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# The product of consecutive integers a and b is 156. What is the value

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Math Expert
Joined: 02 Sep 2009
Posts: 52390
The product of consecutive integers a and b is 156. What is the value  [#permalink]

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15 Apr 2015, 03:57
4
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00:00

Difficulty:

85% (hard)

Question Stats:

33% (01:23) correct 67% (01:26) wrong based on 171 sessions

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The product of consecutive integers a and b is 156. What is the value of b?

(1) b is prime

(2) b > a

Kudos for a correct solution.

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Joined: 22 Aug 2014
Posts: 40
Re: The product of consecutive integers a and b is 156. What is the value  [#permalink]

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15 Apr 2015, 04:10
Bunuel wrote:
The product of consecutive integers a and b is 156. What is the value of b?

(1) b is prime

(2) b > a

Kudos for a correct solution.

ab = 156

ab = 13*2*2*3

1.) b is prime. All 4 nos are prime. So inconclusive

2.) b > a. Many possibilities prevail like (3,52), (4,39). So inconclusive

Combining 1 & 2, we get b to be prime and b> a

The only prime no which is greater than a is 13 > 12.

Option C
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Re: The product of consecutive integers a and b is 156. What is the value  [#permalink]

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15 Apr 2015, 04:58
aj13783, the question specifically mentions consecutive integers, therefore ans should be 'D'
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Re: The product of consecutive integers a and b is 156. What is the value  [#permalink]

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15 Apr 2015, 05:03
The product of consecutive integers a and b is 156. What is the value of b?

(1) b is prime

(2) b > a

a*b = 156 what is b?
10*11 = 110
11*12 = 132
12*13 = 156

a = 12 or 13, or -12 or -13
b = 12 or 13 or -12 or -13
signs must be the same

1) b = prime, no negative primes; b = 13 (Sufficient)
2) b > a, 13 > 12; b = 13 (Sufficient)

D.
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Re: The product of consecutive integers a and b is 156. What is the value  [#permalink]

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15 Apr 2015, 07:14
2
1
Bunuel wrote:
The product of consecutive integers a and b is 156. What is the value of b?

(1) b is prime

(2) b > a

Kudos for a correct solution.

156=12*13 OR -12*-13

1. b is prime.

So the negative option is not possible and b can only be 13.

Sufficient

2. b>a
b could be 13 or -12

Not Sufficient.

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Re: The product of consecutive integers a and b is 156. What is the value  [#permalink]

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15 Apr 2015, 07:40
Hmm second statement got me.

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The product of consecutive integers a and b is 156. What is the value  [#permalink]

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Updated on: 15 Apr 2015, 15:34
156 = 2 × 2 × 3 × 13
Consecutive integers so that means 12 × 13.
Is b 12 or 13?

(1) b is prime
b is 13
sufficient

(2) b > a
13 is greater than 12
-12 is greater than -13
insufficient

Originally posted by peachfuzz on 15 Apr 2015, 11:06.
Last edited by peachfuzz on 15 Apr 2015, 15:34, edited 2 times in total.
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Posts: 7
Re: The product of consecutive integers a and b is 156. What is the value  [#permalink]

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15 Apr 2015, 11:33
axb=156
since we have consecutive intengers we can say
b=a+1

therefore ax(a+1)=156

(1) b=a+1
b = prime --> only solutions 13=12+1
sufficent

(2) still only possible solution since we have consecutive intengers 12x13 = 156
sufficent
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Re: The product of consecutive integers a and b is 156. What is the value  [#permalink]

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15 Apr 2015, 12:47
Product of consecutive int a and b =156
12x13 = 156
also
-12x-13 = 156

St 1) b is prime number out of 12,13,-12,-13 only prime number is 13. Thus Suff
St 2) b>a 13>12 and -12>-13 so values of b = 13 or -12. Thus NS

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Re: The product of consecutive integers a and b is 156. What is the value  [#permalink]

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15 Apr 2015, 13:02
The integer 156 can be written as a product of consecutive integers in two ways

156 = 13 x 12
156= -13 x -12

1) b is prime

Prime nos are positive only.

therefore , b=13

Sufficient

2) b>a

b can be = 13 or -12
as 13>12 and -12>-13

Not sufficient

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Posts: 52390
Re: The product of consecutive integers a and b is 156. What is the value  [#permalink]

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20 Apr 2015, 05:54
1
Bunuel wrote:
The product of consecutive integers a and b is 156. What is the value of b?

(1) b is prime

(2) b > a

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION

You might fall for the trap answer, D. You’ll break down 156 into 13 times 12 (and realize that you can’t break 13 down any further so there’s no other way to recombine the prime factors to find consecutive integers with a prime), and note that b has to be 13 and a has to be 12. So choice A is, indeed, sufficient. And then when you get to statement 2 you’ll think – yeah, freebie. 13 is bigger than 12, so it has to be 13. But wait – why can’t it be -12 while a is -13? You’ve fallen into the trap – you assumed negative! Woe is you…why do you keep falling for these traps?!
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Re: The product of consecutive integers a and b is 156. What is the value  [#permalink]

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15 Feb 2017, 15:22
2
Bunuel wrote:
The product of consecutive integers a and b is 156. What is the value of b?

(1) b is prime

(2) b > a

We are given that the product of consecutive integers a and b is 156. If we let a = x and b = x + 1 (or vice versa), we can create the following equation:

x(x + 1) = 156

x^2 + x - 156 = 0

(x + 13)(x - 12) = 0

x = -13 or x = 12

Thus, in no particular order, a and b could be -13 and -12 or 12 and 13. We must determine the value of b.

Statement One Alone:

b is prime.

Since no negative numbers can be prime and 12 is not a prime, the only possible value of b is 13. Statement one alone is sufficient to answer the question.

Statement Two Alone:

b > a

Using the information in statement two, b could be 13 or -12. Statement two is not sufficient to answer the question.

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Re: The product of consecutive integers a and b is 156. What is the value  [#permalink]

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15 Feb 2017, 20:40
Bunuel wrote:
The product of consecutive integers a and b is 156. What is the value of b?

(1) b is prime

(2) b > a

Kudos for a correct solution.

152 = $$2^2*3*13$$ = 12*13 (consecutive integers a*b) or (-12)*(-13)

St I
b is prime
so b has to be 13 and a must be 12 (since prime numbers cant be negative)-----------Sufficient

St II
b>a
If a,b are positive integers then b=13 and a=12
If a,b are negative integers then a=-13 and b=-12 --------------Insufficient

Hence Option A is correct
Hit Kudos if you liked it
Re: The product of consecutive integers a and b is 156. What is the value &nbs [#permalink] 15 Feb 2017, 20:40
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