Made with
Offline Website Builder MOCK TEST - 5 - 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: 68
Total number of MCQ's Questions: 52
Total Number of Non-MCQ's (TITA) Questions: 18
Total number Quantitative Ability (QA) Questions: 23
Total number Quantitative Ability (QA) MCQ's Questions: 15
Total number Quantitative Ability (QA) non-MCQ's (TITA) Questions: 08
Total number Data Interpretation and Logical Reasoning (DILR) Questions: 21
Total number Data Interpretation and Logical Reasoning (DILR) MCQ's Questions: 16
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: 19
Total number Verbal Ability & Reading Comprehension (VARC) non-MCQ's (TITA) Questions: 05
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.
Directions for questions 1 to 5: These questions are based on the following data.
a + b = 15ab
a - b = 4a/5b
a x b = 7a + 3b
a/b = 3a - 2b
1. The expression [ { (9/2) - 6 } x 4 + 3 ] = ______
Step 1: (9/2) = (3 x 9) - (2 x 2) = 23
Step 2: (23 - 6) = (23 x 4) / (6 x 5) = 3.067
Step 3: (3.067 x 4) = (3.067 x 7) + (4 x 3) = 33.467
Step 4: (33.467 + 3) = 33.467 x 15 x 3 = 1506
Directions for questions 1 to 5: These questions are based on the following data.
a + b = 15ab
a - b = 4a/5b
a x b = 7a + 3b
a/b = 3a - 2b
2. Which of the following is a multiple of 19
Options:
Option a: [{(5 + 6) - 2} / 4]
Option b: [(5 x 6) - 2 + 4]
Option c: [{(5 + 2) - 6} x 4]
Option d: Both, Option a and Option c
Both, Option a and Option c
Directions for questions 1 to 5: These questions are based on the following data.
a + b = 15ab
a - b = 4a/5b
a x b = 7a + 3b
a/b = 3a - 2b
3. The expression [ { (7 x 9) / 11 } - 13 ] = ______
Step 1: (7 x 9) = (7 x 7) + (9 x 3) = 76
Step 2: 76 / 11 = (76 x 3) - (11 x 2) = 206
Step 3: (206 - 13) = (206 x 4) / (13 x 5) = 12.677
Directions for questions 1 to 5: These questions are based on the following data.
a + b = 15ab
a - b = 4a/5b
a x b = 7a + 3b
a/b = 3a - 2b
4. Which of the following is a perfect square?
Options:
Option a: [(10 - 8 x 16) / 4]
Option b: [(10 x 8 - 4) / 16]
Option c: [(10 + 8) - 4) / 22]
Option d: [(10 - 22) x 8) / 4]
[(10 + 8) - 4) / 22]
Directions for questions 1 to 5: These questions are based on the following data.
a + b = 15ab
a - b = 4a/5b
a x b = 7a + 3b
a/b = 3a - 2b
5. The expression [ √(13 x 10) + √(25 / 13) ] = ______.
Step 1: √(13 x 10) = (7 x 13) + (10 x 3) = √121 = 11
Step 2: √(25 / 13) = (25 x 3) - (13 x 2) = √49 = 7
Step 3: (11 + 7) = (15 x 11 x 7) = 1155
Directions for questions 6 to 8: Each item is followed by two statements A and B. Choose the correct data sufficiency option:
6. is x < y?
Statement A: (x - y) (x + y) = o
Statement B: y > 0
Options:
Option a: The question can be answered by one of the statements alone and not by the other:
Option b: The question can be answered by using either statement alone:
Option c: The question can be answered by using both the statements together, but cannot be answered using either statement alone:
Option d: The question cannot be answered even by using both the statements together:
The question can be answered by using both the statements together, but cannot be answered using either statement alone.
Directions for questions 6 to 8: Each item is followed by two statements A and B. Choose the correct data sufficiency option:
7. 50% of the people in a certain city have a Personal Computer and an Air Conditioner. What percent of people in the city have a personal computer but not an Air-Conditioner?
Statement A: 60% of the people in the city have a Personal Computer.
