Built with
Offline Website Creator MOCK TEST - 2 - Quantitative Ability (QA Section)
Quantitative Ability is one of the section of CAT exam along with Data Interpretation and Logical Reasoning and Verbal Ability and Reading comprehension. Practice tests or Mock tests help aspirants to prepare for the exams.
Quantitative Ability is the ability of a person to make empirical enquiries through numerical data gathering and analysis by performing mathematical or statistical computations.
Maximum Time for this section: 40 : 00 (Minutes : Seconds)
Total number of Questions: 66
Total number of MCQ's Questions: 45
Total Number of Non-MCQ's (TITA) Questions: 21
Total number Quantitative Ability (QA) Questions: 22
Total number Quantitative Ability (QA) MCQ's Questions: 14
Total number Quantitative Ability (QA) non-MCQ's (TITA) Questions: 08
Total number Data Interpretation and Logical Reasoning (DILR) Questions: 20
Total number Data Interpretation and Logical Reasoning (DILR) MCQ's Questions: 15
Total number Data Interpretation and Logical Reasoning (DILR) non-MCQ's (TITA) Questions: 05
Total number Verbal Ability & Reading Comprehension (VARC) Questions: 24
Total number Verbal Ability & Reading Comprehension (VARC) MCQ's Questions: 16
Total number Verbal Ability & Reading Comprehension (VARC) non-MCQ's (TITA) Questions: 08
Maximum Time: 40 : 00 (Minutes : Seconds) per section
Note-1: Use of simple calculator is allowed.
Note-2: Not allowed to change section once selected.
If 73% of the Americans like cheese and 84% like apples. Find the range of x% Americans who like both cheese and apples?
Options:
Option (a): 0% <= x <= 22%.
Option (b): 0% <= x <= 28%.
Option (c): 24% <= x <= 57%.
Option (d): 57% <= x <= 73%.
Maximum will be the lower of 73 and 84 = 73%.
To obtain the minimum value, we will use the formula for two sets:
(Apples Cheese)min = Apples + Cheese – (Apples Cheese)max = 73 + 84 – 100 = 57%.
Hence option (d) is the answer.
The present age of a father is 11 times his son's age. In 7 - years time his age will be four times his son's age. In how many years will the father be twice as old as his son.
Options:
Option (a): 27 Years
Option (b): 22 Years
Option (c): 25 Years
Option (d): None of these.
Let the present ages of the father and son be x-years and y-years respectively.
We now have,
x = 11y ----(1)
x + 7 = 4(y + 7) = x - 4y = 21 ----(2)
Solving (1) and (2) we get x = 33 and y = 3.
Let father's age be twice the son's age in 'p' years.
Then we have
33 + p = 2(p + 3) => p = 27.
So, in 27 years the father will be twice as old as his son.
Option (a).
What is the remainder when 4^73 + 3^73 is divided by 7?
aⁿ + bⁿ is divisible by a + b if n is odd. Based on this property the correct answer is 0.
If you divide the sum 2100 into four parts such that four times the first part, three times the second part. twice the third part are each equal to twelve times the fourth part. What is the fourth part?
Options:
Option (a): 84
Option (b): 100
Option (c): 184
Option (d): 44
Let a, b, c and d be the four parts, then we have
4a = 3b = 2c = 12d ---(1)
4a + 3b + 2c + 12d = 2100
3d + 4d + 6d + 12d = 2100
=> 25d = 2100
Therefore, d = 84.
From this we can calculate the value of a, b, c and d as
252,
336,
504,
and 84 respectively.
Option (a)
A swimming pool 100 m long and 40 m wide is 1 meter deep for the first 5 meters of shallow end and 5 m at the deep end. Find the volume of water contained in the pool?
Options:
Option (a): 11360 cubic meters
Option (b): 11760 cubic meters
Option (c): 11600 cubic meters
Option (d): 11500 cubic meters
Area of cross section perpendicular to width
=½ (95) (1 + 5) = 285 sq.m.
Volume = (area of cross section x width) + (area of first 4 m)
= (285 x 40) + (40 x 5 x 1)
= 11400 + (40 x 5 x 1) = 11,600.
A five-rupee note measures 10 cm x 5 cm and a bundle of such five rupee notes 100 notes is 1 cm thick. What is the value of the five rupee notes contained in a box of size 30 cm x 15 cm x 4 cm, if the bundles are tight packed in the box without any empty space?
Options:
Option (a): ₹ 18,000.00/-
Option (b): ₹ 17,500.00/-
Option (c): ₹ 19,000.00/-
Option (d): ₹ 16,500.00/-
Volume of the box = 30 x 15 x 4.
Volume of one bundle of ₹ 5 notes = 10 x 5 x 1.
Number of bundle in the box = (30 x 15 x 4)/(10 x 5 x 1) = 36.
