Quant Ability

If a seller gives a discount of 15% on retail price, she still makes a profit of 2%. Which of the following ensures that she makes a profit of 20%?

  1. Give a discount of 5% on retail price
  2. Give a discount of 2% on retail price
  3. Increase the retail price by 2%
  4. Sell at retail price

An infinite geometric progression a1, a2, a3, ... has the property that an = 3(an+1 + an+2 +…) for every n ≥ 1. If the sum a1 + a2 + a3 + … = 32, then a5 is

  1. 1/32
  2. 2/32
  3. 3/32
  4. 4/32

The minimum possible value of the sum of the squares of the roots of the equation x2 + (a + 3)x - (a + 5) = 0 is

  1. 1
  2. 2
  3. 3
  4. 4

Let f(x) = x2 and g(x) = 2x, for all real x. Then the value of f(f(g(x)) + g(f(x))) at x = 1 is

  1. 16
  2. 18
  3. 36
  4. 40

If x is a real number such that log3 5 = log5 (2 + x), then which of the following is true?

  1. 0 < x < 3
  2. 23 < x < 30
  3. x > 30
  4. 3 < x < 23

If the product of three consecutive positive integers is 15600 then the sum of the squares of these integers is

  1. 1777
  2. 1785
  3. 1875
  4. 1877

The points (2, 5) and (6, 3) are two end points of a diagonal of a rectangle. If the other diagonal has the equation y = 3x + c, then c is

  1. -5
  2. -6
  3. -7
  4. -8

The base of a vertical pillar with uniform cross section is a trapezium whose parallel sides are of lengths 10 cm and 20 cm while the other two sides are of equal length. The perpendicular distance between the parallel sides of the trapezium is 12 cm. If the height of the pillar is 20 cm, then the total area, in sq cm, of all six surfaces of the pillar is

  1. 1300
  2. 1340
  3. 1480
  4. 1520

Let ABCDEF be a regular hexagon with each side of length 1 cm. The area (in sq cm) of a square with AC as one side is

  1. 3√2
  2. 3
  3. 4
  4. √3

Consider three mixtures - the first having water and liquid A in the ratio 1 : 2, the second having water and liquid B in the ratio 1: 3, and the third having water and liquid C in the ratio 1 : 4. These three mixtures of A, B, and C, respectively, are further mixed in the proportion 4 : 3 : 2. Then the resulting mixture has

  1. The same amount of water and liquid B
  2. The same amount of liquids B and C
  3. More water than liquid B
  4. More water than liquid A

Amal can complete a job in 10 days and Bimal can complete it in 8 days. Amal, Bimal and Kamal together complete the job in 4 days and are paid a total amount of Rs 1000 as remuneration. If this amount is shared by them in proportion to their work, then Kamal's share, in rupees, is

  1. 100
  2. 200
  3. 300
  4. 400

A motorbike leaves point A at 1 pm and moves towards point B at a uniform speed. A car leaves point B at 2 pm and moves towards point A at a uniform speed which is double that of the motorbike. They meet at 3:40 pm at a point which is 168 km away from A. What is the distance, in km, between A and B?

  1. 364
  2. 378
  3. 380
  4. 388

If a, b, c are three positive integers such that a and b are in the ratio 3 : 4 while b and c are in the ratio 2 : 1, then which one of the following is a possible value of (a + b + c)?

  1. 201
  2. 205
  3. 207
  4. 210

In a village, the production of food grains increased by 40% and the per capita production of food grains increased by 27% during a certain period. The percentage by which the population of the village increased during the same period is nearest to 

  1. 16
  2. 13
  3. 10
  4. 7

Mayank buys some candies for Rs 15 a dozen and an equal number of different candies for Rs 12 a dozen. He sells all for Rs 16.50 a dozen and makes a profit of Rs 150. How many dozens of candies did he buy altogether?

  1. 50
  2. 30
  3. 25
  4. 45

A tank has an inlet pipe and an outlet pipe. If the outlet pipe is closed then the inlet pipe fills the empty tank in 8 hours. If the outlet pipe is open then the inlet pipe fills the empty tank in 10 hours. If only the outlet pipe is open then in how many hours the full tank becomes half-full?

