CAT 1994 — QA Question 29
Answer the next 3 questions based on the information given below:
Alphonso, on his death bed, keeps half his property for his wife and divide the rest equally among his three sons Ben, Carl and Dave. Some years later Ben dies leaving half his property to his widow and half to his brothers Carl and Dave together, shared equally. When Carl makes his will he keeps half his property for his widow and the rest he bequeaths to his younger brother Dave. When Dave dies some years later, he keeps half his property for his widow and the remaining for his mother. The mother now has Rs. 1,575,000.
Which is the least number that must be subtracted from 1856, so that the remainder when divided by 7, 12, and 16 is 4.
Answer & solution
- A
137
- B
1361
- C
140
172
The LCM of 7, 12 and 16 is 336. The closest multiple of 336 to 1856 is 1680. So 1684 when divided by 7, 12 and 16 leaves a remainder of 4. This is the closest such number, less than 1856.
Hence the number to be subtracted from 1856 to get 1684, must be the least such number. So the answer is (1856 – 1684) = 172.
Alternate method:
Subtract options from 1856 and check.