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If the sum of 3 consecutive integers is 54, then what is the product

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happy1992
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If the sum of 3 consecutive integers is 54, then what is the product [#permalink] New post   17 May 2016, 03:16
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If the sum of 3 consecutive integers is 54, then what is the product of the smallest and largest of these integers?

a) 280
b) 292
c) 312
d) 320
e) 323
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E
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Re: If the sum of 3 consecutive integers is 54, then what is the product [#permalink] New post   17 May 2016, 03:25
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happy1992 wrote:
If the sum of 3 consecutive integers is 54, then what is the product of the smallest and largest of these integers?

a) 280
b) 292
c) 312
d) 320
e) 323



Hi,
since the three integers are consecutive, the average will give the middle number..
Avg = 54/3 = 18....
smallest integer = 17 and largest integer = 19..
17*19 = 323
E..

No need to calculate, last digit of 17*19 has to be 3, ..
Only E fits in
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Re: If the sum of 3 consecutive integers is 54, then what is the product [#permalink] New post   17 May 2016, 03:26
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happy1992 wrote:
If the sum of 3 consecutive integers is 54, then what is the product of the smallest and largest of these integers?

a) 280
b) 292
c) 312
d) 320
e) 323


x + (x + 1) + (x + 2) = 54;

x = 17 --> x + 2 = 19 --> x(x + 2) = 17*19 = ...3

Answer: E.
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Re: If the sum of 3 consecutive integers is 54, then what is the product [#permalink] New post   18 Aug 2018, 20:05
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happy1992 wrote:
If the sum of 3 consecutive integers is 54, then what is the product of the smallest and largest of these integers?

a) 280
b) 292
c) 312
d) 320
e) 323


Since the sum of 3 consecutive integers is 54, the middle integer must be the average, which is 54/3 = 18. So the smallest integer must be 17 and the largest must be 19. So the product is 17 x 19 = 323.

Answer: E
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Re: If the sum of 3 consecutive integers is 54, then what is the product [#permalink] New post   15 Nov 2018, 11:07
happy1992 wrote:
If the sum of 3 consecutive integers is 54, then what is the product of the smallest and largest of these integers?

a) 280
b) 292
c) 312
d) 320
e) 323


Since all consecutive numbers are in arithmetic progression we can assume the three numbers to be: a-1, a, a+1

=> (a+1) + a + (a-1) = 54
=> 3a = 54
=> a = 18

The three numbers are 17, 18, 19

The product of the largest and smallest number = 17*19 = XX3 i.e. units place will be 3 and only one option matches the same.

Hence E is the correct option.
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Re: If the sum of 3 consecutive integers is 54, then what is the product [#permalink]
15 Nov 2018, 11:07
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