Quantitaitve Aptitude Clubbed(Exams > Cat > Quantitaitve Aptitude ) Questions and answers for exam Preparation

Exams > Cat > Quantitaitve Aptitude

QUANTITAITVE APTITUDE CLUBBED MCQs

Total Questions : 1394 | Page 8 of 140 pages

Question 71. Ahmed and Sahil set out together on bicycle traveling at 15 and 12 kilometers per hour, respectively. After 40 minutes, Ahmed stops to fix a flat tire. If it takes Ahmed one hour to fix the flat tire and Sahil continues to ride during this time, how many hours will it take Ahmed to catch up to Sahil assuming he resumes his ride at 15 kilometers per hour? (consider Ahmed's deceleration/acceleration before/after the flat to be negligible)

4.5
3.33
3.5
4

Discuss Question

Answer: Option B. -> 3.33
:
B
A travels 10 km in 40 min
B travels 8 km in 40 min
After one hour, A would have still traveled only 10 km and B would have traveled 20 km
Representing this on a timeline:

\begin{matrix} Time in hours & 1 & 2 & 3 & 4 & 5 & 5 : 20 D i s t a n c e & A & 10 & 10 & 25 & 40 & 55 & 60 D i s t a n c e & B & 8 & 20 & 32 & 44 & 56 & 60 \end{matrix}

A gains this 10 km in

\frac{10}{3} = 3.33

hours.
Answer is Option (b).

Question 72. If this pattern continues, where would the number 289 appear?.

Row 17
Row 18
Row 19
Row 20

Discuss Question

Answer: Option A. -> Row 17
:
A

Perfect squares are the middle term of odd rows.

(17)^{2} = 289

should be middle term of

17^{t h}

row. Option (a).
Alternate Solution:
There is 1 odd number in the

1^{s t}

row.
There are 2 odd numbers in the

2^{n d}

row.
There are 3 odd numbers in the

3^{r d}

row. ...
Hence this can be considered as

a \sum n

question where, n is the number of odd numbers.
As 289 will be

\frac{289}{2} = \frac{144}{145^{t h}}

term in the sequence, find

a \sum n

value which is close to the number. which is equal to 153 and 17 numbers before 153 will be in the

17^{t h}

row. Hence the answer is 17.

Question 73. Tiles are packed into packets of 6, 9 and 50. What is the largest number of tiles that cannot be purchased with any combination of above packets. Tiles cannot be sold loose.

Discuss Question

Answer: Option C. -> 103
:
C
After 6 all multiples of 3 would be covered. After 50+6 all 3x+2 tiles would be covered. After 50+50+6 all 3x+1 tiles would be covered. So for 106 and above all tile combinations are possible. 105 again is possible (it is a multiple of 3), 104 is also possible as it is of the form 3x+2. The largest possible value is 103 which can't be obtained.

Question 74. Four equal jugs are filled with the mixture of sprit and water. The ratio of sprit to water in four jugs is 1:3, 3:5, 5:11 and 7:9. The mixture of the four jugs is emptied into a single vessel. What is the proportion of sprit to water in the vessel?

11:21
11:30
12:24
3:5

Discuss Question

Answer: Option A. -> 11:21
:
A
Let x (in ml) be the volume of each jug.

\begin{matrix} J u g & 1^{s t} & 2^{n d} & 3^{r d} & 4^{t h} S : W & 1 : 3 & 3 : 5 & 5 : 11 & 7 : 9 S & \frac{1}{4} x & \frac{3}{8} x & \frac{5}{16} x & \frac{7}{16} x W & \frac{3}{4} x & \frac{5}{8} x & \frac{11}{16} x & \frac{9}{16} x \end{matrix}

\frac{(\frac{1}{4} x + \frac{3}{8} x + \frac{5}{16} x + \frac{7}{16} x)}{(\frac{3}{4} x + \frac{5}{8} x + \frac{11}{16} x + \frac{9}{16})} = \frac{(\frac{22}{16})}{(\frac{42}{16})} = \frac{22}{42} = \frac{11}{21}

Question 75. If 2x+3y=12; x, y

>

0, then the maximum possible value of

x y^{2}

is ___.

