Quant G Strategy

A bus is 3.5 hours late when traveling at 60 km/hr. The next day, it travels 2/3 of the distance in 1/3 of the time and the remaining at 40 km/hr to reach on time. What is the scheduled arrival time?

All values of x satisfying the inequality 1/(x+5) ≤ 1/(2x−3) are:

When 3333 is divided by 11, the remainder is:

If m and n are natural numbers such that mn = 225 × 340, then m − n equals:

Roots α, β of 3x² + λx − 1 = 0 satisfy 1/α² + 1/β² = 15. Then (α³ + β³)² equals:

If x and y satisfy |x| + x + y = 15 and x + |y| − y = 20, then x − y equals:

Anil invests Rs 22000 for 6 years at 4% p.a. compounded half-yearly. Sunil invests an amount for 5 years in same scheme, then reinvests at 10% simple interest for 1 year. Their final amounts are equal. Find Sunil’s initial investment.

A vessel contains an acid-water solution. After adding 2 litres water and then 15 litres acid, concentrations change from 50% to 80%. Find the original water:acid ratio.

The coordinates of a triangle are (1, 2), (7, 2), and (1, 10). Find the inradius.

Bina sells a product at Rs. 4860 and incurs 19% loss. Had she sold it at Hari’s purchase price, she would have made 17% profit. Find Shyam's profit.

Amal and Vimal can complete a task in 150 days; Vimal and Sunil in 100. Work pattern alternates. Find total days to complete the task.

Function f:N→W such that f(xy) = f(x)f(y) + f(x) + f(y) and f(p)=1 for primes. Find f(160000).

When Rajesh’s age was equal to Garima’s current age, their age ratio was 3:2. When Garima becomes Rajesh’s current age, what will be their age ratio?

Find the sum of the infinite series: (1/5)(1/5 − 1/7) + (1/5)²((1/5)² − (1/7)²) + …

A fruit seller has mangoes, bananas, and apples. 40% are mangoes. He sells half the mangoes, 96 bananas, and 40% apples. If 50% of stock is sold, find the minimum initial total stock.

Three identical circles touch each other. Two larger circles X and Y also touch them. If radius of X > Y, find ratio of their radii.

In 2022, average bonus of first 30 employees was Rs. 40,000; last 30 was Rs. 60,000; first and last 10 combined was Rs. 50,000. In 2023, first 10 doubled, last 10 tripled. Find average bonus in 2023.

ABCD is a trapezium with AB = 2 cm, CD = 1 cm, and perimeter = 6 cm. AD and BC intersect at E. Find perimeter of triangle AEB.

If 4x² + 4y² − 4xy − 6y + 3 = 0, find value of (4x + 5y).

P, Q, R, and S are towns. Paths between them are defined. 62 ways exist from P to S; 27 ways from Q to R. Find number of direct paths between Q and R.

If a > 10 ≥ b ≥ c and given a logarithmic equation involving a, b, c, find the greatest possible integer value of a.

A circular plot of land is divided into two regions by a chord of length 10√3 meters such that the chord subtends an angle of 120° at the center. Then, the area, in square meters, of the smaller region is:

If (a + b√3)² = 52 + 30√3, where a and b are natural numbers, then a + b equals:

The number of distinct real values of x, satisfying the equation max{x, 2} − min{x, 2} = |x + 2| − |x − 2| is:

The average of three distinct real numbers is 28. If the smallest number is increased by 7 and the largest number is reduced by 10, the order remains unchanged. The new mean is 2 more than the middle number and the new difference between largest and smallest is 64. Find the largest original number.

Aman invests Rs 4000 at compound interest. The ratio of the value after 3 years to after 5 years is 25:36. Find the minimum number of years required for the investment to exceed Rs 20000.

Rajesh and Vimal own 20 and 30 hectares of land. Vimal grows wheat and mustard in 5:3 ratio. Total wheat:mustard ratio is 11:9. Find the wheat:mustard ratio in Rajesh’s land.

If 10⁶⁸ is divided by 13, the remainder is:

The number of distinct integer solutions (x, y) of the equation |x + y| + |x − y| = 2 is:

A train travelled a certain distance at uniform speed. If speed increased by 6 km/hr, time reduces by 4 hrs. If speed decreased by 6 km/hr, time increases by 6 hrs. Find the distance in km.

Given a sequence defined as t1 = 1, t2 = −1, and tn = (n−3)/(n−1) × tn−2 for n ≥ 3. Find the value of 1/t2 + 1/t4 + 1/t6 + … + 1/t2024.

If 3^a = 4, 4^b = 5, 5^c = 6, 6^d = 7, 7^e = 8, 8^f = 9, then find the value of a×b×c×d×e×f.

Gopal’s salary becomes 187.5% of original after two successive increments. The second increment is twice the first. Find the percentage increase in the first increment.

For non-zero real x, if f(x) + 2f(1/x) = 3x and f(x) = 3, find the sum of all such x.

A 300-litre container is partially filled with water, rest milk. Twice the water is removed, then refilled with water. Final mix is 72% milk. How much water was initially added?

In a group of 250 students (44% to 60% girls), 50% boys and 80% girls swim; 70% boys and 60% girls run. Find minimum and maximum number of students who do both.

Solve: 10^x + 4/(10^x) = 81/2. Find sum of all real values of x.

