When positive integer \(k\) is divided by 5, the remainder is 2. When \(k\) is divided by 6, the remainder is 5. If

[M7MBA]

When positive integer \(k\) is divided by 5, the remainder is 2. When \(k\) is divided by 6, the remainder is 5. If \(k\) is less than 40, what is the remainder when \(k\) is divided by 7?

A. 2
B. 3
C. 4
D. 5
E. 6

Answer: B

Source: Magoosh

[Brent@GMATPrepNow]

When positive integer \(k\) is divided by 5, the remainder is 2. When \(k\) is divided by 6, the remainder is 5. If \(k\) is less than 40, what is the remainder when \(k\) is divided by 7?

A. 2
B. 3
C. 4
D. 5
E. 6

Answer: B

Source: Magoosh

When it comes to remainders, we have a nice rule that says:
If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc.
For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.

When positive integer k is divided by 5, the remainder is 2
The possible values of k are: 2, 7, 12, 17, 22, 27, 32, 37, 42, . . .

When k is divided by 6, the remainder is 5.
The possible values of k are: 5, 11, 17, 23, 29, 35, 41. . . .

Since 17 is the only number (less than 40) that both lists share, it must be the case that k = 17

What is the remainder when k is divided by 7?
17 divided by 7 = 2 with remainder 3

Answer: B

Cheers,
Brent

[Scott@TargetTestPrep]

When positive integer \(k\) is divided by 5, the remainder is 2. When \(k\) is divided by 6, the remainder is 5. If \(k\) is less than 40, what is the remainder when \(k\) is divided by 7?

A. 2
B. 3
C. 4
D. 5
E. 6

Answer: B

Solution:

We are given that k < 40. Since, when positive integer k is divided by 5, the remainder is 2:

k = 5Q + 2

So k can be 2, 7, 12, 17, 22, 27, 32, or 37.

Since, when k is divided by 6, the remainder is 5:

k = 6P + 5

So k can be 5, 11, 17, 23, 29, or 35.

Thus, we see that k must be 17, and 17/7 = 2 remainder 3.

Alternate Solution:

Since, when positive integer k is divided by 5, the remainder is 2:

k = 5Q + 2

Since, when k is divided by 6, the remainder is 5:

k = 6P + 5

We see that k - 2 = 5Q = 6P + 3 is divisible by both 5 and 3; therefore, k - 2 must be divisible by 15.

The only numbers divisible by 15 and which would produce a k-value less than 40 are 0, 15 and 30. If k - 2 is 0, 15 or 30; then k is 2, 17 or 32, respectively. We see that only k = 17 produces a remainder of 2 when divided by 5 and a remainder of 5 when divided by 6. The remainder when k = 17 is divided by 7 is 3.

Answer: B