IBPS PO Prelims 2019 Quantitative Aptitude Questions with Solutions

Explanation

Solving equation I: x³ = 2744 yields x = ∛2744 = 14. Solving equation II: y² = 324 yields y = √324 = 18 or y = -18.

Comparing each possible pair of roots: When y = 18, x = 14 < 18. When y = -18, x = 14 > -18.

Because x is greater than y in one case and less than y in another case, no definite relation can be established between x and y.

Explanation

Solving quadratic equation I: 7x² - 17x + 6 = 0 Factoring gives 7x² - 14x - 3x + 6 = 0, which simplifies to (7x - 3)(x - 2) = 0. Roots are x = 2 or x = 3/7 ≈ 0.43.

Solving quadratic equation II: 5y² - 24y + 16 = 0 Factoring gives 5y² - 20y - 4y + 16 = 0, which simplifies to (5y - 4)(y - 4) = 0. Roots are y = 4 or y = 4/5 = 0.8.

Comparing roots: When x = 2 and y = 4, x < y. When x = 2 and y = 0.8, x > y. Since x is smaller than y in one pair and larger in another, no relation can be established between x and y.

Explanation

Solving equation I: 13x² + 9x - 4 = 0 Factoring gives 13x² + 13x - 4x - 4 = 0, leading to (13x - 4)(x + 1) = 0. Roots are x = 4/13 ≈ 0.31 and x = -1.

Solving equation II: 2y² + y - 3 = 0 Factoring gives 2y² - 2y + 3y - 3 = 0, leading to (2y + 3)(y - 1) = 0. Roots are y = 1 and y = -1.5.

Comparing roots: 0.31 < 1, but 0.31 > -1.5. Since x is less than y for one root combination and greater than y for another, no relationship can be established between x and y.

Explanation

Solving equation I: x² + 13x + 42 = 0 Factoring gives (x + 6)(x + 7) = 0. Roots are x = -6 and x = -7.

Solving equation II: y² + 8y + 12 = 0 Factoring gives (y + 6)(y + 2) = 0. Roots are y = -6 and y = -2.

Comparing roots: For x = -6 and y = -6, x = y. For x = -6 and y = -2, x < y. For x = -7 and y = -6, x < y. For x = -7 and y = -2, x < y. In all cases, x is less than or equal to y (x ≤ y).

Explanation

Solving equation I: x² + 21x + 108 = 0 Factoring gives (x + 12)(x + 9) = 0. Roots are x = -12 and x = -9.

Solving equation II: y² + 14y + 48 = 0 Factoring gives (y + 8)(y + 6) = 0. Roots are y = -8 and y = -6.

Comparing roots: -12 < -8 -12 < -6 -9 < -8 -9 < -6 Every value of x is strictly less than every value of y, so x < y.

Explanation

Rearranging equation I: x² + 24x + 119 = 0 Factoring gives (x + 17)(x + 7) = 0. Roots are x = -17 and x = -7.

Rearranging equation II: 3y² + 10y + 7 = 0 Factoring gives 3y² + 3y + 7y + 7 = 0, leading to (3y + 7)(y + 1) = 0. Roots are y = -7/3 ≈ -2.33 and y = -1.

Comparing roots: -17 < -2.33 -17 < -1 -7 < -2.33 -7 < -1 Every value of x is strictly smaller than every value of y, so x < y.

Explanation

Solving equation I, 2x² + 7x - 60 = 0: Factorizing by splitting the middle term gives 2x² + 15x - 8x - 60 = 0, which simplifies to (2x + 15)(x - 4) = 0. This yields roots x = -15/2 = -7.5 and x = 4.

Solving equation II, 3y² - 28y + 64 = 0: Factorizing by splitting the middle term gives 3y² - 12y - 16y + 64 = 0, which simplifies to (3y - 16)(y - 4) = 0. This yields roots y = 16/3 ≈ 5.33 and y = 4.

Comparing all pairs of roots: When x = -7.5, x < 4 and x < 5.33. When x = 4, x = 4 and x < 5.33. Therefore, x ≤ y holds true for all root pairs.

Explanation

Let the speed of the bus be 6s and the speed of the car be 7s. Since both start from the same point in the same direction, the relative speed of the car with respect to the bus is 7s - 6s = s. The distance between them after 4 hours is given as 28 km. Distance = Relative speed × Time 28 = s × 4 ⇒ s = 7 km/h.

Speed of the car = 7 × 7 = 49 km/h. Time required by the car to cover 196 km = Distance ÷ Speed = 196 ÷ 49 = 4 hours.

Explanation

Original average weight of 45 girls = 53 kg. Sum of wrong weights read = 49 + 57 = 106 kg. Sum of correct actual weights = 45 + 52 = 97 kg. Net change in total weight = Correct sum - Wrong sum = 97 - 106 = -9 kg.

Change in class average weight = Net change in total weight ÷ Number of girls Change in average = -9 ÷ 45 = -0.20 kg.

Actual average weight = Original average + Change in average Actual average weight = 53 - 0.20 = 52.80 kg.

