A batsman makes a score of 270 runs in the 87th inning and thus increases his average by certain number of runs which is a natural number. Find the possible values of the new average.

Solution

Ans: A, B, C

Let the average for 86 inning be x

∴ Total runs scored in 86 innings = 86x

Suppose, there is an increase of 1 run in the average after 87th inning.

∴ New average of 87 innings is x + 1

⇒ Runs scored in 87 innings - Runs scored in 86 innings = Runs scored in 87th inning

87(x -1) - 86x = 270

87x + 87 - 86x = 270 X = 183

:. Possible value of new average ⇒ x + 1 = 183 + 1 = 184 Runs

Supposing an increase of 2 runs

87(x + 2) - 86x = 270

87x+ 174 - 86x = 270

X = 270 - 174= 96

∴ Value of new average can be = x + 2

= 96 + 2 = 98

An increase of 3 runs;

87 (x + 3) - 86x = 270 87x - 261 - 86x = 270 X = 9

New Average = 9 + 3 = 12

Which of the following would result in zero increase in the initial value?

A. Quantity increased by 25% and then decreased by 20%
B. Quantity increased by 12.5% and then decreased by 11.11 %
C. Quantity increased by 33.5% and then decreased by 33.33%
D. Quantity increased by 50% and then decreased by 50%

Solution

Ans: A, B

Take the initial value as 100 and check the option OR

If a quantity is increased by ⁿ⁄_d (fraction) then in order to get the original value it should be decreased by

\(\frac{n}{d+n}\)

Increased by 25% = ¹⁄₄ =ⁿ⁄_d

Decrease = \(\frac{n}{d+n}=\frac{1}{4+1}= 5\)

= 20%

Option A results in an increase. Similarly, Check for other options.

Solution

Ans: A, B, D, F

Number of diagonals of a polygon=\(\frac{n(n-3)}{2}\)

2,4,6,8,n,3,5,7,9

In the list above, if n is an integer between 1 and 10 inclusive, the median has the values:

Solution

Rearranging, the actual numbers in ascending order, we get,

2,3,4,5,6,7,8,9

'n' has to be an integer

if n ≤ 5, then 5 is middle most number among 9 numbers under consideration. So median = 5

If n ≥, then median is 6

'n' cannot take values between 5 and 6 because 'n' is an integer.

∴ Value of n is 5 or 6.

A computer routine was developed to generate two numbers (x, y), the first being a random number between 0 and 100 inclusive, and the second being less than or equal to square root of the first number. Which of the following routines are possible:

A. 99, 10
B. 85, 9
C. 50, 7
D. 1, 1

Solution

Ans: B, C, D, E

Consider the Option.

B → 85> (9)²

C → 50> (7)²

D → 1 = (1)²

E → 1> (0)²

But, In A 99 < (10)²

Solution

Ans:B,C,D,E

4n is definitely a multiple of 4. 2n + 2, 2n and n + 3 can be multiple of 4 but 4n + 2 cannot be a multiple of 4.

If x, y, z are consecutive positive integers such that x < y < z and xyz is even, which of the following options are true? [mpcheck] [mccheck]A. x + z is even[/mccheck]

B. yz is even

C. z – y is odd

[/mpcheck]

Solution

Ans: A, B, C

x < Y < z ; xyz = even. Since x, y, z, are consecutive positive integers we can have; odd, even, odd OR Even, odd, even Any of these 2 combinations satisfies the options A, B, C

If n is the average (Arithmetic Mean) of five numbers, which of the following must be true?

A. At least one of the five numbers is greater than or equal to n
B. At least one of the five numbers is less than or equal to n
C. At least two of the five numbers are greater than or equal to n

Solution

Ans:A,B

Average of a group of numbers is always between the smallest and largest of the numbers. For example, average often numbers between,5 and 10 can never be 12 or 3, it will always be between 5 and 10. hence the first and second statement are true but the third one is a possibility and not a certainty

The least of the three numbers is 8 and the greatest is 14. Which of the following are the possible values of the average of the three numbers?

Solution

Ans: B, C, D, E

The third number will be at least (it says three numbers, not three distinct numbers) 8 and at most 14. Hence, the sum of the three numbers will be at least 30 and at most 36. Hence average will be at least 10 and at most 12.

Three cities X, Y, Z are located so that the line segments joining them form a triangle. If the distance between city X and city Y is 50 miles and the distance between city Y and city Z is 75 miles, which of the following can be the possible distance in miles from X to Z?

Solution

Ans:B,C,D,E

If angle 'y' is very very small i.e. 10, then YX and YZ will almost overlap. Even then the distance between x and z will be more than 25 miles. Also in any triangle, the difference in lengths of the two sides is always less than the third side. Since the difference between the lengths of XY and YZ is 25 miles, the third side has to be more than 25 miles.

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