General Aptitude

The article depends on the first sound of the next word, not on its first letter.

• younger starts with a consonant “y” sound, so it takes a.
• university also starts with a “y” sound (“yoo”), so it takes a, not an.
• The “h” in honorable is silent, so the word starts with a vowel sound and takes an.

Only option A gives a; a; an.

Answer: A

The decision is criticised for chasing short-term gains at the cost of long-term stability, so “myopic” is used here in the sense of “unable to look ahead”. Shortsighted says exactly this. Visionary and progressive describe people who plan for the future, the reverse of the intended meaning, and innovative is about novelty, not foresight.

Answer: B

Fixing the wrong entry raises the class total by \(42 - 24 = 18\) marks, and this raises the average by \(31.4 - 30.8 = 0.6\). If the class has \(n\) students, the average rises by \(\frac{18}{n}\), so \(\frac{18}{n} = 0.6\) and \(n = 30\). Check: \(30 \times 30.8 = 924\) and \(924 + 18 = 942 = 30 \times 31.4\).

Answer: C

S and T are sisters, so both are daughters of Q. R is the mother of Q, and P, being Q's brother, is also R's son.

• (1) True: R is the mother of S's parent Q, so R is S's grandmother.
• (2) True: P is the brother of the parent of S and T, so P is their uncle.
• (3) Cannot be concluded: P is one son of R, but Q's gender is not given, so Q may be a second son.
• (4) False: Q has at least two daughters, S and T.

Answer: A

North is at the top of the map; 1st Main Road separates west from east and 5th Cross Road separates north from south.

• (A) False: the library is level with the canteen, so it is to the west of it, not the northwest.
• (B) False: the hospital is directly north of the chemistry lab.
• (C) True: the physics lab is in the north-west block and the chemistry lab is in the south-east block, so the chemistry lab is to its southeast.
• (D) False: the classrooms and the canteen are in diagonally opposite blocks.

Answer: C

The passage calls the pocket-knife “the type of all human tools, the infant of the sword”, so (C) is stated directly.

• (A) No mirror is mentioned; “reflected” here means “thought about”.
• (B) The author planned a book of poems about the things in his pocket, not a poem on epics, and he gave up the plan.
• (D) He says only that the age of great epics is past; he never calls epics inconvenient to write.

Answer: C

Let the distance from P to QR be \(h\). ST is \(\frac{h}{2}\) from QR, so it is also \(\frac{h}{2}\) from P. Because ST is parallel to QR, triangle PST is similar to triangle PQR with scale factor \(\frac{1}{2}\), so its area is \(\left(\frac{1}{2}\right)^2 = \frac{1}{4}\) of the area of PQR. The trapezium SQRT is the remaining \(\frac{3}{4}\), so the required ratio is \(\frac{1/4}{3/4} = \frac{1}{3}\).

Answer: A

In one roll, a 6 comes with probability \(\frac{1}{6}\) and any other face with probability \(\frac{5}{6}\), and the three rolls are independent. The single 6 can be on the first, second or third roll, so \(P = 3 \times \frac{1}{6} \times \left(\frac{5}{6}\right)^2 = 3 \times \frac{25}{216} = \frac{75}{216}\).

Answer: A

The two folds run along the two diagonals, so (IV) has four layers: its top side is the four outer edges of the sheet, its left side lies on the first fold (top-left to bottom-right diagonal) and its right side on the second fold. Unfolding mirrors every cut across both diagonals.

• The top triangle appears at the middle of all four edges, each pointing towards its edge, which rules out (C).
• The half-square on the first fold opens into a full square with sides parallel to the edges, near the top-left and near the bottom-right corner, which rules out (B) (diamonds) and (D) (one square at the centre).
• The bar touching the second fold joins its mirror image to form the step shapes near the other two corners.

Answer: A

Since the order does not matter, a purchase is fixed by how many scoops of each flavour are taken, that is, by whole numbers \(a, b, c, d \ge 0\) with \(a + b + c + d = 3\). By the stars and bars formula, the count is \(\binom{3 + 4 - 1}{3} = \binom{6}{3} = 20\). Check by cases: all three of one flavour gives 4 ways, two of one flavour and one of another gives \(4 \times 3 = 12\) ways, and three different flavours gives \(\binom{4}{3} = 4\) ways, a total of 20.

Answer: B