When a number x is divided by 5 it leaves a reminder of 3 and when divided by 7 it leaves a remainder of 4. If another number y leaves a reminder of 3 when divided by 5 and a reminder of 4 when divided by 7 and x is bigger than y. Which of the following must be a factor of x-y?
a) 10
b) 15
c) 20
d) 25
e) 35
Remainders
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- anuprajan5
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I assume that the answer must be e
x = 5a+3 and 7b+4, assuming a and b are the quotients
y = 5c+3 and 7d+4, assuming c and d are the quotients
Subtracting x - y = 5 (a-c) and 7 (b-d). By that, we know that 5 and 7 are factors. Therefore the answer is 35
Regards
Anup
x = 5a+3 and 7b+4, assuming a and b are the quotients
y = 5c+3 and 7d+4, assuming c and d are the quotients
Subtracting x - y = 5 (a-c) and 7 (b-d). By that, we know that 5 and 7 are factors. Therefore the answer is 35
Regards
Anup
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- Brent@GMATPrepNow
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We can also solve the question by plugging in numbers. Along that line, how do we find numbers that satisfy the given conditions? There's a nice rule that goes like this:mgasset wrote:When a number x is divided by 5 it leaves a reminder of 3 and when divided by 7 it leaves a remainder of 4. If another number y leaves a reminder of 3 when divided by 5 and a reminder of 4 when divided by 7 and x is bigger than y. Which of the following must be a factor of x-y?
a) 10
b) 15
c) 20
d) 25
e) 35
If, when N is divided by D, the remainder is R, then the possible values of N include: R, R+D, R+2D, R+3D,. . .
When a number x is divided by 5 it leaves a reminder of 3
So, the possible values of x include 3, 8, 13, 18, 23, 28, 33, 38, 43, 48, 53,...
When x is divided by 7 it leaves a remainder of 4.
So, the possible values of x include 4, 11, 18, 25, 32, 39, 46, 53,...
So, we can see that x could equal 18 or 53, or some other values, which we need not concern ourselves with.
Since y has the same attributes as x, y could also equal 18 or 53, or some other values (which we need not concern ourselves with).
Given all of this, one possible value of x-y could be 35, since 53-18 = 35.
Since answer choices A, B, C and D are not factors of 35, we can eliminate them.
This leaves us with E, the correct answer.
Cheers,
Brent