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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: 77

Kudos [?]: 151 [0], given: 6

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

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20 Mar 2013, 13:55
00:00

Difficulty:

15% (low)

Question Stats:

84% (00:56) correct 16% (01:51) wrong based on 106 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

[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, 04:46, edited 1 time in total.
Edited the question and the tags.

Kudos [?]: 151 [0], given: 6

Math Expert
Joined: 02 Sep 2009
Posts: 41872

Kudos [?]: 128503 [0], given: 12179

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
Expert's post
1
This post was
BOOKMARKED
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.

_________________

Kudos [?]: 128503 [0], given: 12179

Intern
Status: Currently Preparing the GMAT
Joined: 15 Feb 2013
Posts: 30

Kudos [?]: 25 [1], given: 11

Location: United States
GMAT 1: 550 Q47 V23
GPA: 3.7
WE: Analyst (Consulting)
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
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

Kudos [?]: 25 [1], given: 11

Manager
Joined: 14 Aug 2005
Posts: 83

Kudos [?]: 13 [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, 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

[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!
_________________

One Last Shot

Kudos [?]: 13 [0], given: 2

Math Expert
Joined: 02 Sep 2009
Posts: 41872

Kudos [?]: 128503 [0], given: 12179

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

[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).
_________________

Kudos [?]: 128503 [0], given: 12179

Re: If the product of the integers a, b, c and d is 546 and if 1   [#permalink] 21 Mar 2013, 09:39
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