Test: CAT Quantitative Aptitude- 6 - CAT MCQ

# Test: CAT Quantitative Aptitude- 6 - CAT MCQ

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## 22 Questions MCQ Test Quantitative Aptitude (Quant) - Test: CAT Quantitative Aptitude- 6

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Test: CAT Quantitative Aptitude- 6 - Question 1

### How many zeroes are there in 60!?

Detailed Solution for Test: CAT Quantitative Aptitude- 6 - Question 1

Number of zeros can be found by calculating highest power of 10 in the number.

As 10 = 2 x 5? so the number of zeros will be equal to the highest power of 5 in the number.

Highest power of 5 in 60! = (60 / 5) + (60 / 25) = 12 + 2 = 14 The number of zeros in 60! = 14 Answer: 14

Option 2

Test: CAT Quantitative Aptitude- 6 - Question 2

### Sum of the first 11 and 12 terms of an A.P. is 420 and 555 respectively. Fourth term of a G.P. (First term of the G.P. is 5) is equal to the 12th term of the A.P. What will be the common ratio of the G.P.?

Detailed Solution for Test: CAT Quantitative Aptitude- 6 - Question 2

12th term of an A.P. = Sum of first 12 terms - Sum of first 11 terms = 555 - 420= 135

4thterm of G.P. = 12th term of an A.P. =135

Let the first term and common ratio of G.P. be a and r.

4th term pf G.P. = ar3 = 135 .

∴ r = 135/5 = 27

∴ r = 3 Answer: 3

Option 3

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*Answer can only contain numeric values
Test: CAT Quantitative Aptitude- 6 - Question 3

### f(x) = 13x g(x) = |x| h(x) = x2 What is the sum of all possible values of x for which hog(x) + fog(x) = 30?

Detailed Solution for Test: CAT Quantitative Aptitude- 6 - Question 3

As per the given condition,
hog(x) + fog(x) = 30
x2 + 13|x| - 30 = 0
(For x > 0, |x| = x)
When x = +ve,
x2 + 13x - 30 = 0
(x + 15)(x - 2) = 0
x = 2, x = -15 (rejected as x > 0)
When x = -ve,
x2 - 13x - 30 = 0
(x + 2)(x - 15) = 0
x = -2, x = 15 (rejected because x < 0)
Sum = -2 + 2 = 0

Test: CAT Quantitative Aptitude- 6 - Question 4

Find the number of four digit numbers such that the number formed by tens place and ones place in that order is equal to the sum of the digits at hundreds and thousands place.

Detailed Solution for Test: CAT Quantitative Aptitude- 6 - Question 4

The digits at thousands place can be anything from 1 to 9 and the digit at hundreds place can be anything from 0 to 9.

The sum of the two digits will be either a single or double digit.

∴ The number of required numbers = 9 x 10 = 90

Hence, option 4.

Test: CAT Quantitative Aptitude- 6 - Question 5

Atul is standing at point P. P is 10 m away from a tree. Atul turns to his left and walks till point S. S is 5 m away from the tree. Baljit, who is facing the tree, also turns left from P through some angle and walks till point R. The angle traced by Baljit is twice of that by Atul. If R, S and the tree are along the same line, find the distance travelled by Baljit, if the distance between R and S is 3 m.

Detailed Solution for Test: CAT Quantitative Aptitude- 6 - Question 5

Let T be the position of tree.

m∠TPR = 2 x m∠TPS

∴ PS is the angle bisector.

∴  x = 6 meters

Hence, option 2.

Test: CAT Quantitative Aptitude- 6 - Question 6

A is standing on the foremost point of a train moving at 270 km/hr in a straight line. He starts moving in the direction opposite to that of the train at 3 m/s. At the same time B standing on the rearmost part of the train starts moving in the direction of the train at 4 m/s. A person standing outside notices that when A moves 1800 m, B is 2100 m away from A. Find the length of the train.

