#### Nonverbal Reasoning

• ( 1 ) Nitin's age was equal to square of some number last year and the following year it would be cube of a number. If again Nitin's age has to be equal to the cube of some number, then for how long he will have to wait?

• 1) 10
• 2) 38
• 3) 19
• 4) 64
• Discussion in forum
Solution : Clearly, we have to first find two numbers whose difference is 2 and of which the smaller one is a perfect square and the bigger one a perfect cube. Such numbers are 25 and 27.
Thus, Nitin is now 26 years old. Since the next perfect cube after 27 is 64,
so required time period = (64 - 26) years = 38 years.

discussion

• ( 2 ) The taxi charges in a city comprise of a fixed charge, together with the charge of the distance covered. For a journey of 16 km, the charges paid are Rs. 156 and for a journey of 24 km, the charges paid are Rs. 204. What will a person have to pay for travelling a distance of 30 km?

• 1) Rs. 236
• 2) Rs. 240
• 3) Rs. 248
• 4) Rs. 252
• Discussion in forum
Solution : Let the fixed charge be Rs. x and variable charge be Rs.y per km. Then,
x + 16y = 156. . . . . . . . . . . .(1) and
x + 24y = 204. . . . . . . . . . . . (2)
Solving (1) and (2), we get: x = 60, y = 6.
Therefore Cost of travelling 30 km = 60 + 30 y = Rs. (60 + 30 × 6) = Rs. 240.

discussion

• ( 3 ) Jayesh is as much younger to Anil as he is older to Prashant. If the sum of the ages of Anil and Prashant be 48 years, what is the age of Jayesh?

• 1) 20
• 2) 24
• 3) 30
• 4) cannot be determined
• Discussion in forum
Solution : Let the age of Anil and Prashant be x and (48 - x) years, respectively

discussion

• ( 4 ) A certain number of horses and an equal number of men are going somewhere. Half of the owners are on their horses' back while the remaining ones are walking along leading their horses. If the number of legs walking on the ground is 70, how many horses are there ?

• 1) 10
• 2) 12
• 3) 14
• 4) 16
• Discussion in forum
Solution : Let number of horses = number of men = x.
Then, number of legs = 4x + 2 $\frac{x}{2}$ = 5x.
So, 5X = 70 or x = 14.

discussion

• ( 5 ) Five bells begin to toll together and toll respectively at intervals of 6, 5, 7, 10 and 12 seconds. How many times will they toll together in one hour excluding the one at the start ?

• 1) 7 times
• 2) 8 times
• 3) 9 times
• 4) 11 times
• Discussion in forum
Solution : L.C.M. of 6, 5, 7, 10 and 12 is 420.
So, the bells will toll together after every 420 seconds i.e. 7 minutes.
Now, 7 × 8 = 56 and 7 × 9 = 63.
Thus, in 1-hour (or 60 minutes), the bells will toll together 8 times, excluding the one at the start.

discussion

• ( 6 ) A motorist knows four different routes from Bristol to Birmingham. From Birmingham to Sheffield he knows three different routes and from Sheffield to Carlisle he knows two different routes. How many routes does he know from Bristol to Carlisle?

• 1) 12
• 2) 24
• 3) 48
• 4) 60
• Discussion in forum
Solution : Total number of routes from Bristol to Carlisle = ( 4 × 3 × 2) = 24.

discussion

• ( 7 ) A farmer built a fence around his square plot. He used 27 fence poles on each side of the square. How many poles did he need altogether?

• 1) 54
• 2) 84
• 3) 104
• 4) 108
• Discussion in forum
Solution : Since each pole at the corner of the plot is common to its two sides.
Therefore total number of poles needed = 27 × 4 - 4 = 104.

discussion

• ( 8 ) In a caravan, in addition to 5o hens, there are 45 goats and 8 camels with some keepers. If the total number of feet be 224 more than the number of heads in the caravan, the number of keepers is

• 1) 5
• 2) 8
• 3) 10
• 4) 15
• Discussion in forum
Solution : Let the number of keepers be x. Then,
Total number of feet = 2 × 50 + 4 × 45 + 4 × 8 + 2x = 2x + 312.
Therefore (2x + 312 ) = ( 103 + x) + 224 or x = 15.

discussion

• ( 9 ) If 100 cats kill 100 mice in 100 days, then 4 cats would kill 4 mice in how many days?

• 1) 1 day
• 2) 4 days
• 3) 40 days
• 4) 100 days
• Discussion in forum
Solution : Less cats, more days
Less mice, less days
Let the required number of days be a.
$\begin{array}{}\text{Cat 4 : 100}\text{Mice 100 : 4}\end{array}}$ : : a : 100
=> 100 × 4 × a = 4 × 100 × 100
a = $\frac{4×100×100}{100×4}$ = 100.

discussion

• ( 10 ) A number consists of two digits whose sum is 11. If 27 is added to the number, then the digits changed their places. What is the number?

• 1) 47
• 2) 65
• 3) 83
• 4) 92
• Discussion in forum
Solution : Let the ten's digit be x.
Then, unit's digit = (11 - x)
So, number = 10x + (11 - x) = 9x + 11.
(9x + 11) + 27 = 10(11 - x) + x
=> 9x + 38 = 110 - 9x
=> 18x = 72
=> x = 4.
Thus, ten's digit = 4 and unit's digit = 7. Hence, required number = 47.

discussion