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CAT Sample Questions: ›› Analytical Reasoning

# Analytical Section : Analytical Reasoning

Read properly the data given and then answer the CAT analytical reasoning questions according to the description.

Question 46

Garry drove from a certain place say X to a certain place say Y at an average speed of 40 km. He took rest over there for some time and again drove from place Y to place X at an average speed of 50 km/hr. The distance between place X and place Y is 100 km. What is Garry's average speed per hour for the round trip?

1. 50 km/hr
2. 45 km/hr
3. 44.44 km/hr
4. 60 km/hr
5. 40 km/hr

Explanation:

Average speed is equal to the total distance divide by the time taken. In this case, total distance travelled by Garry is 200 km i.e. (100 km from X to Y and 100 km from Y to X). The time taken from X to Y is 2.5 hours i.e. (100 km/40 minutes). The time taken from Y to X is 2 hours i.e. (100 km/50 minutes). Therefore, the total time taken for the entire journey is 4.5 hours i.e. (2.5 hours + 2 hours) and the average speed for the entire round trip is 44.44 km/hr i.e. (200 miles/4.5 hours).

Question 47

P, Q, R, S and T are playing a game of cards. P says to Q, "If you give me six cards, you will have as many cards as T has and if I give you three cards, you will have as many cards as S has." P and Q together have 20 cards more than what S and T together have. If Q has two cards more than what R has and the total number of cards be 133, how many cards does Q have?

1. 23
2. 22
3. 30
4. 35
5. 25

Explanation:

Given data:

Q - 3 = T---------(I)
Q + 3 = S--------(II)
P + Q = S + T + 20--------(III)
Q = R + 2--------(IV)
P + Q + R + S + T = 133----------(V)
From (I) and (II), we have: 2Q = S + T---------(VI)
From (III) and (VI) we have: P = Q + 20----------(VII)

Using equations (IV), (VI) and (VII) in equation (V), we get:

(Q + 20) + Q + (Q - 2) + 2Q =133 ↔ 5Q = 125 ↔ Q = 25

Question 48

Certain number of girls made a plan for one day trip. Their budget to spend on snacks was Rs. 192. But, one of them did not turn up for the trip. Because of this, the remaining girls had to contribute Rs. 8 each in extra. Find out the number of girls who went for the trip.

1. 8
2. 12
3. 16
4. 24
5. 28

Explanation:

Let x be the number of girls who attended the trip. Then,
(192/x-4) - (192/x) = 4 ↔ (1/x-4) - (1/x) = (4/192) ↔ (x-(x-4)/x(x-4)) = 1/48
↔ x2 - 4x - 192 = 0 ↔ (x - 16) (x + 12) = 0 ↔ x = 16
Hence, required number = x - 4 = 8

Question 49

The sum of ages of Tim, Tom and Jerry is 160 years at present. Then, what was the sum of their ages five years ago?

1. 144 years
2. 145 years
3. 148 years
4. 154 years
5. 200 years

Explanation:

Required sum = (160 - 3 * 5) years = (160 - 15) = 145

Question 50

Two train tickets from city X to city Y and three tickets from city X to city Z cost Rs. 80 but three tickets from city X to Y and two tickets from city X to Z cost Rs. 70. What are the fares for cities Y and Z from X?

1. Rs. 4 and Rs. 23
2. Rs. 13 and Rs. 17
3. Rs. 10 and Rs. 20
4. Rs. 17 and Rs. 13
5. Rs. 14 and Rs. 13

Explanation:

Let Rs. m be the fare of train ticket of city Y from city X and Rs. n be the fare of train ticket of city Z from city X.
Then, 2m + 3n = 80-------(i)
And, 3m + 2n = 70---------(ii)
Now, multiplying equation (i) by 3 and equation (ii) by 2 and subtracting the results, we get:
5n = 100 ↔ n = 20
Substituting n = 20 in equation (i), we get, 2m + 60 = 80 ↔ 2m = 20
Therefore, m = 10
Hence, m = 10 and n = 20

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CAT Analytical Reasoning Question Number : 1-5 | 6-10 | 11-15 | 16-20 | 21-25 | 26-30 | 31-35 | 36-40 | 41-45 | 46-50 | 51-55 |56-59 | 60-64 | 65-69 | 70-74 | 75-79 | 80-84
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