Detailed Solution for Test: CAT Quantitative Aptitude- 6 - Question 6

The speed of the train = 270 km/hr = 75 m/s The time after which the difference in position of A is 1800 m = 1800/(75 - 3) = 25 seconds Now, in these 25 seconds,

• A walks 25 x 3 = 75 m towards rearmost part of the train.
• B walks 25 x 4 = 100 m towards foremost point of the train.

At his stage, there is distance of 2100 m between them.

∴ The length of the train = 75 + 2100+100 = 2275 m

Hence, option 4.

Test: CAT Quantitative Aptitude- 6 - Question 7

Which of the following is the range of values of x?

1. -16 <x < 4

2. x > 6 orx < —16

3. 3 < x < 4

4. - 1 6 < x < 3 or 4 < x < 6

Detailed Solution for Test: CAT Quantitative Aptitude- 6 - Question 7

*Answer can only contain numeric values
Test: CAT Quantitative Aptitude- 6 - Question 8

The integers 5417 and 5223 when divided by a two digit number N leave the same remainder. N = _______

Detailed Solution for Test: CAT Quantitative Aptitude- 6 - Question 8

When two numbers divided by a common number N leave the same remainder, then their difference must be divisible by N.
Thus must be divisible by N.
194 = 97 x 2
Since N is of two digits, the number is 97.

Test: CAT Quantitative Aptitude- 6 - Question 9

A whole saler buys 100 watches from on estate at the rate of Rs.45.45 per watch and sells the mall in his own state for Rs 6817.5 He pays a certain percentage of the cost price as the tax. If he earns a total of 20% by selling the watches, then find the tax percentage levied over the purchased price.

Detailed Solution for Test: CAT Quantitative Aptitude- 6 - Question 9

Total purchase price = 45.45 x 100 = Rs. 4545 Let the tax paid be Rs. x

∴ (6817.5 - 4545 - x)/(4545 + x) = 0.2

∴ 2272.5 - x = 909 + 0.2x

∴ x = 1136.25
The tax percentage levied over cost price = (1136.25/4545) x 100 = 25%

Test: CAT Quantitative Aptitude- 6 - Question 10

What will be the remainder when 3136 is divided by 12 ?

Detailed Solution for Test: CAT Quantitative Aptitude- 6 - Question 10

When 31,32, 33 and 34 divided by 12 leaves remainder 3, 9, 3 and 9 respectively.

As the pattern repeats itself after 2 steps, 3 odd number leaves remainder 3 and 3even number leaves remainder 9.

∴ R em ainder of 3136 when divided by 12 = 9

Hence, option 3.

Test: CAT Quantitative Aptitude- 6 - Question 11

A bank pays 4.5% compound interest per month for a principal amount P.
The amount becomes Pm in m months. Which of the following options best represent the graph between Pm (y-axis) and m (x-axis) will be:

Detailed Solution for Test: CAT Quantitative Aptitude- 6 - Question 11

From the given conditions;

We can see that Pm increases exponentially as m increases.

Option 3 is the only possible answer.

Hence, option 3.

Test: CAT Quantitative Aptitude- 6 - Question 12

Let g(x +1) g(x - 1) = g(x). then for what integral values of p would we have g(x+p) = g(x)?

Detailed Solution for Test: CAT Quantitative Aptitude- 6 - Question 12

Let g(x) = a and g(x - 1 ) = b

Let x = x + 1

Similarly, g(x + 3) = l/a, g(x + 4) = bla, g(x + 5) = b, g(x + 6) = a .. .and so on.
∴ g(x + 6) = g(x)

*Answer can only contain numeric values
Test: CAT Quantitative Aptitude- 6 - Question 13

Let, x and y be positive real numbers such that log2(x2 - y2) - log2(x + y) = 1 and log3x + log3y = 1. Then the value of y is

Detailed Solution for Test: CAT Quantitative Aptitude- 6 - Question 13

log2(x2 - y2) - log2(x + y) = 1

x - y = 2 ....(1)
log3x + log3y = 1
log3(x . y) = 1
xy = 31 = 3
Put the value of x from equation (1) in (2):
(2 + y)y = 3
y2 + 2y - 3 = 0
y = 1, -3
y = -3 rejected
So, the value of y is 1.

