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05 Apr 2019, 00:47
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
56% (01:48) correct
44%
(02:02)
wrong
based on 203
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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
1. 2(a + b + c) = 6(a + 1)
2. 1/2(a + b + c) = a + 23
05 Apr 2019, 16:01
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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.
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.
05 Apr 2019, 22:33
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AkshdeepS
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)