A regular octagon has side 6 cm. Find area of square formed by vertices A, C, E, G.

System of equations: px − 4y = 2 and 3x + ky = a. Find condition for no solution.

Gopi marks price to make 20% profit. Ravi gets 10% discount and saves Rs 15. Find Gopi's profit in rupees.

Triangle ABC has midpoints M, N, P on AB, BC, AC. Medians intersect MP, MN, NP at X, Y, Z. If area of ABC = 1440 sq cm, find area of triangle XYZ.

Number of all positive integers ≤ 500 with non-repeating digits:

Sam alone does work in 20 days. Mohit is 2× Sam, 3× Ayna. They work alternately in pattern: Sam+Mohit, Sam+Ayna, Mohit+Ayna. What fraction of total work is done by Sam?

A shop wants to sell a certain quantity (in kg) of grains. It sells half the quantity and an additional 3 kg of these grains to the first customer. Then, it sells half of the remaining quantity and an additional 3 kg of these grains to the second customer. Finally, when the shop sells half of the remaining quantity and an additional 3 kg of these grains to the third customer, there are no grains left.

The selling price of a product is fixed to ensure 40% profit. If the product had cost 40% less and had been sold for 5 rupees less, then the resulting profit would have been 50%.

If (a + b√n) is the positive square root of 29 − 12√5, where a and b are integers, and n is a natural number, then the maximum possible value of (a + b + n) is

A glass is filled with milk. Two-thirds of its content is poured out and replaced with water. If this process of pouring out two-thirds the content and replacing with water is repeated three more times, then the final ratio of milk to water in the glass is.

Renu would take 15 days working 4 hours per day to complete a certain task whereas Seema would take 8 days working 5 hours per day to complete the same task. They decide to work together to complete this task. Seema agrees to work for double the number of hours per day as Renu, while Renu agrees to work for double the number of days as Seema. If Renu works 2 hours per day, then the number of days Seema will work is.

Suppose X1, X2, X3, . . . , X100 are in arithmetic progression such that X5 = −4 and 2X6 + 2X9 = X11 + X13. Then, X100 equals

Consider two sets A = {2, 3, 5, 7, 11, 13} and B = {1, 8, 27}. Let f be a function from A to B such that for every element b in B, there is at least one element a in A such that f(a) = b. Then, the total number of such functions f is

Let x, y, and z be real numbers satisfying 4(x² + y² + z²) = a, 4(xyz) = 3 + a. Then a equals:

The sum of all real values of k for which the equation x²²⁷⁶ = x²²⁷⁶ holds true is. If k = 1, 32768, then the value of k is

In September, the incomes of Kamal, Amal and Vimal are in the ratio 8 : 6 : 5. They rent a house together, and Kamal pays 15%, Amal pays 12% and Vimal pays 18% of their respective incomes to cover the total house rent in that month. In October, the house rent remains unchanged while their incomes increase by 10%, 12% and 15% respectively. In October, the percentage of their total income that will be paid as house rent is nearest to.

If the equations x² + mx + 9 = 0, x² + nx + 17 = 0, and x² + (m + n)x + 35 = 0 have a common negative root, then the value of 2m + 3n is

For any natural number n, let an be the largest integer not exceeding √n. Then the value of a1 + a2 + · · · + a50 is

When 10¹⁰⁰ is divided by 7, the remainder is

A fruit seller has a total of 187 fruits consisting of apples, mangoes, and oranges. The number of apples and mangoes are in the ratio 5 : 2. After she sells 75 apples, 26 mangoes, and half of the oranges, the ratio of number of unsold apples to number of unsold oranges becomes 3 : 2. The total number of unsold fruits is

Two places A and B are 45 kms apart and connected by a straight road. Anil goes from A to B while Sunil goes from B to A. Starting at the same time, they cross each other in exactly 1 hour 30 minutes. If Anil reaches B exactly 1 hour 15 minutes after Sunil reaches A, the speed of Anil, in km per hour, is.

There are four numbers such that average of first two numbers is 1 more than the first number, average of first three numbers is 2 more than average of first two numbers, and average of first four numbers is 3 more than average of first three numbers. Then, the difference between the largest and the smallest numbers is

ABCD is a rectangle with sides AB = 56 cm and BC = 45 cm, and E is the midpoint of side CD. Then, the length, in cm, of radius of incircle of â–³ADE is

The sum of all four-digit numbers that can be formed with the distinct non-zero digits a, b, c, and d, with each digit appearing exactly once in every number, is 153310 + n, where n is a single digit natural number. Then, the value of (a + b + c + d + n) is

The surface area of a closed rectangular box, which is inscribed in a sphere, is 846 sq cm, and the sum of the lengths of all its edges is 144 cm. The volume, in cubic cm, of the sphere is

In the XY-plane, the area, in sq. units, of the region defined by the inequalities y ≤ x + 4 and −4 ≤ x² + y² + 4(x − y) ≤ 0 is.

If x is a positive real number such that 4 log₁₀ x + 4 log₁₀₀ x + 8 log₁₀₀₀ x = 13, then the greatest integer not exceeding x is

An amount of Rs 10000 is deposited in bank A for a certain number of years at a simple interest of 5% per annum. On maturity, the total amount received is deposited in bank B for another 5 years at a simple interest of 6% per annum. If the interests received from bank A and bank B are in the ratio 10 : 13, then the investment period, in years, in bank A is