How many 4-digit positive integral numbers are there in base 7, if you are count

Question 1. A fishing motor boat sails at a speed of 50 kmph without any iron boxes on it. For every iron box of added to it, the speed of engine reduces by

10 %

of the earlier speed. At most how many boxes can be added so that the ship can cover a distance of 225 km in a maximum of 10 hrs? (Assume that the only additions which impede the performance of the boat are iron boxes and that all iron boxes have a weight of 7 kgs)

5
6
7
8

Answer: Option C
: C

Minimum speed at which the boat can go = 22.5 kmph

Now go from answer options

If 8 boxes are added, the speed after reduction will be

(0.9)^{8} \times 50 =< 22.5

kmph Thus, the maximum number of boxes which can be added will very close to and slightly less than 8. Answer is 7 boxes

Question 2. What is the remainder when

10^{25} - 7

is divided by 3?

1
2
3
0

Answer: Option D
: D

10^{x}

when divided by 3, gives a remainder of 1 always. Also

\frac{7}{3}

gives a remainder of 1. Thus 1-1=0. Remainder when

10^{25} - 7

is divided by 3=0.

Question 3. In a group of 100 girls, each has to opt for one or more of the three hobby classes: Music, Cooking and Stitching. The number of students who opted for Stitching is more than the number of those who opted for Music which is more than the number of those who opted for Cooking which is more than the number of those who opted for exactly two of the three hobbies, which in turn is more than those who opted for all three hobbies. It is known that at least one student opted for all the three hobbies.

Determine the minimum number of girls who attend Stitching Classes.

27
36
38
35

Answer: Option D
: D

We know that number of girls attending stitching classes is maximum. Now to assign the minimum value to this, we need to minimize the number of girls attending exactly two and exactly three classes, and then distribute the rest of the numbers as equally as possible.

So, number girls attending stitching class = 32 + 2 + 1 = 35. Hence option (d)

Question 4. A grid is set up as shown using 5 horizontal and 6 vertical lines. What are the no. of ways one can go from point P to point Q walking along the grids but not moving upwards or left or retracing a grid?

21
35
56
None of these

Answer: Option D
: D

There are 4 rows and 5 columns. Using the one-zero method, number of paths will be

^{9}

C

_{4}

= 126 ways

Question 5. A merchant mixes three varieties of rice costing Rs.20/kg, Rs.24/kg and Rs.30/kg and sells the mixture at a profit of

20 %

at Rs.30/kg. How many kgs of the second variety will be in the mixture if 2 kgs of the third variety is there in the mixture?

5 kg
12 kg
15kg
8 kg

Answer: Option A
: A

When he sells the mixture at Rs. 30/kg, he makes a profit of

20 %

. This means the cost price of that mixture is

\frac{30}{1.2}

= Rs. 25/kg. Combine the variety 1 and variety 3 first to get a mixture with price Rs. 25/kg Applying Alligation:

So, variety 1

&

variety 3 are required in the ratio 1 : 1. Now, combine variety 2 and variety 3 to get a mixture with price Rs. 25/kg

Variety 1: Variety 3 = 1: 1 Variety 2: Variety 3 = 5: 1 So, the required ratio in which all three have to be mixed = 1: 5: 2 If third variety is 2 kgs then second variety has to be 5 kg. Hence option (a)

Question 6. In the figure shown below, all the vertical lines are parallel to each other & are equally spaced. All the horizontal lines are parallel to each other and are equally spaced. What fraction of the area of ABCD, is shaded?

12
13
14
23

Answer: Option C
: C

The image can be redrawn as follows, by joining all the points

Thus, there are 24 unit squares. The number of unit squares shaded = 6. Required ratio =

\frac{1}{4}

	A.	2058
	B.	5666
	C.	6000
	D.	None of these

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