When positive integer k is divided by 5, the remainder is 2.

BTGModeratorVI wrote: ↑

Tue Mar 10, 2020 7:27 am

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

From the information, "k is divided by 5, the remainder is 2," we have k = 7, 12, 17, 22, 27, 32, and 37.

From the information, "k is divided by 6, the remainder is 5," we have k = 11, 17, 23, 29, 35.

The only common value for k is 17. Thus, k = 17.

The remainder when k = 17 is divided by 7 = 3

The correct answer: B

Hope this helps!

-Jay
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BTGModeratorVI wrote: ↑

Tue Mar 10, 2020 7:27 am

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

BTGModeratorVI wrote: ↑

Tue Mar 10, 2020 7:27 am

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

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