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18 Mar 2011, 14:07
Kudos
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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:
55%
(hard)
Question Stats:
57% (01:35) correct
43%
(01:34)
wrong
based on 125
sessions
History
Date
Time
Result
Not Attempted Yet
If x > 1, what is the value of integer x?
(1) There are x unique factors of x.
(2) The sum of x and any prime number larger than x is odd.
OPEN DISCUSSION OF THIS QUESTION IS HERE: if-x-1-what-is-the-value-of-integer-x-110661.html
(1) There are x unique factors of x.
(2) The sum of x and any prime number larger than x is odd.
This is the answer in the book but I just don't get it..
Statement (1) tells us that there are x unique factors of x. In order for this to be true,
EVERY integer between 1 and x, inclusive, must be a factor of x. Testing numbers, we can
see that this property holds for 1 and for 2, but not for 3 or for 4. In fact, this property does
not hold for any higher integer, because no integer x above 2 is divisible by x-I. Therefore,
x = 1 or 2. However, the original problem stem told us that x > 1, so x must equal 2.
SUFFICIENT.
Statement (2) tells us that x plus any prime number larger than x is odd. Since x > 1, x must
equal at least 2, so this includes only prime numbers larger than 2. Therefore, the prime
number is odd, and x is even. However, this does not tell us which even number x could be.
INSUFFICIENT. The correct answer is (A): Statement (1) is sufficient to answer the ques-
tion, but Statement (2) is insufficient.
Statement (1) tells us that there are x unique factors of x. In order for this to be true,
EVERY integer between 1 and x, inclusive, must be a factor of x. Testing numbers, we can
see that this property holds for 1 and for 2, but not for 3 or for 4. In fact, this property does
not hold for any higher integer, because no integer x above 2 is divisible by x-I. Therefore,
x = 1 or 2. However, the original problem stem told us that x > 1, so x must equal 2.
SUFFICIENT.
Statement (2) tells us that x plus any prime number larger than x is odd. Since x > 1, x must
equal at least 2, so this includes only prime numbers larger than 2. Therefore, the prime
number is odd, and x is even. However, this does not tell us which even number x could be.
INSUFFICIENT. The correct answer is (A): Statement (1) is sufficient to answer the ques-
tion, but Statement (2) is insufficient.
OPEN DISCUSSION OF THIS QUESTION IS HERE: if-x-1-what-is-the-value-of-integer-x-110661.html
18 Mar 2011, 14:39
Kudos
Bookmarks
even i was confuse for the first time. But I think the answer explainations tells, if say x = 5, then it needs 5 unique factor, but for 5 it is only 1 and 5. For 4 it is 1,2, and 4. So for any number greater than 2 there is no way you can have as many factor as the number itself. hence it should be 2. I hope I interpreted right, but as I said it is a confusing question.
18 Mar 2011, 15:34
Kudos
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Well here is how i would do it.
1. x has x factors
meaning if you take any integer , that should have that many factors
1 has 1 factor (i.e 1 , meets the criteria)
2 has 2 factors (i.e 1 and 2)
3 has 2 factors (i.e 1 and 3, doesnt meet the criteria, to satisfy this should have had 3 factors)
take any other number lets say 17 , to meet this criteria this should have 17 factors. not satisfied.
so only 1 and 2 satisfies the condition, then again in the question it says x has to be greater than 1 . so that rules out 1 . Hence x =2 .
So sufficient.
2. x + ( prime >x )has to be odd
primes (2,3,5,7,11....)
2+ (prime >2)
= 2 +3 = odd (x could be 3)
2+5 = odd (x could be 5)
Not sufficient as there are more possible values for x.
Answer is A.
1. x has x factors
meaning if you take any integer , that should have that many factors
1 has 1 factor (i.e 1 , meets the criteria)
2 has 2 factors (i.e 1 and 2)
3 has 2 factors (i.e 1 and 3, doesnt meet the criteria, to satisfy this should have had 3 factors)
take any other number lets say 17 , to meet this criteria this should have 17 factors. not satisfied.
so only 1 and 2 satisfies the condition, then again in the question it says x has to be greater than 1 . so that rules out 1 . Hence x =2 .
So sufficient.
2. x + ( prime >x )has to be odd
primes (2,3,5,7,11....)
2+ (prime >2)
= 2 +3 = odd (x could be 3)
2+5 = odd (x could be 5)
Not sufficient as there are more possible values for x.
Answer is A.
