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MBA CAT 2022
193

Answer:

The main idea of the given paragraph is that driven by ambition and fear, developing countries are becoming leaders in innovation and are highly competitive both domestically and globally. Option C touches upon all key ideas of the paragraph.
Option A states that developing countries have invented new business models solely to remain competitive domestically. This is incorrect.
Option B is true but is not as comprehensive a summary as option C.
Option D states that production and distribution models are going through innovations ‘worldwide’. The paragraph given only talks about developing countries innovating and transforming.

The answer is 'Competition has driven emerging economies, once suppliers of cheap labour, to become innovators of business models that have enabled them to move up the value chain and go global.'

Choice C is the correct answer.

194

CAT 2021 VA RC Question:

The passage given below is followed by four alternate summaries. Choose the option that best captures the essence of the passage.

Foreign peacekeepers often exist in a bubble in the poor countries in which they are deployed; they live in posh compounds, drive fancy vehicles, and distance themselves from locals. This may be partially justified as they are outsiders, living in constant fear, performing a job that is emotionally draining. But they are often despised by the locals, and many would like them to leave. A better solution would be bottom-up peacebuilding, which would involve their spending more time working with communities, understanding their grievances and earning their trust, rather than only meeting government officials.

A. The environment in poor countries has tended to make foreign peacekeeping forces live in enclaves, but it is time to change this scenario.
B. Peacekeeping duties would be more effectively performed by local residents given their better understanding, knowledge and rapport with their own communities.
C. Peacekeeping forces in foreign countries have tended to be aloof for valid reasons but would be more effective if they worked more closely with local communities.
D. Extravagant lifestyles and an aloof attitude among the foreigners working as peacekeepers in poor countries have justifiably make them the target of local anger.

195

Answer:

The paragraph given states that while foreign peacekeepers, due to some valid reasons, tend to live in a bubble in the poor countries where they are deployed, a bottom-up peacebuilding approach working in concert with the locals would be more effective. Option C summarises the paragraph well.
Option A does not touch upon the idea of bottom-up peace building. So, it is incorrect.
The paragraph does not say locals would be better at peacekeeping; B is incorrect.
The paragraph also does not say local anger against foreign peacekeepers makes them ‘the target of local anger’. Option D is also incorrect.

The answer is 'Peacekeeping forces in foreign countries have tended to be aloof for valid reasons but would be more effective if they worked more closely with local communities.'

Choice C is the correct answer.

196

CAT 2020 Quant Question: Number Theory

Q. 1. How many 3-digit numbers are there, for which the product of their digits is more than 2 but less than 7?

197

Answer:

Let the digits of the 3-digit number be p, q, & r.
2 < p × q × r < 7
Therefore, p × q × r can take the values 3, 4, 5, or 6.

Let’s start with prime numbers 3 & 5.
Since they are prime, they can’t be splitted, and hence if one of p,q or r is 3, the remaining two should be 1.

So, the possible combinations are
1, 1, 3
1, 3, 1
3, 1, 1
1, 1, 5
1, 5, 1
5, 1, 1

4 can be splitted as 2 × 2. Therefore, the possible combinations of p, q, r are
1, 1, 4
1, 4, 1
4, 1, 1
1, 2, 2
2, 1, 2
2, 2, 1
6 can be split as 3 × 2. Therefore, the possible combinations of p, q, r are
1, 1, 6
1, 6, 1
6, 1, 1

1, 2, 3 will also yield a product of 6. We can 3! = 6 combinations of p, q, r with 1, 2, 3
1, 2, 3
1, 3, 2
2, 1, 3
2, 3, 1
3, 1, 2
3, 2, 1

Therefore, the total number of possibilities are 3 + 3 + 3 + 3 + 3 + 6 = 21

Hence, the answer is, "21"

198

CAT 2020 Quant Question:

Q. 2. If f(5 + x) = f(5 - x) for every real x and f(x) = 0 has four distinct real roots, then the sum of the roots is

A. 0
B. 40
C. 10
D. 20

199

Answer:

Given f (5 + x) = f (5 – x)
When x = 1, f(6) = f(4)
When x = 2, f(7) = f(3)
Imagine a graph and while joining (6,4) and (7,3) it looks symmetrical about 5
Given 4 distinct real roots. Assume 12 as one of the roots.
f(12) = 0 → Then f(5 + 7) = 0 which is same as f(5 – 7) = f(-2) = 0
So the roots are in the form (5 + k) and (5 – k) {This is one pair}
Sum of the roots = 5 + k + 5 – k = 10
We have 4 roots, So two pairs =10 + 10 = 20

Hence, the answer is, "20"

200

CAT 2020 Quant Question:

Q. 3. Veeru invested Rs 10000 at 5% simple annual interest, and exactly after two years, Joy invested Rs 8000 at 10% simple annual interest. How many years after Veeru’s investment, will their balances, i.e., principal plus accumulated interest, be equal?

