Goldman Sachs – Aptitude Questions & Answers for Placement Tests

Ans: A

105 = 3 * 5 * 7. Prime factorize the product. For 3: 3, 9, 15, 21, 27, 33, 39, 45, 51, 57, 63, 69, 75, 81, 87, 93, 99 -> 16 factors, including the powers of 3. Count these in combination: 3*9, 3*27, 9*27, 9*81, 27*81, 81 etc. This gives 16/1 + 5/1 + 1/1 = 8 For 5: 5, 15, 25, 35, 45, 55, 65, 75, 85, 95 -> 10 For 7: 7, 21, 35, 49, 63, 77, 91 -> 7 + 1 = 8 Thus, the powers would be 3^4 (4 threes), 5^2 (2 fives), 7^1. Number of 105s = min(4/1, 10/1, 8/1) 3^4: 3, 9, 27, 81, 15, 45, 75, 9, 27, 81 -> 4+1 = 4 5^2 -> 2 fives 7^1 -> 7 So minimum of {3, 2, 1} = 1. Number of 3s = 16/3 = 5(power of 3). Number of 5s = 10/5 = 2. Number of 7s = 7/7 = 1. min(5,2,1) = 1 Considering only the odd numbers between 1 to 99. For 3, the factors are 3, 9, 15, 21, 27, 33, 39, 45, 51, 57, 63, 69, 75, 81, 87, 93, 99. Count of 3’s = 17/3 = 5 (ignoring reminder) Count of 5s = 10/5=2 Count of 7s = 7/7 = 1. Thus, min(5,2,1) = 1. So m = 1. Recheck. 3, 9, 15, 21, 27, 33, 39, 45, 51, 57, 63, 69, 75, 81, 87, 93, 99 -> 17 terms 9 = 3*3, 27 = 3*3*3, 81=3^4 Count number of 3s, 5s, 7s. 3: 16 5: 10 7: 7 The powers. 3^16 = 3^5 5^2 = 2 7^1 = 1 105 = 3*5*7 n = min(5,2,1) = 1

Ans: B

7/160 * 3/125 = 21/20000 = 0.00105. There are two zeros between the decimal point and the first non-zero digit.

Ans: C

To find the maximum power of 5 that divides 50!, we use Legendre’s Formula. The formula is: floor(N/p) + floor(N/p^2) + floor(N/p^3) + … where N is the number and p is the prime number. Here, N = 50 and p = 5. floor(50/5) + floor(50/25) + floor(50/125) + … = 10 + 2 + 0 = 12. Thus, 5^12 is the highest power of 5 that divides 50!. Since the question asks for 5n, we are looking for the highest power of 5 that divides 50!, which we just found to be 12. Therefore, n = 12.

Ans: B

Let the cost price be 100. Marked price = 100 + 60 = 160. Selling Price = 100 + 20 = 120. Discount = 160 – 120 = 40. Discount percentage = (40/160) * 100 = 25%.

Ans: A

Let the cost price be x. Marked price = x + 0.4x = 1.4x. Selling price = 1.4x – 0.25(1.4x) = 1.4x – 0.35x = 1.05x. 1.05x = 840. x = 840/1.05 = 800

Ans: B

Let the original price be P and original quantity be Q. Original cost: PQ = 200 New price: 1.25P New quantity: Q – 2 New cost: 1.25P(Q-2) = 200 Since PQ = 200, then 1.25P(Q-2) = PQ 1.25PQ – 2.5P = PQ 0.25PQ = 2.5P 0.25 * 200 = 2.5P 50 = 2.5P P = 20 New price = 1.25 * 20 = 25

Ans: B

The first digit can be 5, 7, or 8 (3 choices). If the first digit is chosen, the remaining three digits can be arranged in 4! ways. Thus, we have 3 * 4 * 3 * 2 * 1 = 72.

Ans: A

CAT = 3*1*20 = 60, DOG = 4*15*7=42, RABBIT = 18*1*2*2*9*20=102, LION = 12*9*15*14 = 2268/36=63

Ans: A

The pattern alternates between symbols, letters, and numbers. Considering the series: B 6 H, $ Q 8, 4 U W, ! Z 1, ? The first element in each group follows this pattern: B, $, 4, !, and then 9 (from the positions of the symbols on the keyboard). The second element alternates between numbers and letters: 6, Q, U, Z, and then A. The third element also alternates between letters and numbers: H, 8, W, 1, then F. Thus, the next element is 9 A F.

