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Re: The number m yields a remainder p when divided by 14 and a remainder q [#permalink]
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Hi All,

This question can be solved with some basic arithmetic, 'brute force' and TESTing THE ANSWERS.

We're told that the number M yields a remainder P when divided by 14 and a remainder Q when divided by 7. We're also told that P = Q + 7. We're asked which one of the following COULD be the value of M.

Since the question asks which answer COULD be the value of M, then that means that there's more than one possible answer. As such, we really just have to play around with the answers that are here and when we find a 'match', we can stop working.

Let's TEST Answer A: 45

IF....
M = 45
45/14 = 3r3 so P = 3
45/7 = 6r3 so Q = 3
3 does NOT = 3+7 though, so this is NOT the answer.

Let's TEST Answer B: 53

IF....
M = 53
53/14 = 3r11 so P = 11
53/7 = 7r4 so Q = 4
11 DOES = 4+7, so this MUST be the answer.

Final Answer:

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Re: The number m yields a remainder p when divided by 14 and a remainder q [#permalink]
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jhabib wrote:
The number m yields a remainder p when divided by 14 and a remainder q when divided by 7. If p = q + 7, then which one of the following could be the value of m ?

(A) 45
(B) 53
(C) 72
(D) 85
(E) 100


Let’s go through the answer choices because they are not difficult to work with.

(A) 45

45/14 = 3 r 3 and 45/7 = 6 r 3

We see that p = 3 and q = 3, but it’s given that p = q + 7, so A can’t be the answer.

(B) 53

53/14 = 3 r 11 and 53/7 = 7 r 4

We see that p = 11 and q = 4, and p = q + 7, so B is the answer.

(We will leave the readers to verify that C, D and E couldn’t be the answer either.)

Answer: B
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Re: The number m yields a remainder p when divided by 14 and a remainder q [#permalink]
jhabib wrote:
The number m yields a remainder p when divided by 14 and a remainder q when divided by 7. If p = q + 7, then which one of the following could be the value of m ?

(A) 45
(B) 53
(C) 72
(D) 85
(E) 100


m/7 gives these successive possible values of m: q, q+7, q+14, q+21, q+28, q+35, q+42, q+49
m/14 gives these successive possible values of m: q+7, q+21, q+35, q+49
q+7, q+21, and q+35 won't work, as q>divisor 7
testing q+49=53,
q=4; q+7=11 yes
m=53
B
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Re: The number m yields a remainder p when divided by 14 and a remainder q [#permalink]
jhabib wrote:
The number m yields a remainder p when divided by 14 and a remainder q when divided by 7. If p = q + 7, then which one of the following could be the value of m ?

(A) 45
(B) 53
(C) 72
(D) 85
(E) 100


TESTING VALUES IS BEST WAY HERE:

Start with (C)

72/14 = 5 rem 2 (p)

72/7 = 10 rem 2 (q)

p - q = 0, but we need p - q = 7

Go for (B)

53/14 = 3 rem 11

53/7 = 7 rem 4

p - q = 11 - 4 = 7

Hence (B)
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Re: The number m yields a remainder p when divided by 14 and a remainder q [#permalink]
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I solved this question in the following way:

Q<7 so Q can be from 0 to 6 and P<14 so P can be from 0 to 13, BUT the constraint is P=Q +7 so this will mean that P can be in the range from 7 to 13.

m=14k + P or m= 14k + 7 to 13 and look at the answeras, place different values for k, B will give 53 which is 14*3 + 10, the other answers are out of the range
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Re: The number m yields a remainder p when divided by 14 and a remainder q [#permalink]
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Given that The number m yields a remainder p when divided by 14 and a remainder q when divided by 7. And we need to find If \(p = q + 7\), what can be the value of m

Theory: Dividend = Divisor*Quotient + Remainder

Now, m when divided by 14 gives p remainder and p = q + 7

m -> Dividend
14 -> Divisor
a -> Quotient (Assume)
q + 7 -> Remainders
=> m = 14a + q + 7 = 7*2a + 7 + q = 7*(2a + 1) + q = odd multiple of 7 + q (where q is less than 7)

let's take each option choice and check which one satisfies this

(A) 45 = 42 + 3 = Even multiple of 7 + 3 => NOT POSSIBLE

(B) 53 = 49 + 4 = Odd multiple of 7 + 4 => POSSIBLE
In Test we don't need to check further but I am solving to complete the solution

(C) 72 = 70 + 2 = Even multiple of 7 + 2 => NOT POSSIBLE

(D) 85 = 84 + 1 = Even multiple of 7 + 1 => NOT POSSIBLE

(E) 100 = 98 + 2 = Even multiple of 7 + 2 => NOT POSSIBLE

So, Answer will be B
Hope it helps!

Watch the following video to learn the Basics of Remainders

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