Since each bundle is of value ₹ 500.
the total amount in the box is = 36 x 500 = ₹ 18,000.00/-
The total number of digits in the product of 5^44 and 16^11 is?
Options:
Option (a): 44.
Option (b): 45.
Option (c): 46.
Option (d): 47.
The number of digits in the product of 5^44 and 16^11 is
5^44, (2^4)11
= (5x2)^44
= 10^44
= 44 + 2 = 46
A school consisting of 276 students in class V, 184 students in class VI, 230 students in class VII. The Head Mistress being a mathematician herself wants to divide the students into sections in such a way that there are an equal number of students in all the sections. Find is the minimum number of sections would be needed in order to achieve this objective and the number of students in each sections that ?
HCF of 184, 230 and 276 = 46.
Thus, the minimum number of sections is
184/46 + 230/46 + 276/46 = 4 + 5 + 6
= 15 sections with 46 students each.
Pipe A can fill a tank in 16 minutes; Pipe B in 24 minutes and Pipe C can empty a tank in 48 minutes. If all of them work together, find the time taken to fill the empty tank?
Options:
Option (a): 14 minutes
Option (b): 12 minutes
Option (c): 16 minutes
Option (d): 18 minutes
Work done by the 3 pipes together in 1 minute
= (1/16) + (1/24) - (1/48)
= 4/48
= 1/12.
So, the empty tank will be filled in 12 minutes.
An employee reaches his office 25 minutes late by walking at 5 km/h from his house. The next day he increases his speed by another 5 km/h and reaches on time. Find the distance from his house to his office?
Options:
Option (a): approx 5.167 km
Option (b): approx 4.167 km
Option (c): approx 6.167 km
Option (d): approx 7.167 km
Let the distance be x.
Then, time taken on the 1st day = x/5.
Time taken 2nd day = x/10.
We are given, x/5 - x/10 = 25/60
=> x = (25 x 10)/60
= approx 4.167 km
Raju and Madhu were doing separate business but shared money between them when required. If Raju were to give $500.00/- of his money to Madhu, Madhu would have three times as much money as Raju. But if Madhu were to give $400.00/- of his money to Raju instead, Raju would then have $100.00/- less than Madhu had before they traded. How much money does Raju have to begin with?
Let the amount with Raju and Madhu started with be 'r' and 'm' respectively.
As per the given conditions in the question
3(r - 500) = m + 500,
and r + 400 = m - 100.
Solving the above two equations we get
m = $1750.00/- and r = $1,250.00/-.
Directions for questions 12 to 16: These questions are based on the following data.
a → b = a^2/b
a ← b = (2 x a)/b
a ↑ b = (2a + b)^2 + (2a - b)^2
a ↓ b = (2a + b)^2 - (2a - b)^2
a ⇿ b = (2a + b) (2a - b)
The value of the expression [{(3/2 → 3) ← 1/4} ↓ 5] ⇿ 7 is ______
Step 1: (3/2 → 3) = ³/₄
Step 2: (3/4 ← 1/4) = 6
Step 3: (6 ↓ 5) = 240
Step 4: (240 ⇿ 7) = 2,30,351
Directions for questions 12 to 16: These questions are based on the following data.
a → b = a^2/b
a ← b = (2 x a)/b
a ↑ b = (2a + b)^2 + (2a - b)^2
a ↓ b = (2a + b)^2 - (2a - b)^2
a ⇿ b = (2a + b) (2a - b)
The value of the expression [{(4 → 8) ↑ 6} ↓ 3] ← 4 is ______
Step 1: (4 → 8) = 2
Step 2: (2 ↑ 6) = 104
Step 3: (104 ↓ 3) = 2496
Step 4: (2496 ← 4) = 1,248
Directions for questions 12 to 16: These questions are based on the following data.
a → b = a^2/b
a ← b = (2 x a)/b
a ↑ b = (2a + b)^2 + (2a - b)^2
a ↓ b = (2a + b)^2 - (2a - b)^2
a ⇿ b = (2a + b) (2a - b)
Which of the following statement is true for all positive values of a and b?
Options:
Option (a): a → b is always greater than a ← b.
Option (b): a ↓ b is always lesser than a ⇿ b.
Option (c): a ↑ b is always greater than a ⇿ b.
Option (d): None of the above.
Option (c): a ↑ b is always greater than a ⇿ b.
Directions for questions 12 to 16: These questions are based on the following data.
a → b = a^2/b
a ← b = (2 x a)/b
a ↑ b = (2a + b)^2 + (2a - b)^2
a ↓ b = (2a + b)^2 - (2a - b)^2
a ⇿ b = (2a + b) (2a - b)
c = b/a^2
d = b/(2 x a)
Which of the following is always true ?