  1. 20
  2. 30
  3. 40
  4. 45

The manufacturer of a table sells it to a wholesale dealer at a profit of 10%. The wholesale dealer sells the table to a retailer at a profit of 30%. Finally, the retailer sells it to a customer at a profit of 50%. If the customer pays Rs 4290 for the table, then its manufacturing cost (in Rs) is

  1. 1500
  2. 2000
  3. 2500
  4. 3000

The average height of 22 toddlers increases by 2 inches when two of them leave this group. If the average height of these two toddlers is one-third the average height of the original 22, then the average height, in inches, of the remaining 20 toddlers is

  1. 30
  2. 28
  3. 32
  4. 26

Out of the shirts produced in a factory, 15% are defective, while 20% of the rest are sold in the domestic market. If the remaining 8840 shirts are left for export, then the number of shirts produced in the factory is

  1. 13600
  2. 13000
  3. 13400
  4. 14000

Arun drove from home to his hostel at 60 miles per hour. While returning home he drove half way along the same route at a speed of 25 miles per hour and then took a bypass road which increased his driving distance by 5 miles, but allowed him to drive at 50 miles per hour along this bypass road. If his return journey took 30 minutes more than his onward journey, then the total distance traveled by him is

  1. 55 miles
  2. 60 miles
  3. 65 miles
  4. 70 miles

Bottle 1 contains a mixture of milk and water in 7 : 2 ratio and Bottle 2 contains a mixture of milk and water in 9 : 4 ratio. In what ratio of volumes should the liquids in Bottle 1 and Bottle 2 be combined to obtain a mixture of milk and water in 3 : 1 ratio?

  1. 27 : 14
  2. 27 : 13
  3. 27 : 16
  4. 27 : 18

What is the remainder when the number (4444)4444 is divided by 9?

  1. 4
  2. 6
  3. 7
  4. 8

What is the solution of the equation
x log10 (10/3) + log10 3 = log10 (2 + 3x) + x?

  1. 10
  2. 3
  3. 1
  4. 0

If α and β are the roots of the equation x2 + px + q = 0, then what is α2 + β2 equal to?

  1. p2 – 2q
  2. q2 – 2p
  3. p2 + 2q
  4. q2 – q

The pair of linear equations kx + 3y + 1 = 0 and 2x + y + 3 = 0 intersect each other, if

  1. k = 6
  2. k ≠ 6
  3. k = 0
  4. k ≠ 0

The number of prime numbers which are less than 100 is

  1. 24
  2. 25
  3. 26
  4. 27

The cost of a diamond varies directly as the square of its weight. A diamond broke into four pieces with their weights in the ratio of 1:2:3:4. If the loss in total value of the diamond was the ₹ 70,000, what was the price of the original diamond?

  1. ₹ 1,00,000
  2. ₹ 1,40,000
  3. ₹ 1,50,000
  4. ₹ 1,75,000

In a 100 m race, A runs at a speed of 5/3 m/s. If A gives a start of 4 m to B and still beats him by 12 seconds, what is the speed of B?

  1. 5/4 m/s
  2. 7/5 m/s
  3. 4/3 m/s
  4. 6/5 m/s

If 15 men take 21 days of 8 hours each to do a piece of work, then what is the number of days of 6 hours each that 21 women would take, if 3 women would do as much work as 2 men?

  1. 18
  2. 20
  3. 25
  4. 30

Leela got married 6 years ago. Today her age is 1¼ times her age at the time of her marriage. Her son’s age is 1/10 times her age. What is the present age of her son?

  1. 1 year
  2. 2 years
  3. 3 years
  4. 4 years

A and B working together can finish a piece of work in 12 days while B alone can finish it in 30 days. In how many days can A alone finish the work?

  1. 18 days
  2. 20 days
  3. 24 days
  4. 25 days

The values of x which satisfy the equation 51+x + 51–x = 26 are

  1. –1, 1
  2. 0, 1
  3. 1, 2
  4. –1, 0

If 5 men can do a piece of work in 10 days and 12 women can do the same work in 15 days, the number of days required to complete the work by 5 men and 6 women is

  1. 7½ days
  2. 8 days
  3. 9½ days
  4. 12 days

A passenger train departs from Delhi at 6 pm for Mumbai. At 9 pm, an express train, whose average speed exceeds that of the passenger train by 15 km/hour leaves Mumbai for Delhi. Two trains meet each other mid-route. At what time do they meet, given that the distance between the cities is 1080 km?

