Question
When Arpita was going through her address book, she glanced upon the telephone number of her old friend, Gita. However, the last two digits were erased. But being a math freak, Arpita remembered that Gita had a 6 digit telephone number starting with 2345_ _ whose digital sum =7 (digital sum is the sum of the digits of a number till a single digit number is obtained). Find the maximum number of trials till she dials the right number.
Answer: Option D
:
D
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D
As of now the sum is 14. Let the last two digits be a and b.
With an upper limit of 9 for a and b:
a+b = 2 and a+b = 11
Number of solutions for a+b = 2 is 3 [(0,2), (2, 0), (1, 1)].
Number of solutions for a+b = 11 is 8 (12C1−4=8)
Total number of ways = 11
Shortcut:
The question is about an AP with common difference = 9 in a span of 100 numbers. Answer is 1009=11.
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