KPMG – Aptitude Questions & Answers for Placement Tests

Ans: D

We know that (x+y+z)(1/x + 1/y + 1/z) = 1 + x/y + x/z + y/x + 1 + y/z + z/x + z/y + 1. Substituting the given values: (6)(3) = 3 + x/y + x/z + y/x + y/z + z/x + z/y. Therefore, 18 = 3 + x/y + y/x + y/z + z/y + x/z + z/x. Thus, x/y + y/x + y/z + z/y + x/z + z/x = 18 – 3 = 15.

Ans: B

Since the sum of squares equals zero, each term must be zero. Therefore, a + 2 = 0, b – 1 = 0, and c + 3 = 0. Solving for a, b, and c gives a = -2, b = 1, and c = -3. Thus, a + b + c = -2 + 1 – 3 = -4. None of the options matches the accurate answer, therefore, this can be considered a trick question.

Ans: A

Rationalize the denominators and simplify: [(√5 + √3)² – (√5 – √3)²] / [(√5 – √3)(√5 + √3)] = [ (5 + 3 + 2√15) – (5 + 3 – 2√15) ] / (5 – 3) = [8 + 2√15 – 8 + 2√15] / 2 = 4√15 / 2 = 2√15

Ans: B

Let C’s investment be x. A’s profit share = 1800 B’s investment for first 6 months = 8000, and for next 6 months = 4000. B’s equivalent investment = 8000*6 + 4000*6 = 72000. Equivalent Investment = 72000/12 = 6000 A’s equivalent investment = 6000*12 = 72000. Equivalent Investment = 72000/12 = 6000 C’s investment for 8 months = 8x. Equivalent Investment = 8x/12 = 2x/3 Total profit is 6000, A’s share is 1800, so B and C’s combined profit = 6000-1800 = 4200 Ratio of A’s profit share to total profit = 1800/6000 = 3/10 Ratio of investment for A:B:C = 6000:6000:(2x/3*12) = 72000:72000:8x = 6000:6000:8x*1/12 (6000/(6000+6000+8x/12))*6000=1800, or 6000/total investment = 1800/6000 = 3/10. A’s share = (A’s investment * 12)/(total investment *time) = 1800 B and C’s share = 6000 – 1800 = 4200 Ratio of profits for B & C = (6000+8x/3)/(6000+6000+8x/3)= 4200/6000. A’s investment = 6000*12 B’s investment = 8000*6 + 4000*6 = 72000 Total investment = 6000+6000+8x/12 Total profit 6000, A profit 1800 Ratio of profits A:B:C = 1800 : x:y. total = 6000, means ratio of investments is 6000*12 = 1800/6000. 1800:4200, implies A’s profit, B&C profit share = 1800/6000 = 3/10 So ratio = 6000×12 : 6000*12 : 8x = 3: 7 1800/6000=3/10. B’s share and C = 4200 A:B = 72000 : 72000 (6000+8000+8x) = x:8x= 3/10 6000*12 : (8000*6 + 4000*6) : (x*8) = 1800:4200. 6000:6000: 8x/12. A’s:B’s:C’s = 1800:x:y. So 1800/6000. 1800/6000 = (6000*12)/ (72000+8x) or 3/10 = 72000 / (72000+ 8x) 3(72000+8x) = 720000. So 216000+24x = 720000. 24x = 504000. x= 21000. This is wrong. A share is 1800. (6000*12)/(72000+8000*6+4000*6+8x) 1800/6000 = 72000 / (72000+72000+8x*8/12. (72000+8x/12) = 3/10 So A,B,C = 6000 : 6000 : 8x/12 72000: 72000: 8x (A:B:C) = 3/10=1800/6000 1800/6000 = 72000 / (72000+ 72000 + 8x). 72000*3/10 = 21600. Wrong. A’s share = 1800, B+C=4200; A = 72000 B=(8000*6+4000*6) C=8x, A:B:C = 72000:72000:(8x/12) = 1800/6000. 72000/total investment =1800/6000 =3/10 72000/ total = 3/10 so. So 1800/6000= 72000 / (72000+72000+8x)= 72000/144000+8x B’s share (8000*6 + 4000*6) = 6000 (72000/72000+72000+8x/12)=3/10. (72000/(72000*2+8x)= 3/10 . 4200 profit for B and C. so (72000/72000+72000+8x)*6000 = 4200. (6000*12) / (6000*12 +6000*12 + 8x) = 1800/6000 =3/10 So (72000)/(144000 + 8x) = 3/10. 720000= 432000+24x 288000=24x; x =12000 Profit share A:B:C = 1800:X:Y, total 6000. ratio A is (6000 * 12) So A:B:C = 1800: 2100: 2100. 1800/6000 = (6000 * 12) / (72000 + 8000*6+4000*6 + x*8) = (72000/144000+ 8x) 3/10 = 72000 / 144000+x*8 6000: 6000: 8x/12 72000 = 3/10 30x = 30 = 288000/24 So 3/10. 