Question : If $r$ is the remainder when each of 6454, 7306, and 8797 is divided by the greatest number $d(d>1)$, then $(d-r)$ is equal to:
Option 1: 126
Option 2: 64
Option 3: 137
Option 4: 149
Correct Answer: 149
Solution : If the remainder in each case is the same. 7306 – 6454 = 852 8797 – 7306 = 1491 8797 – 6454 = 2343 HCF of 852, 1491, and 2343:
HCF = 213 So, the greatest number, $d$ = 213 Remainder, $r$ = 64 $\therefore d - r$ = 213 – 64 = 149 Hence, the correct answer is 149.
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Question : If r is the remainder when each of 4749, 5601, and 7092 is divided by the greatest possible number d(>1), then the value of (d + r) will be:
Option 1: 276
Option 2: 282
Option 3: 298
Option 4: 271
Question : What is the greatest number of six digits, which when divided by each of 16, 24, 72, and 84 leaves the remainder 15?
Option 1: 999981
Option 2: 999951
Option 3: 999963
Option 4: 999915
Question : A number, when divided by 729, gives a remainder of 56. What will we get as a remainder if the same number is divided by 27?
Option 1: 4
Option 2: 2
Option 3: 0
Option 4: 1
Question : When 2388, 4309, and 8151 are divided by a certain 3-digit number, the remainder in each case is the same. The remainder is:
Option 1: 23
Option 2: 19
Option 3: 39
Option 4: 15
Question : Find the greatest number which when divided 261, 853, and 1221, leaves a remainder of 5 in each case.
Option 1: 19
Option 2: 18
Option 3: 17
Option 4: 16
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