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# A four-digit number with consecutive positive integers is a product of

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VP
Joined: 07 Dec 2014
Posts: 1156
A four-digit number with consecutive positive integers is a product of  [#permalink]

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14 Sep 2018, 12:57
2
4
00:00

Difficulty:

55% (hard)

Question Stats:

61% (02:41) correct 39% (02:23) wrong based on 70 sessions

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A four-digit number with consecutive positive integers is a product of 2x and x^2. What is the sum of these two factors?

A. 80
B. 99
C. 168
D. 224
E. 288
Math Expert
Joined: 02 Aug 2009
Posts: 7334
A four-digit number with consecutive positive integers is a product of  [#permalink]

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14 Sep 2018, 20:37
4
gracie wrote:
A four-digit number with consecutive positive integers is a product of 2x and x^2. What is the sum of these two factors?

A. 80
B. 99
C. 168
D. 224
E. 288

Number is 4-digit and =2x*x^2=2x^3, thus an even number..
Cases
1) 1234..
$$2x^3=1234....x^3=617... Between 8^3--9^3$$ , so no integer value possible
2) 3456..
$$2x^3=3456......x^3=1728......x=12$$, so we have a possible value
We are looking for $$2x+x^2=2*12+12^2=24+144=168$$

C
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

GMAT Expert

Manager
Joined: 12 Sep 2017
Posts: 132
Re: A four-digit number with consecutive positive integers is a product of  [#permalink]

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05 Jan 2019, 16:42
chetan2u wrote:
gracie wrote:
A four-digit number with consecutive positive integers is a product of 2x and x^2. What is the sum of these two factors?

A. 80
B. 99
C. 168
D. 224
E. 288

Number is 4-digit and =2x*x^2=2x^3, thus an even number..
Cases
1) 1234..
$$2x^3=1234....x^3=617... Between 8^3--9^3$$ , so no integer value possible
2) 3456..
$$2x^3=3456......x^3=1728......x=12$$, so we have a possible value
We are looking for $$2x+x^2=2*12+12^2=24+144=168$$

C

Hello!

Do you have another approach?

Kind regards!
Re: A four-digit number with consecutive positive integers is a product of   [#permalink] 05 Jan 2019, 16:42
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# A four-digit number with consecutive positive integers is a product of

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