When 20 is Divided by the Positive Integer k, the Remainder is k – 2 GMAT Problem Solving

Question: When 20 is divided by the positive integer k, the remainder is k – 2. Which of the following is a possible value of k ?

1. 8
2. 9
3. 10
4. 11
5. 12

Correct Answer: D
Solution and Explanation:
Approach Solution 1:

Dividend=divisor * quotient + remainder
20=k*q+k-2......k*q+k=20+2=22
k(q+1)=22=2*11=1*22
Possible values of k are 2 and 11 or 22.

Approach Solution 2:
20/11= 11∗1+11−2
Answer must be (D)

Approach Solution 3:
When 20 is divided by a positive integer n, the remainder is k−2.
Thus, 20= nk+(k-2), where k is a positive integer
=> 20= kk+k-2
=> 22= k(k+1)
The divisors of 22 are 1, 2, 11, 22.
Thus, the possible value of (k,k+22) are (1,22),(22,1),(11,2),(2,11)
Now, (1,22),(22,1),(11,2),(2,11) does not satisfy our initial equation 20=nk+(k-2).
Therefore k= 11 is the positive value.

“When 20 is divided by the positive integer k, the remainder is k – 2.”- is a topic of the GMAT Quantitative reasoning section of GMAT. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.

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