71. What is the next number in the sequence0, 1, 1, 2, 4, 7, 13, 24, ________
(A) 30
(B) 37
(C) 41
(D) 44
Answer:
(D) 44
Explanation:
This is a “Tribonacci” sequence, where each term is the sum of the three preceding terms. $0+1+1 = 2$; $1+1+2 = 4$; $1+2+4 = 7$; $2+4+7 = 13$; $4+7+13 = 24$. The next term is $7+13+24 = 44$.
72. What is the value of q? p, q, r are real numbers. Statement I: q – p = r – q Statement II: p + r = 10
(A) If statement I alone is sufficient but statement II alone is not sufficient
(B) If statement II alone is sufficient but statement I alone is not sufficient
(C) If both statements I and II together are sufficient but neither of statements alone is sufficient
(D) If statement I and II together are not sufficient
Answer:
(C) If both statements I and II together are sufficient but neither of statements alone is sufficient
Explanation:
(Note: This is a classic data sufficiency logic puzzle. The OCR scan of the original paper severely garbled the algebra variables). Statement I establishes an arithmetic progression ($q-p = r-q$, which simplifies to $2q = p+r$). By itself, it gives no numerical value. Statement II provides a sum ($p+r = 10$). By substituting II into I, we get $2q = 10$, so $q = 5$. Therefore, both statements working together are necessary and sufficient to find the value.
73. Rana travels 10 km to the north, turns left and travels 4 km, and then again turns right and covers another 5 km, and then turns right and travels another 4 km, How far is he from the starting point?
(A) 15 km
(B) 4 km
(C) 5 km
(D) 10 km
Answer:
(A) 15 km
Explanation:
Let’s track the movements: He goes 10 km North. He turns left (West) for 4 km. He turns right (North) for 5 km. He turns right (East) for 4 km. The East movement of 4 km cancels out the West movement of 4 km. He is now on the same vertical axis as his starting point, exactly $10 + 5 = 15$ km North of where he began.
74. Anuradha walks 3 km northward and then she turns left and moves 2 km. She again turns left and goes 3 km and turns to her right and starts walking straight. In which direction is she walking now?
(A) North
(B) East
(C) South
(D) West
Answer:
(D) West
Explanation:
Track the directions: 3 km North. Turns left -> facing West (walks 2 km). Turns left -> facing South (walks 3 km). Turns right -> facing West. She is currently walking straight toward the West.
75. If a box a sweets is divided among 24 children, they will get 5 sweets each. How many would each get, if the no. of children is reduced by 4?
(A) 6
(B) 7
(C) 8
(D) 9
Answer:
(A) 6
Explanation:
First, find the total number of sweets in the box: $24 \text{ children} \times 5 \text{ sweets/child} = 120 \text{ sweets}$. If the number of children is reduced by 4, there are now 20 children. Divide the sweets evenly: $120 \div 20 = 6$ sweets each.
