Number, Ranking and Time Sequence Test Questions and Answers

Answer: C

There is 1 such odd number.

Among single digits, the perfect cubes are 1 and 8, and the perfect squares are 1, 4 and 9. An odd digit is needed with a cube just before it and a square just after it.

The only place this happens is 8 3 1 at positions 6, 7 and 8: 3 is odd, 8 before it is a cube (\(2^{3}\)), and 1 after it is a square. Every other odd digit fails on one side, for example the 3 at position 16 has 1 before it but 5 after it.

Answer: C

The number is 132.

Rearrange each number's digits in descending order:

324 → 432, 456 → 654, 572 → 752, 683 → 863, 726 → 762, 132 → 321.

The smallest result, 321, comes from 132. 683, 572 and 456 become 863, 752 and 654, all larger.

Answer: C

There are two even numbers.

Swap the first and third digits of each number:

324 → 423, 456 → 654, 572 → 275, 683 → 386, 726 → 627, 132 → 231.

A number is even when its last digit is even; after the swap, the last digit is the old first digit. Only 654 and 386 end in an even digit, so the count is two.

Answer: B

24 students have ranks above Raju.

90% of 250 = 225 students are ranked below Raju. Raju himself is one student. So the number above him is

\[ 250 - 225 - 1 = 24 \]

25 forgets to exclude Raju himself, and 26 or 23 come from mis-adding the one. Raju's rank is therefore 25th.

Answer: D

Paul's rank is 20th.

In a class of 50, if 10 students rank below Raghu, Raghu's rank is 50 - 10 = 40th. Raghu's rank is twice Paul's, so Paul's rank is 40/2 = 20th.

The other options come from misreading Raghu's rank: 10th or 5th would follow if Raghu were 20th or 10th, which ignores the 10 students ranked below him, and 15th fits no reading.

Answer: B

Umar arrived at 9:15 a.m.

Work backwards. The meeting finished at 11:00 a.m., 30 minutes after Arvind arrived, so Arvind arrived at 10:30 a.m. He was 45 minutes late, so the meeting was scheduled to start at 9:45 a.m. Umar came 30 minutes before that time: 9:15 a.m.

9:45 a.m. is the scheduled start, not Umar's arrival. 9:00 a.m. and 9:30 a.m. result from adding or subtracting one of the intervals in the wrong direction.

Answer: B

There are 32 girls in the row.

Work from Sheela, whose position from the left is given. Sheela is 4th to the right of Rama, so Rama is 4 places to her left. Radha is 10 places to the right of Rama (Rama is 10th to the left of Radha):

\[ \begin{aligned} \text{Rama} &= 10 - 4 = 6\text{th from left} \\ \text{Radha} &= 6 + 10 = 16\text{th from left} \\ \text{Total} &= 16 + 17 - 1 = 32 \end{aligned} \]

Radha is counted in both her position from the left and from the right, so one is subtracted. Adding 16 and 17 without subtracting gives 33, a common slip, and 31 or 30 come from miscounting Rama's place.

Answer: D

His rank from the last is 43.

Rank from the top plus rank from the bottom equals the total number of students plus one, because the student himself is counted in both:

\[ 59 - 17 + 1 = 43 \]

42 is the number of students below him, 59 - 17, which forgets to count Manoj himself. 17 and 18 confuse the rank from the top with the rank from the bottom.

Check with a small case: in a class of 3, the student ranked 1st from the top is 3rd from the bottom, and 3 - 1 + 1 = 3.

Answer: A

There are 49 students in the class.

If Mahesh is 15th from the bottom, there are 14 students below him; if he is 35th from the top, there are 34 above him. Counting him once:

\[ \begin{aligned} \text{total} &= 15 + 35 - 1 \\ &= 49 \end{aligned} \]

50 counts Mahesh twice, and 51 and 48 come from adding or subtracting one too many.

Answer: A

The fourth ranker is Charan.

Kiran is 2nd and Tarun 3rd. The first ranker is the shortest and is not Charan; Sravan is taller than one person, so he is not the shortest either. The first ranker is therefore Pavan, the shortest, and Sravan is the second shortest.

Charan and Sravan take ranks 4 and 5. The fourth ranker is the tallest, and Sravan is second shortest, so Charan is 4th and tallest, and Sravan 5th. Tarun is taller than Kiran, which fixes the middle heights.

Pavan is the first ranker, Tarun is stated to be third, and Sravan, as the second shortest, cannot be the tallest person who holds fourth rank.