201

Answer:

Let assume its equal after N years
Veeru’s investment after N years = 10000 + 10000 × image × N
Joy’s investment after N years = 8000 + 8000 × image × (N – 2)
Equating both
10000 + 10000 × image × N = 8000 + 8000 × image ×(N – 2)
10000 + 500N = 8000 + 800N – 1600

3600 = 300N

N = 12

The answer is, " 12"

202

CAT 2020 Quant Question: Speed, time & distance

Q. 4. A train travelled at one-thirds of its usual speed, and hence reached the destination 30 minutes after the scheduled time. On its return journey, the train initially travelled at its usual speed for 5 minutes but then stopped for 4 minutes for an emergency. The percentage by which the train must now increase its usual speed so as to reach the destination at the scheduled time, is nearest to

A. 58
B. 67
C. 50
D. 61

203

Answer:

Let’s take speed of the train to be x and the time taken be t
image
Since the speed is one-third, time taken will be tripled. T = 3t
This 3t is after the scheduled time, So extra 2t = 30 mintues
t = 15 minutes
Train travels at x km/hr takes 15 minutes and
image
So, the train usually takes 15 minutes to cover the distance.

image
image793×90 5.57 KB

image
image782×146 8.29 KB

image
image785×149 10.2 KB

The answer is, "67"

204

CAT 2020 Quant Question: Logarithms

Q. 5 image

205

Answer:

image
image428×583 19.4 KB

Hence, the answer is, " 36"

206

CAT 2020 Quant Question: Exponents & Powers

Q. 6. The number of real-valued solutions of the equation image

A. infinite
B. 0
C. 1
D. 2

207

Answer:

image is of the form y + image
Minimum value the expression can take is ≥ 2

So image ≥ 2
Now, 2 – image is ≥ 0
So 2 – (x – 2)2 ≤ 2 (From 2 we are subtracting a non-negative number)

Maximum value the expression can have is 2

The only possibility is both sides are = 2
If value = 2
Then x = 0
image
2 ≠ – 2
There is no case where LHS = RHS = 2
Hence 0 real-valued solutions

Hence, the answer is, "0"

208

CAT 2020 Quant Question: Speed, time & distance

Q. 7. A straight road connects points A and B. Car 1 travels from A to B and Car 2 travels from B to A, both leaving at the same time. After meeting each other, they take 45 minutes and 20 minutes, respectively, to complete their journeys. If Car 1 travels at the speed of 60 km/hr, then the speed of Car 2, in km/hr, is

A. 90
B. 80
C. 70
D. 100

209

Answer:

Let the meeting point be D. Let’s assume C1 takes t minutes to reach the meeting point. Then C2 takes same t minutes to reach the meeting point.

image

After reaching the destinations…
C1 takes t minutes to cover AD, while C2 takes 20 minutes
C1 takes 45 minutes to cover DB, while C2 takes t minutes

the ratio of speeds of C1 and C2 on the stretch AD will be equal to the ratio of their speed on the stretch DB.
When the distances are the same, the ratio of speeds is the inverse ratio of time taken.

ratio of speeds of C1 and C2 on the stretch AD = image

ratio of speeds of C1 and C2 on the stretch DB = image
Therefore, image
t × t = 45 × 20

image = 900

t = 30.

image

Speed of C2 = 90 kmph

The answer is, "90"

210

CAT 2020 Quant Question: Averages

Q. 8. Let A, B and C be three positive integers such that the sum of A and the mean of B and C is 5. In addition, the sum of B and the mean of A and C is 7. Then the sum of A and B is

A. 6
B. 4
C. 7
D. 5

211

Answer:

a + image = 5 —> 2a + b + c = 10

b + image = 7 —> 2b + a + c = 14

Solving these two, we get b – a = 4
b = a + 4
Substituting this in the first equation
2a + a + 4 + c = 10
3a + c = 6
Given all three as positive integers, maximum value we can get for a = 1
Ex: When substituting a = 2, c = 0 (Not possible)
So a = 1, then b = 5
Sum of a + b = 6

Hence, the answer is, "6"

212

CAT 2020 Quant Question: Exponents & Powers

Q. 9. If x = image then which of the following equals 64?

image