Number System
- What least value must be assigned to ‘*’ so that the number 451 * 603 is exactly divisible by 9?
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If the sum of the digits of a number be divisible by 9, the number is divisible by 9.
Sum of the digits of 451 * 603 = 4 + 5 + 1 + * + 6 + 0 + 3Correct Option: B
If the sum of the digits of a number be divisible by 9, the number is divisible by 9.
Sum of the digits of 451 * 603 = 4 + 5 + 1 + * + 6 + 0 + 3
Sum of the digits of 451 * 603 = 19 + *
If * = 8, then 19 + 8 = 27 , which is divisible by 9.
- What least value must be assigned to ‘*’ so that the number 63576*2 is divisible by 8 ?
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A number is divisible by 8 if number formed by the last three digits is divisible by 8.
Correct Option: C
A number is divisible by 8 if number formed by the last three digits is divisible by 8.
∴ If * is replaced by 3, then 632 ÷ 8 = 79
Hence required answer is 3 .
- The least number that must be subtracted from 1294 so that the remainder when divided by 9, 11 and 13 will leave in each case the same remainder 6, is :
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LCM of 9, 11 and 13 = 9 × 11 × 13 = 1287
∴ Required lowest number that leaves 6 as remainder = 1287 + 6 = 1293Correct Option: C
LCM of 9, 11 and 13 = 9 × 11 × 13 = 1287
∴ Required lowest number that leaves 6 as remainder = 1287 + 6 = 1293
∴ Required answer = 1294 – 1293 = 1
- Number of composite numbers lying between 67 and 101 is :
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Number of numbers lying between 67 and 101
⇒ 101 – 67 – 1 = 33
Prime numbers ⇒ 71, 73, 79, 83,Correct Option: A
Number of numbers lying between 67 and 101
⇒ 101 – 67 – 1 = 33
Prime numbers ⇒ 71, 73, 79, 83,
89 and 97 = 6
∴ Composite numbers = 33 – 6 = 27
- The least number that must be added to 8961 to make it exactly divisible by 84 is :
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Correct Option: A
∴ Required number = 84 – 57 = 27