  1. 4 p.m.
  2. 2 a.m
  3. 12 midnight
  4. 6 a.m.

In a class of 49 students, the ratio of girls to boys is 4:3. If 4 girls leave the class, the ratio of girls to boys would be

  1. 11:7
  2. 8:7
  3. 6:5
  4. 9:8

If a + b = 5 and ab = 6, then what is the value of a3+ b3?

  1. 35
  2. 40
  3. 90
  4. 125

What is the LCM of x3 + 8, x2 + 5x + 6 and x3 + 4x2 + 4x?

  1. x (x + 2)2 (x + 3) (x2 - 2x + 4)
  2. x (x - 2)2 (x - 3) (x2 + 2x + 4)
  3. (x + 2)2 (x + 3) (x2 - 2x + 4)
  4. (x - 2)2 (x - 3) (x2 - 2x + 4)

Rajendra bought a mobile with 25% discount on the selling price. If the mobile cost him Rs. 4,875, what is the original selling price of the mobile?

  1. Rs. 6,300
  2. Rs. 6,400
  3. Rs. 6,500
  4. Rs. 6,600

A 225 m long train is running at a speed of 30 km/hour. How much time does it take to cross a man running at 3 km/hour in the same direction?

  1. 40 seconds
  2. 30 seconds
  3. 25 seconds
  4. 15 seconds

The difference between the simple and the compound interest on a certain sum of money at 4% per annum in 2 years is Rs. 10. What is the sum?

  1. Rs. 5,500
  2. Rs. 6,000
  3. Rs. 6,250
  4. Rs. 7,500

If a% of a + b% of b = 2% of ab, then what percent of a is b?

  1. 50%
  2. 75%
  3. 100%
  4. Cannot be determined

5/9 th part of the population in a village are males. If 30% of the males are married, the percentage of unmarried females in the total population is

  1. 20 2/9
  2. 27 2/9
  3. 27 7/9
  4. 29 2/9

Sunil wants to spend Rs.200 on two types of sweets, costing Rs.7 and Rs.10 respectively. What is the maximum number of sweets he can get so that no money is left over?

  1. 25
  2. 26
  3. 27
  4. 28

The HCF of two expressions p and q is 1. What is the reciprocal of their LCM?

  1. p + q
  2. p – q
  3. pq
  4. (pq)-1

A thief is spotted by a policeman from a distance of 100 m. When the policeman starts the chase, the thief also starts running. If the speed of the thief is 8 km/hour and that of the policeman is 10 km/hour, then how far will the thief have to run before he is overtaken?

  1. 200 m
  2. 300 m
  3. 400 m
  4. 500 m

Aman and Alok attempted to solve a quadratic equation. Aman made a mistake in writing down the constant term and ended up in roots (4, 3). Alok made a mistake in writing down the coefficient of x to get roots (3, 2). The correct roots of the equation are

  1. –4, –3
  2. 6, 1
  3. 4, 3
  4. –6, –1

The system of equations 2x + 4y = 6 and 4x + 8y = 8 is

  1. Consistent with a unique solution
  2. Consistent with infinitely many solutions
  3. Inconsistent
  4. None of the above

The ratio of two numbers is 1:5 and their product is 320. What is the difference between the squares of these two numbers?

  1. 1024
  2. 1256
  3. 1536
  4. 1640

25 kg of alloy X is mixed with 125 kg of alloy Y. If the amount of lead and tin in the alloy X is in the ratio 1:2 and the amount of lead and tin in the alloy Y is in the ratio 2:3, then what is the ratio of lead to tin in the mixture?

  1. 1:2
  2. 2:3
  3. 3:5
  4. 7:11

The mean of 5 numbers is 15. If one more number is included, the mean of the 6 numbers becomes 17. What is the included number?

  1. 24
  2. 25
  3. 26
  4. 27

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