Test: CAT Quantitative Aptitude- 6 - Question 14

A petrol distributor adulterates petrol with kerosene and naphthalene. There are two containers of different capacities which contain this adulterated petrol. Container 1 contains 30% petrol and container 2 contains 45% petrol. If both these mixtures are mixed in a larger container in such a ratio that kerosene in it is 25% and naphthalene is 40%. Find the capacity of container 2(in litre) if the capacity of container 1 is 8 litres.

Detailed Solution for Test: CAT Quantitative Aptitude- 6 - Question 14

The correct option is Option B.

Let the capacity of Container 1 be ‘a’ litres and that of Container 2 be ‘6’ litres.

∴ Petrol in container 1 = 0.3a

Petrol in container 2 = 0.456

Similarly, petrol in the new container = 0.35(a + b)

∴ 035 a + 0.45 b = 0.35(a + b)

∴ a = 2b

Since a = 8, b = 4.

Hence, the capacity of container 2 is 8 litres.

Test: CAT Quantitative Aptitude- 6 - Question 15

A square cuts the x m d y axes at (2, 0); (-2, 0) and (0, 2);(0, -2). I f the axes are rotated by 60° in anticlockwise direction, then find the ratio (smaller to larger) in which each side of the square will be divided into by any of the axes.

Detailed Solution for Test: CAT Quantitative Aptitude- 6 - Question 15

As shown in the figure the square PQRS cuts the axes at A(2,0), B(0,2), C (-2,0) and D(0, - 2).
When rotated by 60° the axes will cut the square at A', B', C' and D' respectively.

Hence, option 3.

*Answer can only contain numeric values
Test: CAT Quantitative Aptitude- 6 - Question 16

Oyo Cab service offers free ride to customers for a certain distance and then charges at a constant rate per kilometer. Biswas uses the cab to go to a nearby shopping complex and Amit goes to mall on the cab. The combined bill of Biswas and Amit amounts to Rs. 110. If the distance covered by Biswas on the cab had doubled, he would have paid Rs. 200 as charges to the cab driver, whereas in case of Amit, if the distance had doubled the charges would have been 50% less than the charges paid by Biswas in case of increased distance. What would be the amount paid by Biswas, if he travelled thrice the distance travelled by him initially?

Detailed Solution for Test: CAT Quantitative Aptitude- 6 - Question 16

Let free cab service is for a fixed distance for z km.
Let per kilometer charge = Rs. y
Let the distance covered by Biswas and Amit is 'a' km and 'b' km, respectively.
So,
(a + b - 2z )y = 110 ...(1)
(2a - z)y = 200 …(2)
(2b - z )y = 100 …(3)
(3) + (2) - (1)
We get
(a + b) y = 190
Also, if we add (1) and (3)
(a + b - z ) y = 150 ..(4)
Simplifying (1) and (4), we get
19z = 4a + 4b.. (5)
Also,
2a - 4b = - z …(6)
From (1) and (4)zy = 40
Also,
a = 3z
Biswas initially paid (3a - z)y, if he travelled thrice the distance travelled initially by him which is 8zy = Rs. 320

Test: CAT Quantitative Aptitude- 6 - Question 17

The average age of a village X at the start of the year 2008 is 30 years. Every year starting from 2009, migrants - amounting to 20% of the population of village X in 2008 - move to village X. The average age at entry, for every batch of migrants is 5 years less than that of the village X at the start of 2008. Find the average age of the village X just after the third batch of migrants enter it.

Detailed Solution for Test: CAT Quantitative Aptitude- 6 - Question 17

Let the current population of the village be x.

The population of the village just after the third batch of migrants entre village X = x + 3(0.2x) = 1.6x

The total sum of the ages of the migrants just after the third batch of migrants entre village X = 0.2x x 27 + 0.2x x 26 + 0.2x x 25 = 15.6x

The average age of the village after 3 years = (33x + 15.6x )/1.6x = 30.375 years

Hence, option 4.

Test: CAT Quantitative Aptitude- 6 - Question 18

Roshan has three daughters Riya, Piya and Siya. He divides 21 chocolates among them such that for every chocolate Riya receives, Siya receives 3 chocolates and for every chocolate that Piya receives, Riya receives 5 chocolates. How many chocolates did Siya get?

