gmatcracker2010 wrote:
i dont have any idea to solve the attached problem. Please provide methodology to solve such problems.
Does the integer k have a factor p such that 1<p<k?
(1) k > 4!
(2) 13! + 2<= k <= 13!+13
Target question: Does the integer k have a factor p such that 1 < p < k ? This question is a great candidate for rephrasing the target question.
(We have a free video with tips on rephrasing the target question: http://www.gmatprepnow.com/module/gmat-data-sufficiency?id=1100)Let's look at a few cases to get a better idea of what the target question is asking.
- Try k = 6. Since 2 is a factor of 6, we can see that k DOES have a factor p such that 1<p<k.
- Try k = 10 Since 5 is a factor of 10, we can see that k DOES have a factor p such that 1<p<k.
- Try k = 16. Since 4 is a factor of 14, we can see that k DOES have a factor p such that 1<p<k.
- Try k = 5. Since 1 and 5 are the ONLY factors of 5, we can see that k does NOT have a factor p such that 1<p<k.
Aha, so if k is a prime number, then it CANNOT satisfy the condition of having a factor p such that 1 < p < k
In other words, the target question is really asking us whether k is a non-prime integer (aka a "composite integer")
REPHRASED target question: Is integer k a non-prime integer? Statement 1: k > 4! In other words, k > 24
This does not help us determine whether or not k is a non-prime integer? No.
Consider these two conflicting cases:
Case a: k = 25, in which case
k is a non-prime integerCase b: k = 29, in which case
k is a prime integerSince we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: 13! + 2 ≤ k ≤ 13! + 13 Let's examine a few possible values for k.
k = 13! + 2 = (13)(12)(11)....(5)(4)(3)(
2)(1) +
2 =
2[(13)(12)(11)....(5)(4)(3)(1) + 1]
Since k is a multiple of
2,
k is a non-prime integerk = 13! + 3 = (13)(12)(11)....(5)(4)(
3)(2)(1) +
3=
3[(13)(12)(11)....(5)(4)(2)(1) + 1]
Since k is a multiple of
3,
k is a non-prime integerk = 13! + 4 = (13)(12)(11)....(5)(
4)(3)(2)(1) +
4=
4[(13)(12)(11)....(5)(3)(2)(1) + 1]
Since k is a multiple of
4,
k is a non-prime integerAs you can see, this pattern can be repeated all the way up to k = 13! + 13. In EVERY case,
k is a non-prime integerSince we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer = B
Cheers,
Brent
_________________
Brent Hanneson – Creator of gmatprepnow.com
Before you spend another second preparing for the GMAT, check out my article series, Are you doing it wrong?.
You’ll learn what the GMAT actually tests, and why memorizing a ton of formulas actually makes you less effective.