Number System - Study Mode
[#291] Three friends, returning from a movie, stopped to eat at a restaurant. After dinner, they paid their bill and noticed a bowl of mints at the front counter. Sita took $$frac{1}{3}$$ of the mints, but returned four because she had a monetary pang of guilt. Fatima then took $$frac{1}{4}$$ of what was left but returned three for similar reasons. Eswari then took half of the remainder but threw two back into the bowl. The bowl had only 17 mints left when the raid was over. How many mints were originally in the bowl?
Correct Answer
(D) None of these
Explanation
Solution: $$eqalign{
& { ext{Number of mint before Eswari has taken}}, cr
& = left( {x - {frac{x}{2}} }
ight) + 2 = 17 cr
& Or,,x = 30 cr
& { ext{Number of mint before Fatima has taken}}, cr
& = left( {x - {frac{x}{4}} }
ight) + 3 = 30 cr
& Or,,x = 36 cr
& { ext{Number of mint before Sita has taken}}, cr
& = left( {x - {frac{x}{3}} }
ight) + 4 = 36 cr
& Or,,x = 48 cr
& { ext{Hence,}},{ ext{there}},{ ext{were}},{ ext{48}},{ ext{mints}},{ ext{originally}}{ ext{.}} cr} $$
[#292] If we divide the unknown two-digit number by the number consisting of the same digits written in the reverse order, we get 4 as quotient and 3 as remainder. If we divide the required number by sum of its digits, we get 8 as a quotient and 7 as a remainder. Find the number?
Correct Answer
(C) 71
Explanation
Solution: We go through the options, Checking option (C) $$frac{{71}}{{17}}$$ = 4 quotient and remainder 3. $$frac{{71}}{8}$$ = 8 quotient and remainder 7 as remainder.
[#293] The last three-digits of the multiplication 12345 × 54321 will be
Correct Answer
(B) 745
Explanation
Solution: If we multiply the last three digits of each terms we get the last three digits. 345 × 321 = 110745 So, the last three digits are 745
[#294] Which of the following digits will replace the H marks in the following equation ? 9H + H8 + H6 = 230
Correct Answer
3
Explanation
Solution: 9H + H8 + H6 = 230 ⇒ {(9 × 10) + H} + (10H + 8) + (10H + 6) = 230 ⇒ 21H + 104 = 230 ⇒ 21H = 126 ⇒ H = 6
[#295] What least number must be added to 1056 to get a number exactly divisible by 23 ?
Correct Answer
(A) 2
Explanation
Solution: On dividing 1056 by 23, we get 21 as remainder. ∴ Required number to be added = (23 - 21) = 2