Discuss Question

:
Power of x is 1 and that of y is 2 in

x y^{2} .

So, we split the term with y into two.
2x+2y+y=12
He know that, AM

\geq

GM.

\frac{2 x + 2 y + y}{3} \geq (2 x \times 2 y \times y)^{\frac{1}{3}}

Question 76. If

a_{1} + 2 a_{2} + 3 a_{3} = 1

, where

a_{1}, a_{2} & a_{3}

are all positive numbers; then what is the minimum value of

2^{a 1} + 4^{a 2} + 8^{a 3}

413
(3×2)13
213
(27×2)13

Discuss Question

Answer: Option D. -> (27×2)13
:
D
AM

= \frac{(2^{a_{1}} + 4^{a_{2}} + 8^{a_{3}})}{3}

and GM

= (2^{a_{1}} \times 4^{a_{2}} \times 8^{a_{3}})^{(\frac{1}{3})}

Using condition AM

\geq

GM, we get

\frac{(2^{a_{1}} + 4^{a_{2}} + 8^{a_{3}})}{3} \geq (2^{a_{1}} \times 4^{a_{2}} \times 8^{a_{3}})^{(\frac{1}{3})}

2^{a_{1}} + 4^{a_{2}} + 8^{a_{3}} \geq 3 (2^{a_{1}} \times 2^{2 a_{2}} \times 2^{3 a_{3}})^{(\frac{1}{3})}

\geq 3 (2^{a_{1} + 2 a_{2} + 3 a_{3}})^{(\frac{1}{3})}

But

a_{1} + 2 a_{2} + 3 a_{3} = 1

Answer =

(27 \times 2)^{\frac{1}{3}}

Question 77. On June 1, 2004 two clubs, S1 and S2, are formed, each with n members. Everyday S1 adds b members while S2 multiplies its current number of members by a constant factor r. Both the societies have the same number of members on June 7, 2004 (end of day). If b =10.5n, what is the value of r?

3
2
1.5
Cannot be determined

Discuss Question

Answer: Option B. -> 2
:
B
S1 club members increase in an arithmetic progression.
Hence on June

7^{t h}

,the number of members in club S1 is n+6(10.5n)=64n.
S2 club members increase in an geometric progression.
Hence on June

7^{t h}

,the number of members in club S2 is

n r^{6} = 64 n . . . .

(As given in the question).
Therefore r=2.

Question 78. Let g be a function satisfying g(a+b)= g(a)+g(b) for all a,b which is real. If
g(1)=k, then find g(n), where n is a natural number

Discuss Question

Answer: Option B. -> nk
:
B
Assumption
Assume n=2
Then
g(2) = g(1) +g(1) = 2g(1)= 2k
substitute n=2 in answer options to eliminate wrong options.
Hence, answer is option (b)

Question 79. Find the sum to n terms of the series

\frac{3}{1^{2} \times 2^{2}} + \frac{5}{2^{2} \times 3^{3}} + \frac{7}{3^{2} \times 4^{2}} . . . . . .

n2+1(n+1)2
n2+2n(n+1)2
n2+2(n+1)3
(n+1)3

Discuss Question

Answer: Option B. -> n2+2n(n+1)2
:
B
At n=1, we should get

\frac{3}{4}

(this is the sum to 1 term of the series)
Option (a) gives

= \frac{2}{4} = \frac{1}{2}

Option (b) gives

\frac{3}{4}

Option (c) gives

\frac{3}{8}

Option(d) gives 8
Answer= option b

Question 80. The milk and water in two vessels A and B are in the ratio 4:5 and 7:2 respectively. In what ratio the liquids in both the vessels be mixed to obtain a new mixture in vessel C consisting half milk and half water?

2: 1
5: 1
4: 1
7: 2

Discuss Question

Answer: Option B. -> 5: 1
:
B
Suppose in the vessels A