johnwesley wrote:
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

"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

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.

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Re: If the product of the integers a, b, c and d is 546 and if 1  [#permalink]

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21 Mar 2013, 09:14
1
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
Manager
Joined: 14 Aug 2005
Posts: 56
Re: If the product of the integers a, b, c and d is 546 and if 1  [#permalink]

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21 Mar 2013, 09:25
Bunuel wrote:
johnwesley wrote:
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

"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

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.

Hi Brunel - Can we actually expect such easy questions to come in GMAT? Just trying to make sure i dont get too excited by solving these quicker!
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Joined: 02 Sep 2009
Posts: 58453
Re: If the product of the integers a, b, c and d is 546 and if 1  [#permalink]

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21 Mar 2013, 09:39
surya167 wrote:
Bunuel wrote:
johnwesley wrote:
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

"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

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.

Hi Brunel - Can we actually expect such easy questions to come in GMAT? Just trying to make sure i dont get too excited by solving these quicker!

Yes, this is GMAT like question (~600 level).
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If the product of the integers a, b, c and d is 546 and if 1  [#permalink]

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22 Feb 2019, 09:33
off the wall approach,

If you just plug in a number for A, you can make a very good guess.

If 1<a<b<c<d and you are multiplying. Then try a = 2,

2*3*4*5 = 120, which is the smallest possible. So E is out,
3,4,5,6 = 360 at this point you can tell that A & B are too large.

This will leave you between C or D, which D makes more sense. Although, there is no constraint on a could be 2 and b could be another extreme

But prime factorization is the best way
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Re: If the product of the integers a, b, c and d is 546 and if 1  [#permalink]

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24 Feb 2019, 06:50
johnwesley wrote:
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

Breaking 546 into primes, we have:

546 = 2 x 273 = 2 x 3 x 91 = 2 x 3 x 7 x 13

Thus, b = 3 and c = 7, so the sum of b and c is 10.

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Re: If the product of the integers a, b, c and d is 546 and if 1   [#permalink] 24 Feb 2019, 06:50
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