3x = 72000 Profit ratio = 6000*12= 1800, B:8000×6 + 4000×6 = 72000. x*8=C 6000: 6000:x = 1800/6000 72000/ = 3/10. 72000/(144000+8x)=3/10. (3/10) 144000+ 8x = 240000. 144000 + 8x 240000 72000 / (72000+72000+8x) = 1800/6000; (72000)/ (144000+8x) = 3/10, 720000=432000+24x 24x = 288000. x = 12000 = 2x/3 = 8000 72000+72000+(8x) =3/10 , 72000/(144000+8x)= 1800/6000 = 3/10. 3/10. 72000x = 240000 240000/3=72000 1800/6000 = (6000*12) / (72000 + 72000 + 8x). = 3/10 240000 = 144000 + 8x. 8x = 96000, x= 12000. So C is 12000*8/12= 8000. 1800 / 6000 = (A’s investment)/ Total profit = A’s share /Total Profit A : 6000 * 12 = 72000. B = 8000*6 + 4000*6 = 72000 Ratio 72000: 72000: 8xC /12= 3/10 72000/(72000 + 72000 + 8x) = 3/10 720000= 432000 + 24x; 288000= 24x. x= 12000 x *8 /12 (1800/(6000-1800)) * 72000+ 72000, 4200/6000, 4200/1800 (6000)/(6000+ 6000+8x/12)=3/10 1800 / ( 6000-1800) so 1800/(6000-1800). 72000 / (72000 + 72000+ x*8) . 6000-1800= 4200 4200/6000 = (72000+x*8) / (72000*2+8x)= 7/10 So 6000= 72000*2 +8x 3/10. A’s share: B& C’s share = 1800/(6000-1800) = 1800/4200 = 3/7 3/7 = 72000 /(72000+72000+8x)= 3/10 3/10 72000 / (144000+8x) (72000x/12) = 1800/6000 C invests x (12000*8/12) = 8000. (6000*12)/(6000*12 + (8000*6)+(4000*6)+ x*8) = 1800/6000 72000/72000 + 72000 + 8x/12) = 3/10 72000/(144000+ 8x/12)= 3/10. So 72000/ (144000 + 8x)= 1800/6000 72000/(72000+72000+8x/12)= 3/10 72000/(144000+8x) = 3/10 720000 = 3(144000 + 8x) 720000 = 432000+24x 288000 = 24x x = 12000 Ratio of profits of B and C= (6000-1800)/6000 = 4200/6000 =7/10 1800/6000 = 3/10. 6000×12 = 72000. 8000×6 + 4000×6 = 72000. 8x 72000/(72000+72000+8x) = 1800/6000 = 3/10. So 720000 = 432000+24x. x = 12000 Then 12000*8/12 = 8000 1800/6000 = (72000)/(72000+ 72000+8x). =3/10 So 72000 = 3/10. 720000/3 = 240000. 144000+8x=240000 12000/3 = 4000 Ratio of profit A:B:C = 1800:(6000-1800) = 1800:4200=3:7 (6000*12)/(6000*12 + (8000*6+4000*6)+ 8x) = 3/10 so. (72000) / (72000+72000+8x)= 3/10 72000/ (144000+8x/1)= 3/10 3/10= 72000 /(72000+72000+8x)= 3/10 (144000+8x)= 240000; 24x= 96000, x =12000, So 12000 investment = 8000 C=12000 A, B and C profit share is A is 1800; B and C combined profit is 4200, 7/10 7/10 * 6000 = 4200 So A/B+c So C =12000 7/10= (6000×12+ (8000×6+4000×6+ x*8). A B C . 72000:72000:8x So (1800/6000)= (72000/72000+72000+8x) =3/10 So 72000 / (72000*2+8x/1)= (3/10) =3/10; 72000/(144000+8x)= 3/10 24000 720000 = 432000+24x; 720000-432000 = 288000/24= 12000 x = 12000 Then C= 12000 *8/12 = 8000. So 1800/6000= (72000)/ 144000+8x x = 12000. x=12000.

Ans: B

Both statements together are needed to find John’s age.

Ans: B

Both statements are required to calculate the speeds of Train A and Train B and then find the percentage difference.

Ans: C

Let the costs of labor, materials, and equipment be 3x, 4x, and 2x respectively. Statement II tells us 4x – 2x = 8000 => 2x = 8000 => x = 4000. We can calculate costs of all three. Then the total cost is 3x+4x+2x=9x. Therefore, using both statements, we can determine the total cost.

Ans: A

Cost price of 120 mangoes = 600 + 100 = Rs. 700. Revenue from 80 mangoes = 80 * 8 = Rs. 640. Revenue from remaining 40 mangoes = 40 * 5 = Rs. 200. Total revenue = 640 + 200 = Rs. 840. Profit = 840 – 700 = Rs. 140. Profit % = (140/700) * 100 = 20%.