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# If the product of 3 consecutive integers is 210, then the sum of the

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Math Expert
Joined: 02 Sep 2009
Posts: 53006
If the product of 3 consecutive integers is 210, then the sum of the  [#permalink]

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28 Jan 2019, 03:48
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Difficulty:

5% (low)

Question Stats:

90% (01:28) correct 10% (01:20) wrong based on 31 sessions

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If the product of 3 consecutive integers is 210, then the sum of the two smaller integers is ?

(A) 5
(B) 11
(C) 12
(D) 13
(E) 18

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Joined: 31 Oct 2013
Posts: 1136
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
If the product of 3 consecutive integers is 210, then the sum of the  [#permalink]

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28 Jan 2019, 04:03
Bunuel wrote:
If the product of 3 consecutive integers is 210, then the sum of the two smaller integers is ?

(A) 5
(B) 11
(C) 12
(D) 13
(E) 18

3 consecutive integers.

5 can be the sum of 2 consecutive integer. 3 + 2 = 5. So, 2*3*4 = 24. fail to meet the condition.

11 = 5 + 6 . could be.

12 can't sum of 2 consecutive integers.

13 = 6 + 7 . could be.

18 can't be the sum of 2 consecutive integers

if we consider 6 and 7 are the 2 smaller integers, 3rd will be 8 in this case. but 6*7*8 will not yield 210.

Thus , 3 consecutive integers will be 5*6*7 = 210.

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Re: If the product of 3 consecutive integers is 210, then the sum of the  [#permalink]

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28 Jan 2019, 05:43
Bunuel wrote:
If the product of 3 consecutive integers is 210, then the sum of the two smaller integers is ?

(A) 5
(B) 11
(C) 12
(D) 13
(E) 18

210 = 5*6*7
5+6 = 11
IMO B
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Joined: 07 Dec 2014
Posts: 1156
If the product of 3 consecutive integers is 210, then the sum of the  [#permalink]

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28 Jan 2019, 14:23
Bunuel wrote:
If the product of 3 consecutive integers is 210, then the sum of the two smaller integers is ?

(A) 5
(B) 11
(C) 12
(D) 13
(E) 18

210=(x-1)(x)(x+1)→
x^3-210=x
next perfect cube>210 is 6^3=216
216-210=6=x
x-1=5
5+6=11
B
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Re: If the product of 3 consecutive integers is 210, then the sum of the  [#permalink]

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30 Jan 2019, 18:08
Bunuel wrote:
If the product of 3 consecutive integers is 210, then the sum of the two smaller integers is ?

(A) 5
(B) 11
(C) 12
(D) 13
(E) 18

If the product of 3 consecutive integers is 210, then one of the integers is approximately the cube root of 210. Since ∛210 is approximately (but just less than) 6, we can guess that one of the consecutive integers is 6. Dividing 210 by 6, we obtain 35, which is 5 x 7, so we see that 210 = 5 x 6 x 7. The sum of the two smallest of these consecutive integers is 5 + 6 = 11. .

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Re: If the product of 3 consecutive integers is 210, then the sum of the   [#permalink] 30 Jan 2019, 18:08
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