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When three consecutive integers are multiplied together, the result is

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When three consecutive integers are multiplied together, the result is  [#permalink]

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New post 19 Feb 2019, 01:20
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When three consecutive integers are multiplied together, the result is 17,550. What is the greatest of these three integers?

A. 24
B. 25
C. 26
D. 27
E. 28

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Re: When three consecutive integers are multiplied together, the result is  [#permalink]

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New post 19 Feb 2019, 01:33
D is the answer. Defactorize 17550 to prime numbers - 2 x 3^3 x 5^2 x 13. 28 cant be a number as 28 = 4x7 and 4 is not in the factor. Move down and we have 27 and the others are 26 and 25

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When three consecutive integers are multiplied together, the result is  [#permalink]

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New post 19 Feb 2019, 02:48
Bunuel wrote:
When three consecutive integers are multiplied together, the result is 17,550. What is the greatest of these three integers?

A. 24
B. 25
C. 26
D. 27
E. 28



Prime factorization will help us in this regard.

17550 = 1755 *10 = 5*351*5*2=5*3*117*5*2=5*3*3*39*5*2=5*3*3*3*13*5*2.

5*3*3*3*13*5*2

scan the answer options.

E ) 28. the greatest integer. but it's not possible by any combination of prime. discarded.

D) 27. possible. 3*3*3 = 27. but we have to verify that 27 must be the part of consecutive integers.

3*3*3 = 27
13*2 = 26
5*5=25.

(25)(26)(27) = 17550.

Thus , greatest integer is 27.

D is the correct answer.
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Re: When three consecutive integers are multiplied together, the result is  [#permalink]

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New post 19 Feb 2019, 04:21
Bunuel wrote:
When three consecutive integers are multiplied together, the result is 17,550. What is the greatest of these three integers?

A. 24
B. 25
C. 26
D. 27
E. 28


since the value 17,550 has 0 so one of the integers with which its multiplies has to be ending with 5 or 0
given options we have 25 ; so range can be 23*24*25 , 25*26*27 , 24,25,26
only three possiblities
out of which 25,26,27 fits right
IMO D
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Re: When three consecutive integers are multiplied together, the result is   [#permalink] 19 Feb 2019, 04:21
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