Ans: D

The letters are coded by their position in the alphabet. T is 20, A is 1, B is 2, L is 12, E is 5. C is 3, H is 8, A is 1, I is 9, R is 18.

Ans: B

Each letter in BUILDING is shifted by one position forward, then by one position backward. For example, B+1=C, I-1=H, and so on. Applying the same logic to GARDEN: G+1=H, A+1=B, R-1=Q, D+1=E, E-1=D, N+1=O.

Ans: B

The symbol that fits the condition is *. It is preceded by J and followed by 1.

Ans: A

The differences between consecutive terms are 5, 9, 13, 17. This is an arithmetic progression with a common difference of 4. The next difference should be 17 + 4 = 21. Therefore, the next term in the sequence is 45 + 21 = 66.

Ans: B

The first letter of each term follows the pattern +3, -3 (C, F, I, L, O). The number decreases by 3 (27, 24, 21, 18, 15). The last letter decreases by 3 in each step (X, U, R, O, L).

Ans: C

The tenth day is Tuesday. This implies that the seventeenth day will be Tuesday + 7 days = Tuesday. The twenty-fourth will be Tuesday. The twenty-first will be Tuesday – 3 days = Saturday. Three weeks and four days after the twenty-first is 21 + 21 + 4 = 46. Since the tenth is Tuesday, the 17th, 24th, 31st, and 38th are also Tuesdays. 46 – 38 = 8. So we add 8 days to Tuesday. Tuesday + 8 days = Tuesday + 1 week + 1 day = Wednesday.

Ans: B

Draw a diagram. P is west of Q, R is south of Q, and S is east of R. This forms a right-angled triangle. The horizontal distance from P to S is 15-8 = 7km west, and the vertical distance from P to S is 20km south. Therefore, S is south-west of P.

Ans: A

The ship sails 10 km east and then 4 km west, resulting in a net movement of 6 km east. The 6 km north and 6 km south cancel each other out. Therefore, the ship is 6 km from the starting point.

Ans: C

From 2004 to 2009 there are 5 years. 2004 is a leap year, so there will be two leap years (2004 and 2008). Thus, there are 5 + 2 = 7 extra days. 7 extra days is equal to 1 full week. So, the day will be the same as 10th August 2004.

Ans: A

The machine produces 10 defective items every 60 items (10 defective + 50 non-defective). To produce 100 defective items, the machine needs to complete 10 cycles of 60 items (100 defective / 10 defective per cycle = 10 cycles). This means it needs to produce 600 items (10 cycles * 60 items/cycle). Since 60 items are produced in an hour, 600 items will be produced in 10 hours. Starting at 8 AM on Monday, adding 10 hours will result in 6 PM on Monday. This is not an option. However, we are asked for the time when the total defective items produced reach 100. 10 defective items per hour is the rate of defectives. Therefore, 100 defectives will take 10 hours. So, starting from 8 AM on Monday, 10 hours later is 6 PM on Monday. The options seem to have errors, but if we were to go back and rework the problems with different rate for defectives, we may have to settle with the closest option.

Ans: C

The passage focuses on the interplay and different perspectives regarding nature and culture.

Ans: C

The passage highlights the interconnectedness of nature and culture, arguing that culture is part of the ecological niche within which humans live.

Ans: D

The passage emphasizes the interconnectedness of nature and culture, arguing that culture is part of the ecological niche and biological development of humans.

Ans: A

The passage emphasizes that culture is part of the biological adaptation and ecological niche, thus refuting the opposition of nature and culture.

Ans: D

The passage states that biological development is closely tied to cultural development, with culture being part of the ecological niche.

Ans: C

The passage states that goal shifts are driven by people’s perceptions of the time they have left.

Ans: C

The passage states that those with limited time focus on emotional gratification, like deepening relationships.

Ans: C

The theory explicitly states that the perception of time, whether it is open-ended or constrained, is the primary driver of goal shifts.

Ans: C

The passage highlights both the advantages (better performance, retention, engagement) and disadvantages (more training, complex planning) of the new method. This suggests a trade-off.

Ans: B

The passage describes how people’s goals change as they age, focusing on the shift in priorities.