Number, Ranking and Time Sequence Test Questions and Answers

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: D

There are 6 such odd numbers.

Treating each digit as a number, the perfect squares among single digits are 1, 4 and 9 (1 counts, since \(1 = 1^{2}\)). Reading the sequence 4 3 1 5 7 8 3 1 6 2 9 7 1 2 1 3 5 2 6 8 6 5 4 3 2 1 3 8 7, the odd digits that come straight after one of them are:

4-3, 1-5, 9-7, 1-3, 4-3 and 1-3, at positions 2, 4, 12, 16, 24 and 27.

That makes 6. Leaving out 1 as a perfect square would give only 3 (the pairs after 4 and 9), which is why the smaller options appear.

Answer: D

The number is 5.

The tenth digit from the left is the one in position 10, and seventh to its right is position \(10 + 7 = 17\). Counting along 4 3 1 5 7 8 3 1 6 2 9 7 1 2 1 3 5 ..., position 10 is 2 and position 17 is 5.

Counting seven places from position 10 and landing on position 16 instead (an off-by-one slip) would give 3, one of the distractors.

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

There are 47 girls in the row.

Mamta is 17th from the left and fourth to the right of Rita, so Rita is \(17 - 4 = 13\)th from the left. Parvati is 12 places to the right of Rita, so she is \(13 + 12 = 25\)th from the left.

Parvati is also 23rd from the right, so the total is:

\[ 25 + 23 - 1 = 47 \]

One is subtracted because Parvati is counted in both positions. The other totals come from miscounting one of the positions or forgetting to subtract the shared place.

Answer: C

His rank from the top stays 14th. Rank from the top counts only the students placed above him. New students are added at the bottom of the list, below him, so none of them goes above Sanjiv and the number of students ahead of him is unchanged at 13. The class size rises from 37 to 46, which changes his rank from the bottom (it was \(37 - 14 + 1 = 24\) and becomes 33), but not his rank from the top. The answers 12th, 13th and 15th would need a student to leave from, or join, the part of the list above him, and the question says nothing of the kind.

Answer: A

Fourteen more singers are needed. A singer who is 19th from the top and 38th from the bottom stands in a group of \(19 + 38 - 1 = 56\) singers, because that singer is counted in both ranks. To make the group 70 the number to add is \[ 70 - 56 = 14 \] so 14 more are needed. The options 16 and 18 overshoot the gap, and 10 leaves the group at 66. If the question were read as asking for the group itself, the answer would be 56, which is not offered, so the question is read as the number to be added, which the key confirms.

Answer: A

The number of people in a row is the position from the front plus the position from the back minus one, because the person himself is counted in both positions.

\[ 15 + 25 - 1 = 39 \]

Adding the two positions without subtracting one would give 40, which counts Suresh twice and is the usual wrong answer, and 38 would subtract two. There is no reason to subtract more than the one person who is counted twice. So the queue had 39 people, which is the first option.

Answer: C

The position from the back is the total number of people minus the position from the front, plus one, because the person's own place is counted in both positions.

\[ 65 - 30 + 1 = 36 \]

So Rakesh is 36th from the back. The value 35 (65 minus 30) is the usual slip, and it is not offered, and 34 and 33 and 31 come from subtracting more than needed. Check: the 29 people in front of him, himself, and the 35 behind him make 29 + 1 + 35 = 65, and he is 36th counting from the back since there are 35 people behind him.