When a positive integer x is divided by 5, the remainder is 4. When po

Question

When a positive integer x is divided by 5, the remainder is 4. When positive integer y is divided by 4, the remainder is 3. Which of the following values CANNOT be the sum of x and y?

(A) 12
(B) 15
(C) 18
(D) 21
(E) 24

Bunuel · Answer

When positive integer x is divided by 5, the remainder is 4: x could be 4, 9, 14, 19, ...
When positive integer y is divided by 4, the remainder is 3: y could be 3, 7, 11, 15, 19, ...

If x is 9 and y is 3, then x + y = 12. Eliminate A.
If x is 4 and y is 11, then x + y = 15. Eliminate B.

If x is 14 and y is 7, then x + y = 21. Eliminate D.
If x is 9 and y is 15, then x + y = 24. Eliminate E.

By process of elimination the correct answer must be C.

Answer: C

Bunuel · Answer

This is a copy of the following MGMAT question: https://gmatclub.com/forum/when-positiv ... 72644.html

ArunSharma12 · Answer

When a positive integer x is divided by 5, the remainder is 4. When positive integer y is divided by 4, the remainder is 3. Which of the following values CANNOT be the sum of x and y?

(A) 12
(B) 15
(C) 18
(D) 21
(E) 24

x = 5*p + 4
y = 4*q + 3

x + y = 5*p + 4*q + 7

going through the options one at a time subtracting 7 from the options, only 18 option fits. 
18 - 7 = 11
we can not get 5*p + 4*q = 11 for some integers p and q.

all the rest of the numbers can be formed.
like, 21 - 7 = 14
5*p + 4*q = 14, for p=2 and q=1
Ans: C

MathRevolution · Answer

x = 5p + 4 {For p =1 , 2 , 3... x = 4, 9, 14, 19...}

y = 4q + 3 {For q =1 , 2 , 3... y = 3, 7, 11, 15, 19.....}

x + y = 18 is not possible.

Answer C

rvgmat12 · Answer

x=5k+4
y=4k2+3

x+y = 7+5k+4k2

Only C = 18 doesn't work

bumpbot · Answer

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When a positive integer x is divided by 5, the remainder is 4. When po

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When a positive integer x is divided by 5, the remainder is 4. When po

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