Nilesh was counting down from 34. Sumit was counting down upwards the numbers…
2023
Nilesh was counting down from 34. Sumit was counting down upwards the numbers starting from 2 and he was calling out only the even numbers. What common number will they call out at the same time if they were calling at the same speed?
- A.
23
- B.
22
- C.
24
- D.
They will not call out the same number
Attempted by 21 students.
Show answer & explanation
Correct answer: D
Sumit’s sequence (even numbers upward):
2, 4, 6, 8, 10, 12, 14, 16, …
Pairs of numbers at each call (Nilesh, Sumit):
(34, 2)
(33, 4)
(32, 6)
(31, 8)
(30, 10)
(29, 12)
(28, 14)
(27, 16)
(26, 18)
(25, 20)
(24, 22)
(23, 24)
(22, 26)
(21, 28)
…
At no point do both numbers match.
At call number n, Nilesh says 34 − (n − 1) = 35 − n while Sumit says 2n. Solve 35 − n = 2n to get 3n = 35, so n = 35/3, which is not an integer. Therefore there is no integer call number when both say the same number.
They never call the same number at the same time.
Therefore the correct answer is: They will not call out the same number.