Amit was counting down from 34 , Punit... - Solved

Question 64

Logical Reasoning Syllogism Easy

Amit was counting down from 34 , Punit was counting 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 out at the same speed?

(A) 22

(B) 23

(C) 24

(D) They will not call out the same number

✓ Correct Answer: Option D Verified Solution

📘 Step-by-Step Solution & Detailed Explanation:

Step-by-Step Analysis

To solve this problem, we can list the sequence of numbers called out by Amit and Punit at each time step and see if they ever match. Let's assume they call out one number per second (or any equal time interval).

Method 1: Listing the Sequences

We can create a table to track the numbers called out at the same time:

Time Step	Amit's Number (Counting Down)	Punit's Number (Even Numbers Up)
1	34	2
2	33	4
3	32	6
4	31	8
5	30	10
6	29	12
7	28	14
8	27	16
9	26	18
10	25	20
11	24	22
12	23	24
13	22	26

As we can see from the table, at no point in time do Amit and Punit call out the same number. When Amit says 24, Punit says 22. By the time Punit says 24, Amit has moved on to 23.

Method 2: Algebraic Approach

We can also solve this by creating a formula for each person's number at a given time step 't' (where t starts at 1).

Amit's number: A(t) = 34 - (t - 1) = 35 - t
Punit's number: P(t) = 2 × t

We are looking for a time 't' where A(t) = P(t):

35 - t = 2t

35 = 3t

t = 35 / 3 = 11.66...

Since 't' is not a whole number, there is no integer time step at which they will call out the same number.

Conclusion

Both methods show that they will not call out the same number at the same time.