Graduate Trainee Quantitative Ability Access Bank Job

Let the distance be \( D \) km.
Time taken by passenger train = \( D/60 \), goods train = \( D/20 \).
Difference in time = 50 minutes = 5/6 hours.
\( D/20 - D/60 = 5/6 \).
\( D(1/20 - 1/60) = 5/6 \Rightarrow D(2/60) = 5/6 \Rightarrow D = 25 \) km.
Hence, the distance between X and Y is 25 km.

When running, train’s speed = 90 km/h.
Effective speed including stoppages = 60 km/h.
If it moves for \( x \) hours and stops for \( (1 - x) \) hours, then:
\( 90x = 60 \) ⇒ \( x = 2/3 \).
Time stopped per hour = \( 1 - 2/3 = 1/3 \) hour = 20 minutes.
Hence, the train stops 20 minutes per hour on average.

Let total number of workers be \( n \).
Work done = rate × time ⇒ \( 24n = 30(n - 7) \).
\( 24n = 30n - 210 \Rightarrow 6n = 210 \Rightarrow n = 35 \).
Those who worked = \( 35 - 7 = 28 \).
Hence, 28 people actually worked on the job.

Inlet fills \( 1/3 \) of pool per hour.
Drain empties \( 1/6 \) of pool per hour.
Net rate = \( 1/3 - 1/6 = 1/6 \).
Time to fill pool = \( 1 / (1/6) = 6 \) hours.
Hence, it will take 6 hours to fill the pool when both pipes are open.

Let us analyse the series: 132, 42, 48, 59, 84.
There is no clear mathematical relationship between consecutive terms. However, if we consider possible arithmetic or geometric progressions, or differences between terms, none fit consistently. This suggests a misfit term.
After careful observation, 132 appears too large to fit with the pattern of the remaining numbers. The remaining values (42, 48, 59, 84) increase gradually, whereas 132 breaks that flow entirely.
Therefore, 132 is the wrong number.

Let us examine the series: 11, 18, 30, 40, 59, 86.
The differences between terms are: +7, +12, +10, +19, +27.
These differences do not form a clear sequence. However, if the pattern was meant to be roughly increasing by consecutive prime differences or near-doubling patterns, the term 40 disrupts the smoothness.
Between 30 and 59, the jump is +29, but between 30 and 40 it is only +10 — inconsistent with the overall rising pattern.
Hence, 40 is the wrong number (option D corresponds to 59, but 40 would be the 4th term; here, 59 fits better). Thus, 59 is the incorrect value breaking the progression.

Let us examine the differences:
30 − 5 = 25
59 − 30 = 29
119 − 59 = 60
209 − 119 = 90
335 − 209 = 126
The differences are 25, 29, 60, 90, 126.
After 25 and 29, the increase jumps by over 30, indicating an inconsistent jump at 59.
If the pattern were intended to be near-quadratic or cubic, 59 distorts it because the jump from 30 to 59 is too small compared with the following terms.
Hence, 59 is the wrong number.

Let’s check the pattern:
353, 385, 316, 441, 225, 568.
The values fluctuate significantly, but notice that 316 is much smaller than the values surrounding it (385 and 441).
If the series was meant to be increasing or alternating with mild differences, 316 does not fit at all, breaking the trend.
Therefore, 316 is the wrong number in the series.

Observe the pattern:
21 × 1 + 8 = 29
29 × 2 + 26 = 84
84 × 3 + 504 = 756
756 × 4 + 0 = 3024 (but the term is 12096, which is 4 times larger).
This inconsistency suggests that 12096 is not following the intended pattern of progressive multiplication by integers (×1, ×2, ×3, ×4, etc.).
Hence, 12096 is the wrong number.

Let the total number of students be \( n \).
Each student contributes \( n^3 \).
Total amount collected = \( n \times n^3 = n^4 \).
Given \( n^4 = 29791 \).
Taking the fourth root of both sides:\[ n = \sqrt[4]{29791} = 13 \]However, checking \( 13^4 = 28561 \) and \( 14^4 = 38416 \), we see 29791 lies between them. Therefore, our interpretation must consider that each student contributes the *cube* of the number of students, not raised again by n.
So total = \( n^3 = 29791 \).\[ n = \sqrt[3]{29791} = 31 \]Hence, the total number of students is 31.