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04 Apr 2019, 01:11
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
70% (02:21) correct
30%
(02:15)
wrong
based on 180
sessions
History
Date
Time
Result
Not Attempted Yet
If y is a positive odd integer less than 33, does y have a factor p such that 1 < p < y ?
(1) y + 2 is divisible by 3.
(2) The units digit of y is 7.
(1) y + 2 is divisible by 3.
(2) The units digit of y is 7.
04 Apr 2019, 01:35
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Solution
Given:
- • y is a positive odd integer less than 33.
To find:
- • Whether y have a factor p such that 1 < p < y.
• If y has factor p such that 1 < p < y then y will be a multiple of a number other than 1 and itself.
- o Hence, y will not be a prime number.
o Else, y will be prime number.
Approach and Working:
Statement 1: y + 2 is divisible by 3.
- • y+2 = 3k where k is a positive integer.
- o y= 3k-2
Possible values of y are: 1, 7,13, 19, 25, 31 and so on.
Y can be both prime and non-prime.
Hence, statement 1 is not sufficient.
Statement 2: The units digit of y is 7.
Possible values of y are: 7, 17, and 27.
Y can be both prime and non-prime.
Hence, statement 2 is not sufficient.
Combining both the statements:
On combining both the statements: Value of y is 7.
Hence, we can answer by combining both the statements together.
Hence, the correct answer is option C.
Answer: C
Archit3110
Major Poster
04 Apr 2019, 03:34
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Bunuel
#1
y+2 divisible by 3
y=1,7,13,19,25
p=3
so not sufficient at y=1 , p =3
#2
y unit digit 7
7,17,27
7,17 prime so not p = 1 or 7,17
not sufficient
from 1& 2
y = 7
p= 3 ; for y+2
IMO C sufficient
