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The product of a certain pair of integers

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The product of a certain pair of integers

by gmatdriller » Thu Nov 01, 2012 10:44 am
The product of a certain pair of consecutive integers is less than their sum.
What is the value of their sum?

(1)One of the two numbers is 1.
(2)Neither of the two numbers is 0.

OA is B
picking a pair of numbers was ok, but algebra got stuck:
i used x(x+1) < x + (x+1)
x^2 + x < 2x + 1
x^2 -x - 1 < 0..x cannot be an integer..am i missing something?
Last edited by gmatdriller on Thu Nov 01, 2012 11:29 am, edited 1 time in total.
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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Thu Nov 01, 2012 11:00 am
gmatdriller wrote:The product of a certain pair of consecutive integers is less than their sum.
What is the value of their sum?

(1)One of the two numbers is 1.
(2)Neither of the two numbers is 0.

OA is C
picking a pair of numbers was ok, but algebra got stuck:
i used x(x+1) < x + (x+1)
x^2 + x < 2x + 1
x^2 -x - 1 < 0..x cannot be an integer..am i missing something?
Target question: What is the value of their sum?

Given: Their product is less than their sum.

Statement 1: One of the two numbers is 1.
This statements gives us only two possible cases to consider
Case a: the numbers are 0 and 1, in which case their sum is 1
Case b: the numbers are 1 and 2, in which case their sum is 3
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Aside: Notice that, if the product of a certain pair of consecutive integers is less than their sum, then there are only two pairs of numbers possible.
The numbers must be either 0 and 1 or 1 and 2

Statement 2: Neither of the two numbers is 0
The given information tells that the numbers must be either 0 and 1 or 1 and 2
Statement 2 rules out the possibility that the numbers are 0 and 1, which means the numbers must be 1 and 2, which means the sum must be 3
Since we can answer the target question with certainty, statement 21 is SUFFICIENT

Answer = B

Cheers,
Brent
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by gmatdriller » Thu Nov 01, 2012 11:33 am
Hello Brent,
Thanks the OA is B. I actually tried it out your method
and got it right after having issues with the algebraic approach.
Could you pls check where i must have made an error in the equation?
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by Brent@GMATPrepNow » Thu Nov 01, 2012 12:02 pm
gmatdriller wrote:Hello Brent,
Thanks the OA is B. I actually tried it out your method
and got it right after having issues with the algebraic approach.
Could you pls check where i must have made an error in the equation?
Your equation, x^2 - x - 1 < 0, is correct.
I'm not sure how you concluded (from this) that cannot be an integer.
We can see that the inequality holds true for x=0 and x=1

Cheers,
Brent
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