Statement B: 70% of the people in the city have an Air-Conditioner.
Options:
Option a: The question can be answered by one of the statements alone and not by the other:
Option b: The question can be answered by using either statement alone:
Option c: The question can be answered by using both the statements together, but cannot be answered using either statement alone:
Option d: The question cannot be answered even by using both the statements together:
The question can be answered by using either statement alone:
Directions for questions 6 to 8: Each item is followed by two statements A and B. Choose the correct data sufficiency option:
8. What is the value of x?
Statement A: x is a positive integer.
Statement B: x³ = 216.
Options:
Option a: The question can be answered by one of the statements alone and not by the other:
Option b: The question can be answered by using either statement alone:
Option c: The question can be answered by using both the statements together, but cannot be answered using either statement alone:
Option d: The question cannot be answered even by using both the statements together:
The question can be answered by one of the statements alone (Statement B: x³ = 216.) and not by the other.
Find the length of the bridge, which a train 160 m long travelling at 64 kmph can crosses in 45 seconds.
Speed of the train = 64 kmph
= 64 x ⁵/₁₈ = 20 m/sec.
Distance covered in 45 seconds = 20 x 45 = 900 m
Length of the bridge = 900 - 160 = 740 m.
In how many ways can 8 different envelopes be posted into 4 different letters boxes?
Options:
Option a: 8⁴
Option b: 4⁸
Option c: 32
Option d: ⁹C₄ x 4!
4⁸
Number of distinct terms in the expansion of
(a + b + c)²⁰ is ________.
Options:
Option a: 231
Option b: 253
Option c: 242
Option d: 210
²²C₂ = 231
A shop stores x kg of rice. The first customer buys half this amount plus half a kg of rice. The second customer buys half the remaining amount plus half kg of rice. Then the third customer also buys half the remaining amount plus half a kg of rice. Thereafter, no rice is left in the shop. Which of the following best describes the value of x?
Options:
Option a: 2 ≤ x ≤ 6
Option b: 5≤ x ≤ 8
Option c: 9 ≤ x ≤ 12
Option d: 11 ≤ x ≤ 14
5≤ x ≤ 8
Two pipes A and B can fill a tank in 30 and 15 minutes respectively. There is an outlet C. If all the 3 pipes are opened, the tank will be filled in 20 minutes. How much time will it take for C alone to empty the full tank.
LCM of 30, 15 and 20= 60
60 / 30 = 2
60 / 15 = 4
60 / 20 = 3
2 + 4 - 3 => 60/3 = 20 min.
The maximum possible value of x² + 3y² + 9z², subject to x + 2y + 3z = 12, where x, y and z are 3 different positive integers.
Options:
Option a: 45
Option b: 55
Option c: 65
Option d: None of these.
x² + 3y² + 9z² is maximum when,
z = 2, y = 1 and x = 4 also satisfies x + 2y + 3z = 12.
16 + 3 + 36 = 55
An aluminum sheet of side 12 inches on all sides is converted into a box with an opening on one of its side. Steps involved in the making are as follows -
The sheet is placed on a table and four equal sized squares each of size x inches are marked on the corners. This is then cut to remove, resulting sheet is bet vertically upwards to for a box.
If x is a positive integer, what is the value of x that maximizes the volume of the box.
Options:
Option a: 1
Option b: 2
Option c: 3
Option d: 4
Consider Option a: 1,
The volume of the box will be
10 x 10 x 1 = 100 cubic inches
Consider Option b: 2,
The volume of the box will be
8 x 8 x 2 = 128 cubic inches
Consider Option c: 3,
The volume of the box will be
6 x 6 x 3 = 108 cubic inches
Consider Option d: 4,
The volume of the box will be
4 x 4 x 4 = 64 cubic inches
Option b: 2, maximizes the volume of the box.
The largest four digit number which when divided by 5 and 8 gives remainders of 3 and 6 respectively is _____.
The difference between the divisor and the remainder is 2 in each case.
LCM of 5 and 8 is 40.
