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If the product of the integers a, b, c, and d is 1,155 and if a > b >

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Carcass
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If the product of the integers a, b, c, and d is 1,155 and if a > b > [#permalink] New post   24 Jun 2021, 08:54
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If the product of the integers a, b, c, and d is 1,155 and if a > b > c > d > 1, then what is the value of a – d?

(A) 2
(B) 8
(C) 10
(D) 11
(E) 14
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B
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Re: If the product of the integers a, b, c, and d is 1,155 and if a > b > [#permalink] New post   24 Jun 2021, 09:21
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\(abcd = 1155\) & \(a > b > c > d > 1\)

\(1155 = 3 * 5 * 7 * 11\)

\(a = 11 , b = 7 , c = 5 , d = 3\)

\(a - d = 8\)

Answer B
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Re: If the product of the integers a, b, c, and d is 1,155 and if a > b > [#permalink] New post   24 Jun 2021, 09:25
Carcass wrote:
If the product of the integers a, b, c, and d is 1,155 and if a > b > c > d > 1, then what is the value of a – d?

(A) 2
(B) 8
(C) 10
(D) 11
(E) 14


This question calls for some prime factorization
1,155 = (3)(5)(7)(11)

Since 1 < d < c < b < a, we can conclude that d = 3, c = 5, b = 7 and a = 11

So, a - d = 11 - 3 = 8.

Answer: B
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abrahamtamru27
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If the product of the integers a, b, c, and d is 1,155 and if a > b > [#permalink] New post   21 Jul 2023, 19:07
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I personally did not clearly see the prime factors of 1155 right away

so I started with \( 1155= 1200-45 \)
\( 1155= 5*(240-9) \)
\( 1155= 5*8(80-3) \), we can now clearly break down \( 80-3 to 77= 11*7 \)
\( 1155= 5*8*7*11\) , since 11>7>5>3>1, 11-3 =8.
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If the product of the integers a, b, c, and d is 1,155 and if a > b > [#permalink]
21 Jul 2023, 19:07
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