KRISHNA MOHAN

Friday, 4 August 2017

Quant Mix Quiz

1. The ratio of the no. of boys to the no. of girls in a school of 720 students is 3: 5.

If 18 new girls are admitted in the school, find how many new boys may be admitted so that the ratio of the no. of boys to the no.

of girls may change to 2 : 3.

A) 80

B) 50

C) 42

D) 35

E) None of these

2. The values of x in the equation 7(x+2p)^2 + 5p^2= 35xp + 117p^2 are

A) (4p, –3p)

B) (4p, 3p)

C) (–4p, 3p)

D) (–4p, –3p)

E) None of these.

3. What is the amount of compound interest and effective rate of interest if an amount of Rs.20000 is deposited in a bank -

for one year at the rate of 8% per annum compounded semi annually.

A) 1632, 8.16%

B) 1600, 9.36%

C) 1936, 10.36%

D) 1756, 9.56%

E) None of these.

4. 3 men can complete a piece of work in 6 days. Two days after they started the work,

3 more men joined them. How many days will they take to complete the remaining work?

A) 5 days

B) 2 days

C) 8 days

D) 12 days

E) None of these.

5. Two pipes A and B can fill a tank in 36 min. and 45 min. respectively. A water pipe C can empty the tank in 30 min.

First A and B are opened. After 7 minutes, C is opened. In how much time, the tank is full?

A) 45 minutes

B) 46 minutes

C) 52 minutes

D) 56 minutes

E) None of these.

6. Abhishek purchased 140 shirts and 250 trousers at the rate of Rs. 450 and Rs. 550 respectively.

What should be the overall average selling price of shirts and trousers so that 40% profit is earned? (Rounded off to next integer).

A) Rs.725

B) Rs.710

C) Rs. 720

D) Rs. 700

E) None of these

7. In a college the students in Arts and Commerce faculties were in the ratio of 4:5 respectively.
When 65 more students joined Commerce faculty the ratio became 8:11 respectively. How many students are there in Arts faculty?

A) 520

B) 650

C) 715

D) Cannot be determined

E) None of these

8. An amount of Rs. 10,000 becomes Rs. 14,641 in two years if the interest is compounded half yearly.

What is the rate of compound interest % per annum?

A) 10

B) 20

C) 16

D) 12

E) None of these.

9. Area of a rectangle is equal to the area of the circle whose radius is 21 cm.

If the length and the breadth of the rectangle are in the ratio of 14:11 respectively, what is its perimeter?

A) 142cm

B) 140cm

C) 132cm

D) 150 cm

E) None of these

10. Prashant purchased a TV set for Rs. 12,500 and spent Rs. 300 on transportation and Rs. 800 on installation.

At what price should he sell it so as to earn an overall proﬁt of 15%?

A) Rs. 14,560

B) Rs. 14,375

C) Rs. 15,640

D) Rs. 15,375

E) None of these.

11. Three girls start jogging from the same point around a circular track and each one completes one round in 24 seconds,

36 seconds and 48 seconds respectively. After how much time will they meet at one point?

A) 2 minutes, 20 seconds

B) 2 minutes, 24 seconds

C) 4 minutes, 12 seconds

D) 3 minutes, 36 seconds

E) None of these

12. A 240-metre long train running at the speed of 60 km/hour will take how much time to cross -
another 270 metre long train running in opposite directions at the speed of 48 km/hour?

A) 17 seconds

B) 3 seconds

C) 12 seconds

D) 8 seconds

E) None of these

13. Sarita started a boutique investing an amount of Rs. 50,000. Six months later Meeta joined her with an amount of Rs. 80,000.

At the end of one year they earned a profit of Rs. 18,000. What is Sarita's share in the profit?

A) Rs. 9,000

B) Rs. 8,000

C) Rs. 12,000

D) Rs 10,000

E) None of these

14. A alone can make 100 baskets in 6 days and B alone can make 100 baskets in 12 days.

In how many days can A and B together make 100 baskets?

A) 3 days

B) 5 days

C) 2 (1/2 ) days

D) 3(1/2) days

E) None of these

15. Samir’s age is one-fourth of his father’s age and two third of his sister Reema’s age.
What is the ratio of the ages of Samir, Reema and their father respectively?