By finding the largest four digit multiple of 40 and subtract 2 from it we get,
9960 - 2 = 9958.
The students in a class take either English course or Maths or Both. 24 boys take English and 27 girls take mathematics. 21 girls English and 33 boys only take mathematics. 2 girls take both subjects. How many student are there in the class?
Options:
Option a: 100
Option b: 97
Option c: 103
Option d: indeterminate
103 (46 girls (Hint: use Venn Diagram.), 57 boys. )
How many integers, between 999 and 5000 (both numbers excluded) can be formed only using the digits 0, 1, 2, 3, and 4, if repetition of digits is allowed?
Options:
Option a: 375
Option b: 450
Option c: 501
Option d: 500
500 (Starting with 1 - 125, with 2 - 125, with 3 - 125, with 4 - 125)
If an athlete has to run 3000 m around a circular path of circumference 400 m. Then the angle covered by the athlete in radians is _____.
The athlete makes ³°°°/₄₀₀ = 7 ¹/₂ rounds of the circular path.
1 round = 2π radians.
Therefore, 7 ¹/₂ rounds = 7¹/₂ x 2π radians
¹⁵/₂ x 2π radians = 15π radians
The railway's half ticket cost is half of the full fare and the reservation charge is the same on a half ticket as on a full ticket. A person reserved one full ticket from Hyderabad to Bangalore and paid ₹ 1440. Another person reserved one full and a half ticket between the same destination and paid ₹ 2280. What is the reservation charge?
Options:
Option a: ₹ 240
Option b: ₹ 220
Option c: ₹ 490
Option d: ₹ 480
Let the cost be full fare be f.
Let the cost be reservation charge be r.
Let the cost be full fare and the reservation charge from Hyderabad to Bangalore be a = f + r .
Let the cost be half fare and the reservation charge from Hyderabad to Bangalore be b = f/2 + r.
Let the cost be full fare and the reservation charge from Hyderabad to Bangalore be a = f + r = 1440 ------------ (i).
Let the cost be half fare and the reservation charge from Hyderabad to Bangalore be b = f/2 + r.
Let the cost be half fare & the reservation charge along with full fare & the reservation charge from Hyderabad to Bangalore be c = a + b
c = f + r + f/2 + r = 2280.
c = f + f/2 + 2r = 2280.
c = (3f + 4r) / 2 = 2280.
c = 3f + 4r = 4560 ------------ (ii).
multiply equation (i) by 3,
f + r = 1440 x 3
3f + 3 r = 4320 ------- (iii)
(ii) - (iii) = r = 240
Option a: ₹ 240
Find the maximum value of f(x) = 17 - |9 + x|; x ∈ R.
f(x) = 17 - |9 + x| is maximum when |9 + x| is minimum. As the minimum value of |9 + x| is 0, the maximum value of f(x) is 17.
If the speed of cyclist raiding along with the wind is two third of his speed against the wind. Then what is the ratio of the speed of man to that of wind?
Options:
Option a: 5 : 4
Option b: 5 : 1
Option c: 20 : 1
Option d: 4 : 1
Speed along with the wind = a
Speed against the wind = (2/3)a
speed of man = x =1/2(a + (2/3)a) = 5a/6
speed of wind = y = 1/2( a - (2/3)a)= a/6
ratio of the speed of man to that of wind = x : y = 5a/6 : a/6
ratio of the speed of man to that of wind = 5 : 1
When three dice are thrown simultaneously, what is the probability that the first die shows up a prime number, second die shows up a even number and third die shows up an even prime number?
Let,
A: The event of the first die showing up a prime number.
i.e., 2, 3 and 5.
B: The event of the second die showing up an even number.
i.e., 2, 4 and 6.
C: The event of the second die showing up an even prime number.
i.e., 2.
Their respective probability are
P(A) = ¹/₂
P(B) = ¹/₂
P(C) = ¹/₆
Hence the required probability is
= ¹/₂ x ¹/₂ x ¹/₆ = ¹/₆₄
Page updated in: December 2022
Made with
Offline Website Builder