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# If a, b, and c are three consecutive integers (in the order given), wh

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If a, b, and c are three consecutive integers (in the order given), wh  [#permalink]

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05 Apr 2019, 00:47
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If a, b, and c are three consecutive integers (in the order given), what is the value of c ?

1. 2(a + b + c) = 6(a + 1)

2. 1/2(a + b + c) = a + 23

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If a, b, and c are three consecutive integers (in the order given), wh  [#permalink]

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05 Apr 2019, 16:01
If a, b, c is a list of three consecutive integers in order, which is an equally spaced list, then b is the median and mean, so their sum a+b+c is equal to 3b. Note also that b = a+1. So Statement 1 just becomes

2(a+b+c) = 6(a+1)
2(3b) = 6b
6b = 6b

which is obviously always true, regardless of the value of any of our unknowns, so Statement 1 doesn't tell us anything.

Statement 2 becomes

(1/2)(3b) = (b-1) + 23
(3/2)b = b + 22

which clearly has one numerical solution for b (not that we need to find it, but b = 44), and if we can find b, we can find c, since c = b + 1 (so c = 45). So Statement 2 is sufficient and the answer is B.
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Re: If a, b, and c are three consecutive integers (in the order given), wh  [#permalink]

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05 Apr 2019, 22:33
AkshdeepS wrote:
If a, b, and c are three consecutive integers (in the order given), what is the value of c ?

1. 2(a + b + c) = 6(a + 1)

2. $$\frac{1}{2}$$(a + b + c) = a + 23

The most important part is to realise that consecutive numbers are of the form x, x+1, x+2, x+3 and so on.

a, b, and c are consecutive numbers, so

a

b = a+1

c = a+2

If you are done till this point you can't get this question wrong.

Statement 1 : 2(a + b + c) = 6(a + 1)

Replace b and c with a+1 and a+2 respectively

2a + 2(a+1) + 2(a+2) = 6a + 6

2a + 2a + 2 + 2a + 4 = 6a + 6

6a + 6 = 6a + 6

0 = 0 (we didn't get any value)

Not sufficient

Statement 2: $$\frac{1}{2}$$(a + b + c) = a + 23

Simplifying this we get,

a + b + c = 2a + 46

Replace b and c with a+1 and a+2 respectively

a + a +1 + a + 2 = 2a + 46

3a + 3 = 2a + 46

a = 43

Therefore, c = 45

Sufficient (B)

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If a, b, and c are three consecutive integers (in the order given), wh  [#permalink]

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Updated on: 06 Apr 2019, 23:04
AkshdeepS wrote:
If a, b, and c are three consecutive integers (in the order given), what is the value of c ?

1. 2(a + b + c) = 6(a + 1)

2. 1/2(a + b + c) = a + 23

Question: WHat is the value of c?

Statement 1: 2(a + b + c) = 6(a + 1)

Since a, b and c are consecutive numbers therefore

a = c-2 and b = c-1

i.e. 2(c-2 + c-1 + c) = 6(c-2 + 1)
i.e. 6c - 6 = 6c - 6
i.e. No unique solution of c hence

NOT SUFFICIENT

Statement 2:1/2(a + b + c) = a + 23

i.e. (1/2)*(c-2 + c-1 + c) = (c-2) + 23

i.e. 3c-3 = 2c-4 + 46

i.e. c = 45

SUFFICIENT

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Originally posted by GMATinsight on 05 Apr 2019, 23:51.
Last edited by GMATinsight on 06 Apr 2019, 23:04, edited 1 time in total.
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Re: If a, b, and c are three consecutive integers (in the order given), wh  [#permalink]

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06 Apr 2019, 04:11
AkshdeepS wrote:
If a, b, and c are three consecutive integers (in the order given), what is the value of c ?

1. 2(a + b + c) = 6(a + 1)

2. 1/2(a + b + c) = a + 23

let a=x
b=x+1 and c= x+2
a+b+c = 3x+3

#1
2(a + b + c) = 6(a + 1)
2 (3x+3) = 6x+6
6x+6=6x+6
no info about x ; insufficient
#2
1/2(a + b + c) = a + 23
we get
3x+3/2 = x+23
solve for x = 43 = a .; c = 45
IMO B
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Re: If a, b, and c are three consecutive integers (in the order given), wh  [#permalink]

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06 Apr 2019, 04:15
GMATinsight wrote:
AkshdeepS wrote:
If a, b, and c are three consecutive integers (in the order given), what is the value of c ?

1. 2(a + b + c) = 6(a + 1)

2. 1/2(a + b + c) = a + 23

Question: WHat is the value of c?

Statement 1: 2(a + b + c) = 6(a + 1)

Since a, b and c are consecutive numbers therefore

a = c-2 and b = c-1

i.e. 2(c-2 + c-1 + c) = 6(c-2 + 1)
i.e. 6c - 6 = 6c - 6
i.e. No unique solution of c hence

NOT SUFFICIENT

Statement 2:1/2(a + b + c) = a + 23

i.e. (1/2)*(c-2 + c-1 + c) = (c-2) + 23

i.e. 3c-3 = 2c-4 + 23

i.e. c = 22

SUFFICIENT

GMATinsight ; sir please see highlighted part , calculation error ; c = 45
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Re: If a, b, and c are three consecutive integers (in the order given), wh   [#permalink] 06 Apr 2019, 04:15
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