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29 Jun 2022, 01:30
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A
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:
60% (01:57) correct
40%
(01:52)
wrong
based on 134
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The average (arithmetic mean) of three positive integers \(a, b,\) and \(c\) is 2. Is the range of the three numbers greater than 2?
(1) \(a - b=1\)
(2) \(c\) is the largest of the three numbers.
Are You Up For the Challenge: 700 Level Questions
(1) \(a - b=1\)
(2) \(c\) is the largest of the three numbers.
Are You Up For the Challenge: 700 Level Questions
29 Jun 2022, 02:14
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Pre-think
a + b + c = 6
And all three numbers are positive integers.
(1) Only
a = b +1
If b=1, then a=2, c=3
If b=2, then a=3, c=1
There are no other possible combinations.
In either case, range is 2.
We can answer "No" to the question "Is the range of the three numbers greater than 2".
Sufficient.
(2) Only
We already know the range can be 2.
If c=4, then a=b=1. The range is 3.
We cannot answer the question with certainty.
Insufficient.
The answer is thus (A).
a + b + c = 6
And all three numbers are positive integers.
(1) Only
a = b +1
If b=1, then a=2, c=3
If b=2, then a=3, c=1
There are no other possible combinations.
In either case, range is 2.
We can answer "No" to the question "Is the range of the three numbers greater than 2".
Sufficient.
(2) Only
We already know the range can be 2.
If c=4, then a=b=1. The range is 3.
We cannot answer the question with certainty.
Insufficient.
The answer is thus (A).
29 Jun 2022, 08:18
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Bunuel
Average is 2 .. so sum must be 6 ..
a+b+c = 6
Constraint .. a,b, c are all positive integer
(1) \(a - b=1\)
a = b+1
the numbers are b+1, b, c
2b+c = 5
b, c can be (1,3) or (2, 1)
corresponding values for (a, b, c ) = (2, 1,3) or (3, 2, 1)
both have range 2. So we can definitely answer that range is not greater than 2.
Sufficient
(2) \(c\) is the largest of the three numbers.
if c is greatest, a and b minimum can be 1 and so c will be 4. range =3
if a = 1 and b = 2, c = 3.. range = 2
Insufficient.
Ans A
