If p is an integer and p* = p^2 + 2, what is the value of integer k?
(1) When k + 2 is divided by 5 the remainder is 2.
(2) 18 < k* < 35
a. only statement 1 is sufficient
b. Both statement are sufficient
c. statement 1 is not sufficient and statement 2 is sufficient
d. Both statement are not sufficient
e. statement 2 is sufficient
OA is d
express mathematically why option C is the right answer?
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Data sufficiency
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Either the question is wrong or it is not posted correctly.Roland2rule wrote:If p is an integer and p* = p^2 + 2, what is the value of integer k?
(1) When k + 2 is divided by 5 the remainder is 2.
(2) 18 < k* < 35
OA is d
express mathematically why option C is the right answer?
Statement 1: When k + 2 is divided by 5 the remainder is 2.
k can have many values: 2, 7, 12, 17, 22, ... No unique value. Insufficient.
Statement 2: 18 < k* < 35
=> 18 < k^2 + 2 < 35
=> 16 < k^2 < 33
Since k is an integer, two values of k are eligible. k = ±5. No unique value of k. Insufficient.
Statement 1 & 2:
From Statement 1, we have k = 2, 7, 12, 17, ... and
From Statement 2, we have k = ±5.
We see that no value is common in both the statements, which is not possible. At least one value from each statement should be common.
An official DS question represents a holistic scenario. Statement 1 cannot invalidate Statement 2 and vice-versa. They must exist in sync.
Hope this helps!
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-Jay
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