Problem Solving

If k is 96% greater than its reciprocal, which of the following is an integer?

A) 3k/7
B) 3k/5
C) 5k/7
D) 5k/3
E) 7k/5

Source: www.gmatprepnow.com
Difficulty level: 600-650
Answer: C

Brent@GMATPrepNow wrote:If k is 96% greater than its reciprocal, which of the following is an integer?

A) 3k/7
B) 3k/5
C) 5k/7
D) 5k/3
E) 7k/5

Source: www.gmatprepnow.com
Difficulty level: 600-650
Answer: C

k is 96% greater than its reciprocal
The reciprocal of k is 1/k
So, we can write: k = (1/k) + (96% of 1/k)
In other words: k = (1/k) + 0.96(1/k)
Simplify: k = 1.96(1/k)
Simplify: k = 1.96/k
Multiply both sides by k to get: k² = 1.96
Solve: k = 1.4 of k = -1.4
Rewrite as follows: k = 7/5 of k = -7/5

ASIDE: Although it doesn't change the outcome, we can ELIMINATE the solution k = -7/5
Here's why:
If k = -7/5 then 1/k = -5/7
The question tells us that "k is 96% greater than 1/k, but we can see that k is actually less than 1/k (that is: -7/5 < -5/7)
So, k CANNOT equal -7/5

So, it MUST be the case that k = 7/5


Which of the following is an integer?
If k = 7/5, we can see that answer choice C must be an integer.

C) 5k/7 = (k)(5/7) = (7/5)(5/7) = 35/35 = 1

Answer: C

Cheers,
Brent