# Natural Number and Sweet Sorghum

Section I (QA + DI)

1. The sum of three numbers in A.P. is 45. If the sum of their squares is 683, what is the largest of the three numbers? (a) 16 (b) 19 (c) 17 (d) 18 The average market price of three shares A, B and C is Rs. x. Shares A and C lose Rs. y each and B gains Rs. The value of y is (a) 2 3.

2.

y . As a result, the average market price of the three shares decreases by Re. 1. 2 (b) 3 (c) 4 (d) dependent on x

C(n,r ) =

n! where n! = n × (n − 1) × (n − 2) × K × 2 × 1. r ! × (n − r )!

What is the smallest positive integer ‘k’ such that C(2k, k) is divisible by 200? (a) 23 (b) 61 (c) 13 (d) 11 4. If a, b, and c are positive integers such that (a – b + c)(b – c + a)(c – a + b) = 15, then what is the product of a, b and c? (a) 24 (b) 64 (c) 42 (d) Cannot be determined In the figure given below, ABCD is a trapezium, in which AB||CD and DP||CQ. If AP = 4 units, QB = 2 units and CD = 4 units, then what is the ratio of the area of the triangle COD to that of the triangle AOB?

5.

D

4

C

O A 4

(a) 4 : 25 6.

P

(b) 2 : 5

Q

2

B

(c) 1 : 2 (d) None of these

A watch, which gains time uniformly, was 5 minutes behind the correct time when it showed 11:55 AM on Monday. It was 10 minutes ahead of the correct time when it showed 06:10 PM on the next day. When did the watch show the correct time? (a) 6 AM, Tuesday (b) 6 PM, Monday (c) 2 PM, Tuesday (d) 10 PM, Monday A function f(x) is defined for all real values of x as 2f(x) + f(1 – x) = x2. What is the value of f(5)? (a) 10 (b) 17 (c) 34 3

7.

(d) Cannot be determined

Mock CAT 7 2012

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8.

Two jars contain milk and water in the ratio 7 : 3 and 3 : 2 respectively. In what ratio should the contents of the two jars be mixed such that the final ratio of milk and water in the resultant solution becomes 23 : 17? (a) 1 : 3 (b) 1 : 5 (c) 3 : 5 (d) Data Inconsistent

9.

a+

1 b+ 1 c+ 1 d +K

= 21/ 3

If a, b, c, d etc are positive integers, then what is the value of ‘b’? (a) 2 (b) 4 (c) 3 10.

(d) 5

A car runs on four tyres and has one extra tyre. If each tyre lasts for 10,000 km then what is the maximum distance (in km) that the car can travel using the five tyres? (a) 10,000 (b) 11,000 (c) 12,500 (d) 15,000

Directions for questions 11 to 13: Answer the questions on the basis of the information given below. The political parties mentioned in the graph given below participated in a constituency election. The graph shows the number of votes received by the candidates of six major parties and other smaller parties in Round 1 of the election. The election is held as follows: In Round 1, if a candidate gets more than 50% of the total number of votes cast in that round, (s)he is declared the winner of the election, else, top 5 candidates based on the number of votes move to Round 2. In Round 2, if a candidate gets more than 50% of the total number of votes cast in that round, (s)he is declared the winner of the election, else, top 3 candidates based on the number of votes move to Round 3. In Round 3, the candidate who gets the maximum number of votes in that round is declared the winner of the election. Assume that there are no ties in deciding top 5, top 3 (if Round 2 happens) candidates or the winner (if Round 3 happens) in Round 3.

1800000 16,52,754 16,38,192 16,38,913 16,42,139 16,34,345 16,42,332 1600000 1400000 1200000 1000000 800000 600000 400000 1,51,325 200000 0 AJP Kongress Junda Dal Bajrangi Samajik Hindu Others Dal Party Muslim Party

Number of Votes

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Mock CAT 7 2012

11.

Among the five candidates who moved to Round 2, the candidate with the maximum number of votes in Round 1 got what percentage of the total number of votes in that round? (a) 17.4 % (b) 19.8% (c) 16.5% (d) 18.2% If the votes received by the candidates of Samajik Party and Hindu Muslim Party in Round 1 are not taken into account, then by what percentage points does the share of “Others”...

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