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# The difference between two positive consecutive integers, when each is

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Joined: 02 Sep 2009
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The difference between two positive consecutive integers, when each is  [#permalink]

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10 Jul 2020, 03:59
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15% (low)

Question Stats:

90% (01:12) correct 10% (01:28) wrong based on 48 sessions

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The difference between two positive consecutive integers, when each is squared, equals 29. What is the smaller number?

A. 12
B. 13
C. 14
D. 15
E. 16

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Re: The difference between two positive consecutive integers, when each is  [#permalink]

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10 Jul 2020, 04:03
(n+1)^2 - n^2 = 29

A^2 - B^2 = (A+B)(A-B)

So,
(n+1)^2 - n^2 = 29
=> (n+1+n)(n+1-n) = 29
=> (2n+1)(1) = 29
=> 2n + 1 = 29
=> 2n = 28
=> n = 14

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Re: The difference between two positive consecutive integers, when each is  [#permalink]

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10 Jul 2020, 04:03
Bunuel wrote:
The difference between two positive consecutive integers, when each is squared, equals 29. What is the smaller number?

A. 12
B. 13
C. 14
D. 15
E. 16

Let x and x+1 be the consecutive numbers

as per the question stem, (x+1)^2 - x^2 = 29

=> 2x+1 = 29
=>x=14 & x+1 = 15

Smallest number = 14

OA: C

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Re: The difference between two positive consecutive integers, when each is  [#permalink]

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10 Jul 2020, 04:05
The difference between two positive consecutive integers, when each is squared, equals 29.

A^2-B^2 = 29
(A+B)(A-B) = 29
29 is a prime no.
Therefore A+B = 29
And A-B = 1

Equating both
2A = 30
A = 15
B = 14
Smaller number is 14

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Re: The difference between two positive consecutive integers, when each is  [#permalink]

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10 Jul 2020, 04:30
Since those are consecutive numbers, I assumed that the result of 29 is the sum of the 2 numbers (I can't say exactly why, but looking at the answer choices only 14 and 15 are consecutive and their sum is 29). 15 should be the trap if you didn't look for the smaller number. so (14+1)^2-14^2 cancels the exponent and you left with 28+1 which is exactly 29.
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Re: The difference between two positive consecutive integers, when each is  [#permalink]

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10 Jul 2020, 13:38
Squaring all the options , is one of easy way and checking difference .
12 ^2 =144
13^2= 169
14^2 = 196
15^= 225

altough we get our answer here and no need to go for 16 .

255-196 =29
smallest number is 14 :
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Re: The difference between two positive consecutive integers, when each is  [#permalink]

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11 Jul 2020, 18:09
[(x)^2] - (x+1)^2 = 29
(x^2) - (x+1)(x+1)= 29
(x^2) - (x^2) + 2x +1= 29
2x+1=29
2x=28
x=14 --> C
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Re: The difference between two positive consecutive integers, when each is  [#permalink]

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11 Jul 2020, 19:52
Bunuel wrote:
The difference between two positive consecutive integers, when each is squared, equals 29. What is the smaller number?

A. 12
B. 13
C. 14
D. 15
E. 16

(x-y)(x+y)/(x-y)=29/1→
x+y=29
15-1=14
C
Re: The difference between two positive consecutive integers, when each is   [#permalink] 11 Jul 2020, 19:52