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

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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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20 Mar 2013, 12:55
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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

[Reveal] Spoiler:
"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

[Reveal] Spoiler: OA

Last edited by Bunuel on 21 Mar 2013, 03:46, edited 1 time in total.
Edited the question and the tags.
Math Expert
Joined: 02 Sep 2009
Posts: 37121
Followers: 7255

Kudos [?]: 96650 [0], given: 10775

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, 03:48
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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

[Reveal] Spoiler:
"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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Kudos [?]: 17 [1] , given: 11

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, 08:14
1
KUDOS
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
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Kudos [?]: 12 [0], given: 2

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, 08:25
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

[Reveal] Spoiler:
"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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Posts: 37121
Followers: 7255

Kudos [?]: 96650 [0], given: 10775

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, 08:39
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

[Reveal] Spoiler:
"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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Re: If the product of the integers a, b, c and d is 546 and if 1   [#permalink] 21 Mar 2013, 08:39
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