If you add the digits in a two-digit number and multiply the sum by 7, you get the original number. If you reverse the digits in the two-digit number, the new number is 18 more than the sum of its two digits. What is the original number?

A. 42
B. 24
C. 64
D. 46
E. 36

Question

If you add the digits in a two-digit number and multiply the sum by 7, you get the original number. If you reverse the digits in the two-digit number, the new number is 18 more than the sum of its two digits. What is the original number?

A. 42
B. 24 
C. 64 
D. 46 
E. 36

texaschic101 · Answer

(a + b) * 7 = ab
ba = 18 + (a + b)

I will just use process of elimination...
(A) 42......(4 + 2) * 7 = 42
     24 = 18 + (2 + 4)
     24 = 18 + 6
     24 = 24 (CORRECT)
(B) 24......(2 + 4) * 7 = 42 : NOT CORRECT
(C) 64 ....(6 + 4) * 7 = 70 : NOT CORRECT
(D) 46 ....(4 + 6) * 7 = 70 : NOT CORRECT
(E) 36 ....(3 + 6) * 9 = 81 : NOT CORRECT

ANSWER : A