The number 2^48 - 1 divisible by two numbers between 60 and 70. Their sum is:
(a) 124 (b) 128 (c) 132 (d) 136 (e) None of the above
OA: 128
My doubt: how to distinguish between 128 and 132?
My method:
2^48 will have its one's digit as 6 and so the one's place digit of 2^48 - 1 is 5. One of the number between 60 and 70 that can satisfy this condition is 65. the other number should also be between 60 and 70(given condition). So 60<(options-65)<70 is the condition to satisfy. 128 and 132 satisfies (other number will be 63 or 67). Now how to choose between 63 and 67 without the factorization method??? (by factorization method the factors lying between 60 and 70 is 63 and 65)
(a) 124 (b) 128 (c) 132 (d) 136 (e) None of the above
OA: 128
My doubt: how to distinguish between 128 and 132?
My method:
2^48 will have its one's digit as 6 and so the one's place digit of 2^48 - 1 is 5. One of the number between 60 and 70 that can satisfy this condition is 65. the other number should also be between 60 and 70(given condition). So 60<(options-65)<70 is the condition to satisfy. 128 and 132 satisfies (other number will be 63 or 67). Now how to choose between 63 and 67 without the factorization method??? (by factorization method the factors lying between 60 and 70 is 63 and 65)
