CAT 2017 Question Paper | CAT QA
CAT Question Paper | CAT Previous Year Paper

Let ABCD be the rectangle where A = (2, 5) and C= (6, 3). We know that AC and BD will be the diagonals of the rectangle. It can be represented using the diagram shown below

In the above figure, O is the point of intersection of the 2 diagonals and the mid point of both the diagonals.

Now O also lies on diagonal BD

Hence co-ordinates of O will satisfy the equation

y = 3x + c

∴ 4 = 3 × 4 + c ⇒ c = –8

Hence, option 4.

Let us draw the base of the vertical pillar as shown below

In the above figure EF = AB = 10 cm

Also, as AD = BC, by rule of symmetry

DE = FC

Now DC = DE + EF + FC

Let DE = FC = x

20 = x + 10 + x

⇒ 2x + 10 = 20 ⇒ x = 5

Now in ∆AED, AE = 12 cm and DE = 5 cm

Also given AD = BC

∴ BC = 13 units

New surface area of vertical pilar with base ABCD = Area of Rectangle with side AB and side (Height) 20 cm + Area of Rectangle side AD and side (Height) 20 cm + Area of Rectangle with side BC and side (Height) 20 cm + Area of Rectangle with side DC and side (Height) 20 cm + 2 × Area of Trapezium ABCD

⇒ 200 + 260 + 260 + 400 + 360

⇒ 1480 sq.cm.

Hence, option 3.

ABCDEF is a hexagon with side 1 cm. Let us construct the diagram as shown below

Now if we look at triangle ABC 

\

Further, as AB = BC, â–³ ABC will become a 120° -30° -30° triangle and the ratio of it’s sides will be

Hence, option 2.

Now as liquid A, B and C are mixed in the ratio 4 : 3 : 2.

Now proportion of liquid A in resultant mixture

Similarly proportion of liquid B and liquid C in the resultant mixture is

Hence, statement (1) is false.

So statement (2) is false.

3] Now quantity of water in resultant mixture

Statement (3) is true.

4] Quantity of liquid A in resultant, mixture is

Hence, option 3.

= Rs.10

Hence, option 1.

AS both the car and the bike meet at the point between A and B, sum of the distance travelled by the car and bike will give distance between A and B. The motor bike starts from point A and travels a distance of 168 km in 2 hours 40 minutes.

Speed of Motorbike

= 2 × Speed of Motorbike

= 2 × 63 = 126 km/hr

Now as the car travels for 1 hour 40 minutes.

Distance travelled by the car

Distance between A and B = Distance travelled by Motorbike + Distance travelled by Car

⇒168 + 210 = 378 km

Hence, option 2.

To get a common ratio we take L.C. M(2, 4) = 4

So, we multiply each of b and c by 2

Hence, ratio of b : c = 4 : 2

∴ Ratio of a : b : c = 4 : 2

Now let a = 3x, b = c = 3 : 4 : 2

So a + b + c =3x + 4x + 2x = 9x

As, a, b and c are all positively integers, it implies that the sum of a, b and c will be a positive integer and a multiple of 9.

Out of the given options, only 207 i.e, option [3] is a multiple of 9.

Hence, option 3.

Total Food Production = Total Population × Per Capita Food Production 

Let the initial population be ‘p’ and the initial per capita food production be ‘c’

If f is the total food production f = pc

Now, as per given information, f increases to 1.4f and increases to 1.27c.

So, if p1 is population after increase.

1.4f = p1(1.27c) 

This means that the population of the village has increased by approximately 10%.

Hence, option 3.

Supposing Mayank buys ‘x’ dozen candies at Rs. 15 per dozen and another ‘x’ dozen candies at Rs. 12 per dozen.

Total C.P =15(x) + 12(x) per dozen.

Now he sells these ‘x + x’ or ‘2x’ dozen candies at Rs. 16.50 per dozen.

So total S.P = 16.50 × 2x = 33x

Profit = 33x -27x = 6x

Now 6x = 150 or x = 25

As Mayank buys ‘2x’ dozen candies, number of dozens of candies bought by him

= 2 × 25 or 50

Hence, option 1.

Let the time taken by the outlet pipe to empty the tank be ‘x’ hours. So in 1 hour

Now when the outlet and inlet pipe will empty half the tank in 20 hours.
Hence, option 1. 

Lets the manufacturers C.P. be 100
As he sells it to the wholesaler at 10% profit, his S.P will be 100 + 10 or 110

Now 110 is also the wholesaler’s C.P. Further, as the wholesaler sells it to a retailer at 30%, profit, his S.P will be

Now 143 also the retailers C.P

As the retailer sells it to the customer at

Now 214.5 is the price the customer pays for the table, when the manufacturer’s cost is 100

Let the manufacturer’s cost of the table be Rs. ‘x’ when the price paid by the customer is Rs. 4290

By unitary method

So Rs. 2000 is the manufacturer’s cost

Hence, option 3.

Let the average height of 22 toddlers be ‘x’ inches

Now as the average height of the 2 toddlers who leave the group is one-third the average height of the entire group 22, their

Further, the average height of the balance 20 toddlers in terms of x will be ‘x + 2’ inches. So the average height of all 22 toddlers can be expressed as

So the average height of the balance

20 toddlers will be 30 +2 or 32 inches

Hence, option 3.

Let us assume that the number of shirts produced in the factory is ‘100x’. Now 15% of ‘100x’ or ‘15x’ shirts are defective.

So the number of remaining shirts

= 100x – 15 = 85x

Now 20% of the remaining ‘85x’or ‘17x’ shirts are sold in the domestic market.

So number of shirts left for exports

= 85x – 17x = 68x
As per given information, 8840 shirts are left for exports.

∴ 68x – 8840⇒ x = 130 or 100x = 13000

So number of shirts produced in the factory is 13000.

Hence, option 2.

Let ‘d’ miles be the distance for the onward journey from his home to his hostel.

For the return journey, time taken to cover half distance(i.e. d/2)

Now for the return journey, (after half the distance is covered) taking the bypass road will increase the distance by 5 miles i.e., the remaining distance of the journey is

Total time for return journey

Now as time taken for return journey is half an hour more than onward journey.

Total distance covered (for onward and return journey)

Hence, option 3.

Now using the allegation rule, we get the ratio of milk to water as follows

Hence, option 2.

In a 10 km race, A beats B by 1 km. So in the time A completes 10 km, B completes
9 km. Therefore ratio of their speeds is
10 : 9. In a similar way, ratio of speeds of
B and C is also 10 : 9