Detailed Solution for Test: CAT Quantitative Aptitude- 6 - Question 18

The correct option is Option D.

The number of chocolates received by Siya is multiple of 3.

Among the given options, only 15 is multiple of 3.

So, Siya gets 15 chocolates.

*Answer can only contain numeric values
Test: CAT Quantitative Aptitude- 6 - Question 19

Find the sum of the digits in the expanded product 199,999,997 × 200,000,003.

Detailed Solution for Test: CAT Quantitative Aptitude- 6 - Question 19

Let x = 200,000,000
Then, the factors become (x – 3)(x + 3) = x2 – 9.
So, the product is 40,000,000,000,000,000 – 9 = 39,999,999,999,999,991, whose digit sum is 3 + 15(9) + 1 = 139.

*Answer can only contain numeric values
Test: CAT Quantitative Aptitude- 6 - Question 20

In a computer network, there are 36 identical files to be distributed among 5 users. However, each user receives a number of files in multiples of three. How many ways are there to distribute the files under these conditions?

Detailed Solution for Test: CAT Quantitative Aptitude- 6 - Question 20

Since each user receive files in multiple of three, let us assume that they receive 3a, 3b, 3c, 3d and 3e number of files, respectively, where a, b, c, d and e are natural numbers.
Therefore, 3a + 3b + 3c + 3d + 3e = 36
a + b + c + d + e = 12
So, we have to find in how many ways the sum of five numbers can be 12.
Therefore, number of ways in which the sum of five numbers is equal to 12 = (12 - 1)C(5 - 1) = 330

*Answer can only contain numeric values
Test: CAT Quantitative Aptitude- 6 - Question 21

In a construction project, a group of N workers worked together to complete a building. They finished 70% of the construction in 20 days by working 8 hours a day. However, due to unforeseen circumstances, 15 workers had to leave the project. The remaining workers completed the remaining 30% of the construction in 10 days by working 12 hours a day. If the total work required for the project is considered one unit, key in the value of N?

Detailed Solution for Test: CAT Quantitative Aptitude- 6 - Question 21

Let the unit of work done by 1 man in 1 hour and 1 day be 1 MDH unit (Man, Day, Hour).
According to question,
Work done by N workers working 8 hours per day in 20 days = N × 8 × 20 MDH units.
Since this work is equal to 70% of the total work,
i.e. 70% of the total work = 160N MDH units
Therefore, total work =
So, remaining 30% of the total work =
This work is completed by (N - 15) workers working 12 hours in 10 days = (N - 15) (10)(12) = 120(N - 15)

So,

So, N = 35

*Answer can only contain numeric values
Test: CAT Quantitative Aptitude- 6 - Question 22

Bus A left station S1 at 11 am for station S2. Another bus B having speed 75% of speed of A, left station S2 for station S1 at 12 pm. Two buses met each other at station S3, where the distance between S1 and S3 is 60% of that between S1 and S2. Find the time taken (in hours) by bus A for its journey from S1 to S2

Detailed Solution for Test: CAT Quantitative Aptitude- 6 - Question 22

Given: Speed of bus B = 75% of speed of A = 3/4 of speed of A
i.e. Ratio of speeds of A and B = 4 : 3
Let their speeds be 4V and 3V.

Also, the distance between S1 and S3 is 60% of that between S1 and S2.
i.e. S1S3 = 60/100 of S1S2 = 3/5 of S1S2
So, S1S3 = 3d, S2S3 = 2d and S1S= 5d

Now, time taken by bus A to reach S3 = 3d/4v hours ---(1)
Time taken by bus B to reach S3 = 2d/3v hours ---(2)

We need to find the time taken by A to travel from S1 to S2, i.e. 5d/4v.

Now, bus B started one hour later than bus A.

i.e. The time taken by bus A to reach S3 is one hour more than the time taken by bus B to reach S3.
i.e.

Let d/v = k

=> k = 12

So,  hours

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## Quantitative Aptitude (Quant)

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