Explanation

Perimeter of a rectangular field = Total cost of fencing ÷ Rate per meter Perimeter = 208 ÷ 4 = 52 meters.

Let the breadth be 9x and the length be 4x according to the given ratio 9 : 4. Perimeter formula = 2 × (Length + Breadth) 2 × (9x + 4x) = 52 2 × 13x = 52 26x = 52 ⇒ x = 2.

Breadth = 9 × 2 = 18 meters. Length = 4 × 2 = 8 meters. Area of the rectangular field = Length × Breadth = 18 × 8 = 144 m².

Explanation

Let M and R be the present ages of Megha and Ritu respectively. Sum of present ages: M + R = 18 × 2 = 36 Six years hence: M + 6 = 2 × (R + 6) M - 2R = 6

Subtracting the second equation from the first: 3R = 30 ⇒ R = 10 M = 36 - 10 = 26

Megha's present age is 26 years.

Explanation

Using the weighted percentage change formula: Portion 1: 50% of articles sold at +20% profit = 0.50 × 20% = +10% Portion 2: 50% of remaining (25%) sold at +10% profit = 0.25 × 10% = +2.5% Portion 3: 20% of remaining (5%) sold at -10% loss = 0.05 × (-10%) = -0.5% Portion 4: Rest (20%) sold at -20% loss = 0.20 × (-20%) = -4%

Net profit percentage = 10 + 2.5 - 0.5 - 4 = 8%

Explanation

Number of red balls = 4 Number of yellow balls = 5 Average of red and yellow balls = (4 + 5) / 2 = 4.5 Number of green balls = 2 × 4.5 = 9 Total balls = 4 + 5 + 9 = 18

Probability of choosing 2 red balls = ⁴C₂ / ¹⁸C₂ ⁴C₂ = 6 ¹⁸C₂ = 153 P = 6 / 153 = 2 / 51

Explanation

Treat the 4 girls who must sit together as a single block. Total entities to arrange = (10 - 4 + 1) = 7 Arrangements of 7 entities = 7! = 5040 Internal arrangements of the 4 girls within the block = 4! = 24

Total number of arrangements = 7! × 4! = 5040 × 24 = 120960

Explanation

Let the speed of the stream be y km/h. Speed of boat in still water = y + 300% of y = 4y km/h. Downstream speed = 4y + y = 5y km/h. Upstream speed = 4y - y = 3y km/h.

From downstream motion: (x + 20) / 5y = 5 ⇒ x + 20 = 25y From upstream motion: (x - 5) / 3y = 5 ⇒ x - 5 = 15y

Subtracting the two equations: 25 = 10y ⇒ y = 2.5

Substituting y into x - 5 = 15y: x - 5 = 15 × 2.5 = 37.5 x = 42.5

Explanation

For the first equation, factorizing gives (2x + 9)(x - 3) = 0, yielding x = -4.5 and x = 3. For the second equation, factorizing gives (3y - 14)(y + 3) = 0, yielding y = 14/3 ≈ 4.67 and y = -3. Comparing the roots, x = 3 is greater than y = -3, but x = -4.5 is smaller than y = -3. Therefore, no relation can be established between x and y.

Explanation

Solving x² - 2x - 15 = 0 gives (x - 5)(x + 3) = 0, so x = 5 and x = -3. Solving y² - 4y - 12 = 0 gives (y - 6)(y + 2) = 0, so y = 6 and y = -2. Comparing x = 5 with y = -2 gives x > y, but comparing x = 5 with y = 6 gives x < y. Since the relationship varies depending on the chosen roots, no relationship can be established between x and y.

Explanation

Solving x² - 20x + 96 = 0 gives (x - 12)(x - 8) = 0, so x = 12 and x = 8. Solving y² - 10y + 24 = 0 gives (y - 6)(y - 4) = 0, so y = 6 and y = 4. Comparing all pairs of roots: 12 > 6, 12 > 4, 8 > 6, and 8 > 4. Since x is strictly greater than y in all cases, x > y.

Explanation

Solving 6x² + 13x + 5 = 0 gives roots x = -5/3 ≈ -1.67 and x = -1/2 = -0.5. Solving 3y² + 11y + 10 = 0 gives roots y = -2 and y = -5/3 ≈ -1.67. Comparing these values shows that -0.5 is greater than both -2 and -1.67, while -1.67 is equal to -1.67 and greater than -2. Thus, x ≥ y.

Explanation

Multiplying 6x + 7y = 52 by 2 gives 12x + 14y = 104. Multiplying 14x + 4y = 35 by 3.5 gives 49x + 14y = 122.5. Subtracting the first resulting equation from the second gives 37x = 18.5, so x = 0.5. Substituting x = 0.5 into 6x + 7y = 52 gives 3 + 7y = 52, which yields y = 7. Since 0.5 < 7, x < y.

Explanation

Solving x² - 12x + 32 = 0 yields x = 8 and x = 4. Solving y² - 18y + 77 = 0 yields y = 11 and y = 7. Comparing the roots shows that x = 8 is greater than y = 7, but x = 8 is less than y = 11. Because x can be both greater than and less than y, no relationship can be established between x and y.