Options:
Option (a): (a ← b) is always completely divisible by c but not d.
Option (b): (a ⇿ b) is always completely divisible by both c and d.
Option (c): (a ↑ b) (a ↓ b) is always completely divisible by c but not d.
Option (d): (a ↑ b) (a ↓ b) is always completely divisible by both c and d.
Option (a): (a ← b) is always completely divisible by c but not d.
Directions for questions 12 to 16: These questions are based on the following data.
a → b = a^2/b
a ← b = (2 x a)/b
a ↑ b = (2a + b)^2 + (2a - b)^2
a ↓ b = (2a + b)^2 - (2a - b)^2
a ⇿ b = (2a + b) (2a - b)
Which of the following statement is true?
Options:
Option (a): a = 6, b = 3 then a → b is 12.
Option (b): a = 5, b = 2 then a ← b is 10.
Option (c): a = 11, b = 7 then a ↑ b is 113.
Option (d): a = 15, b = 8 then a ↓ b is 2022.
Option (a): a = 6, b = 3 then a → b is 12.
(- 1/64)^(-2/3) = ?
(- 1/64)^(-2/3)
=(-(1/2)⁶)^(-2/3)
=-(½)⁻⁴
=-¹/(½)⁴
= -¹/(¹/₁₆)
= 16
If the ages of n siblings of a family are integers that form an arithmetic progression with a common difference of d and has a sum of 200 years, which of the following is a possible value of n and d?
Options:
Option (a): 4, 7
Option (b): 5, 4
Option (c): 9, 7
Option (d): 14, 1
Consider, Option (a): 4, 7
Sn = n/2[2a + (n − 1) × d]
200 = 4/2[2a + (4 - 1) x 7]
200 = 2[2a + 3 x 7]
200 = 4a + 21
179 = 4a
179/4 = a - not an integer.
4, 7 doesn't satisfies the condition.
Consider, Option (b): 5, 4
Sn = n/2[2a + (n − 1) × d]
200 = 5/2[2a + (5 - 1) x 4]
200 = 5/2[2a + 4 x 4]
200 = 5/2 [2a + 16]
400 = 10a + 80
400 - 80 = 10a
a = 320/10 = 32
5, 4 satisfies the condition.
Consider, Option (c): 9, 7
Sn = n/2[2a + (n − 1) × d]
200 = 7/2[2a + (9 - 1) x 4]
400 = 7[2a + 8 x 4]
400 = 7[2a + 32]
400 = 14a + 224
400 - 224 = 14a
a = 176/14 = 12.57 - not an integer.
5, 4 satisfies the condition.
Consider, Option (d): 14, 1
Sn = n/2[2a + (n − 1) × d]
200 = 14/2[2a + (14 - 1) x 1]
400 = 14[2a + 13]
400 = [28a + 182]
400 - 182 = 28a
218 = 28a
a = 218/28 = 7.786 - not an integer.
14, 1 satisfies the condition.
If 0 < p < 1, which of the following has the least value?
Options:
Option (a): 1/(p^2 + 1)
Option (b): 1/sqrt(p)
Option (c): 1/p^2
Option (d): 1/(p + 1)^2
Option (c): 1/p^2
There are 4 tanks P, Q, R and S in a dairy. Each tank has 1200 liters of milk. Milk is pumped from one tank to another as shown below:
From P to Q @ 30 lts/min
From R to P @ 80 lts/min
From P to S @ 20 lts/min
From R to S @ 60 lts/min
From Q to R @ 100 lts/min
From S to Q @ 110 lts/min.
Which tank gets emptied first and how long would it take to get emptied after pumping starts (in min)?
Options:
Option (a): P, 40.
Option (b): Q, 60.
Option (c): R, 30.
Option (d): R, 40.
P = -30 + 80 - 20 = 30
Q = +30 - 100 +110 = 40
R = -80 -60 + 100 = - 40 => 1200 - 40n => n = 30
S = + 20 + 60 - 110 = - 30
Option (c): R, 30.
Two people A and B leave a point at the same time. Person A travels South at a speed of 32 km/hr and person B travels towards East at a speed of 24 km/hr. What is the distance between them after 2 hrs.
Let the staring point be named as O. After 2 hrs, person A will be at point X (say) travelling towards South, which will be 2 x 32 = 64 km from point O.
Person B travels East and reach point Y (say), which will be 2 x 24 = 48 km from O in the perpendicular direction to OX (Direction South and East being the reason).
Using Pythagoras theorem, we can find the third side XY (Distance between A and B) as
√(64² + 48²) = 80 km.
Hence A and B will be 80 km from each other.
If S = ((1/n) + 1)^n where n = 2. Find S.
(½ + 1)² = (³/₂)² = 2.25
Page updated in: December 2022
Built with
Offline Website Creator