CAT 2002 — QA Question 29
Sum of first n natural numbers = S(n)
Sum given by student = 575
S(10) = 55
S(20) = 210
S(30) = 465
S(40) = 820
∴ The student stopped counting somewhere between 30 and 40.
Consider S(35) = 630
The student stopped somewhere before 35.
∴ S(31) = 496, S(32) = 528, S(33) = 561 and S(34) = 595
But the student gave 575 as the sum, so the student missed on the number 20.
Hence, option 4.
Amar went for a holiday to his friend's place. They together either went for yoga in the morning or played tennis in the evening but not both. 14 mornings and 24 evenings, they both stayed home and they both went out together for 22 days. How many days did Amar stay at his friend's place?
Answer & solution
- A
20
- B
16
30
- D
40
Let y be the number of days that they went for Yoga, t be the number of days that they played Tennis and f be the number of days that they were Free.
On 14 mornings they did not do anything, then they either played tennis in the evening or did nothing.
∴ 14 = t + f ...(i)
Similarly, 24 = y + f ...(ii)
Also, 22 = t + y …(iii)
Adding (i) and (ii) and substituting in (iii), we get,
2f = 16
∴ f = 8 days
∴ Total number of days Amar stayed = 22 + f = 22 + 8 = 30 days
Hence, option (c).