Explanation

The area of the square is 64 sq.cm, so its side length is √64 = 8 cm. The diagonal of the square, which equals the height of the cylinder, is 8√2 cm. Using the volume formula V = π r² h with radius r = 7 cm and height h = 8√2 cm gives V = (22/7) × 7² × 8√2 = 22 × 7 × 8√2 = 1232√2 cm³.

Explanation

Since the principal doubles in 3 years at simple interest, the interest equals the principal, so SI = P × R × 3 / 100 = P, which gives R = 100/3% per annum. For compound interest, the total amount after 2 years on Rs 5000 is A = P(1 + R/100)² = 5000 × (1 + 1/3)² = 5000 × (4/3)² = 80000/9 ≈ Rs 8888.89. The compound interest is 8888.89 - 5000 = Rs 3888.89, which rounds to Rs 3889.

Explanation

Since 7 men or 10 women can complete the work in 10 days, 7 men = 10 women, and total work = 10 × 10 = 100 woman-days. To complete the work in 4 days, the daily requirement is 100 / 4 = 25 women per day. With 15 women already working, an additional workforce equivalent to 10 women per day is required. Since 10 women are equivalent to 7 men, 7 men are needed to assist the 15 women.

Explanation

Let Rajesh's salary be 100. Guthi earns 30% more than Rajesh, so Guthi's salary is 130. Chappu earns 20% less than Guthi, so Chappu's salary is 130 × 0.8 = 104. Dinesh earns 50% more than Chappu, so Dinesh's salary is 104 × 1.5 = 156. Comparing Dinesh's salary of 156 to Rajesh's salary of 100 gives a difference of 56, meaning Dinesh's salary is 56% more than Rajesh's.

Explanation

The pattern in the series is: 2 × 2 - 1 = 3 3 × 3 - 2 = 7 7 × 4 - 3 = 25 25 × 5 - 4 = 121 121 × 6 - 5 = 721

Explanation

The pattern in the given series is: 5 × 2 + 9 = 19 19 × 2 + 7 = 45 45 × 2 + 5 = 95 95 × 2 + 3 = 193 193 × 2 + 1 = 387

Explanation

The differences between successive terms are: 8 - 2 = 6 20 - 8 = 12 = 6 × 2 56 - 20 = 36 = 12 × 3 200 - 56 = 144 = 36 × 4

The next difference will be 144 × 5 = 720. The missing term is 200 + 720 = 920.

Explanation

The pattern of operations in the series is: 32 × 1 = 32 32 ÷ 2 = 16 16 × 3 = 48 48 ÷ 4 = 12 12 × 5 = 60

Explanation

The pattern of differences between successive terms is: 6 + 2² = 6 + 4 = 10 10 + 3² = 10 + 9 = 19 19 + 2³ = 19 + 8 = 27 27 + 3³ = 27 + 27 = 54 54 + 2⁴ = 54 + 16 = 70

Explanation

The nth term of the series is given by Tₙ = (n - 2)⁴: T₁ = (1 - 2)⁴ = 1 T₂ = (2 - 2)⁴ = 0 T₃ = (3 - 2)⁴ = 1 T₄ = (4 - 2)⁴ = 16 T₅ = (5 - 2)⁴ = 81 T₆ = (6 - 2)⁴ = 256 T₇ = (7 - 2)⁴ = 625

Explanation

Let the total amount be T. Intended ratio = 1 : 3 : 5 (total parts = 9) Actual ratio = 2 : 3 : 6 (total parts = 11)

B's intended share = T / 3 B's actual share = 3T / 11

Difference in B's share = T / 3 - 3T / 11 = 2T / 33 = 42 T = (42 × 33) / 2 = 693

The amount intended to be received by A = (1 / 9) × 693 = 77

Explanation

Train speed = 72 km/h = 72 × (5 / 18) = 20 m/s Relative speed of train with respect to the man = 20 - 2 = 18 m/s

Length of train = Relative speed × Time = 18 × 10 = 180 m

When crossing the tunnel of length L: Total distance = Length of train + Length of tunnel = 180 + L Speed = 20 m/s, Time = 54 s

180 + L = 20 × 54 = 1080 L = 1080 - 180 = 900 m

Explanation

Let Neeraj's initial investment be 3x and Arun's initial investment be 5x.

Neeraj's investment for 12 months = 3x × 12 = 36x Arun's investment for first 4 months = 5x × 4 = 20x Arun's reduced investment for remaining 8 months = (5x - x) × 8 = 32x Total investment units for Arun = 20x + 32x = 52x

Ratio of profit shares (Neeraj : Arun) = 36 : 52 = 9 : 13 Neeraj's profit share = (9 / 22) × 880 = 360

Explanation

Upstream speed = Boat speed - Stream speed = 17 kmph Stream speed = 3 kmph

Boat speed in still water = 17 + 3 = 20 kmph Downstream speed = Boat speed + Stream speed = 20 + 3 = 23 kmph