A) 3:2:8

B) 3:4:8

C) 2:3:8

D) 4:3:8

E) None of these

Answers & Explanation:

1.(C) The ratio of the no. of boys to the no. of girls = 3 : 5
Sum of the ratios = 3 + 5 = 8
So, the no. of boys in the school = (3 × 720)/8 = 270
And the no. of girls in the school = (5 × 720)/8 = 450
Let the no. of new boys admitted be x, then the no. of boys become (270 + x).
After admitting 18 new girls, the no. of girls become 450 + 18 = 468
According to given description of the problem, (270 + x)/468 = 2/3
or, 3 (270 + x) = 2 x 468
or, 810 + 3x = 936 or, 3x = 126 or, x = 42.
Hence the no. of new boys admitted = 42.

2.(A) 7(x+2p)^2+5p^2= 35px+117 p^2
7x^2+33p^2+28px = 35px+ 117 p^2
x^2-px+12p^2 = 0
on solving x= 4p,-3p

3.(A) Interest = 20000[(1+4/100)^2-1]= 1632
Efeective rate of interst = 1632/20000*100= 8.16%

4.(B) Work done by 3 men in 2 days = (1/6x 2 )=1/3.
Remaining work = (1 – 1/3)= 2/3
Now 3 men's 1 day's work =1/6
1 man's 1 day's work = 1/18
6 men's 1 day's work = (6 x 1/18=1/3
Now, 1/3 work is done by them in 1 day.
2/3 work is done by them in (3 x2/3)= 2 days.

5.(B) Part filled in 7 min = 7[ 1/36 + 1/45] = 7/20
Remaining part = [ 1- 7/20] = 13/20
Net part filled in 1 min. When A,B and C are opened
= [ 1/36 + 1/45 + 1/30 ] = 1/60
Now, 1/60 part is filled in 1 min.
13/20 part is filled in [60x13/20] = 39 min
Total time taken to fill the tank = (39 + 7) min. = 46 min.

6. (C); CP of 140 shirts and 250 trousers
= Rs (140 * 450 + 250 * 550)
= Rs. (63000 + 137500) = Rs 200500
SP for 40% profit = Rs (140/100 ×200500)=280700
Average selling price = Rs (280700/(140+250) )=Rs.720

7. (A): Let the initial number of students in Arts and Commerce faculties be 4x and 5x respectively.
According to the question,
4x/(5x+65)=8/11
44x = 40x + 520
= x = 520/4 = 130
Number of students in Arts faculty = 4 * 130 = 520

8. (B) Time = 4 half years
Rate = R% per half year
A = P (1+R/100)^T
14641 = 10000 (1+R/100)^4
(1+R/100)^4 = 14641/10000= (11/10)^4
1+R/100=11/10 ? R/100=1/10
R =10%
Rate % per annum = 20%

9. (D); Area of rectangle = Area of circle
= 22/7 * 21 * 21 = 1386 sq.cm
Let the length and breadth of rectangle be 14x and 11x cm respectively. Then,
14x * 11x = 1386
x^2=1386/(14 ×11)=9
x = v9=3
Perimeter of rectangle = 2(14x + 11x)
= 50x = 50 * 3 = 150cm.

10.(C); Total cost of TV = Rs (12500 = 300 + 800) = Rs 13600
For a profit of 15%
Selling price = Rs. (115/100 ×13600)=Rs.15640

11. (B); required time = LCM of 24, 36 and 48 second = 144 sec. = 2 min 24 sec.

12. (A); Relative speed = (60 + 48) kmph = 108 kmph
= (108 ×5/18) m/sec = 30m/sec
Total distance = (240 + 270) metre = 510 metre
Time taken in crossing = (510/30) = 17 seconds

13. (D); Ratio of equivalent capitals of Sarita and Neeta for 1 month = 50000 * 12 : 80000 * 6
Sarita's share = Rs (5/9 ×18000) = Rs. 10000

14. (E) A's 1 day's work = 1/6
B's 1 day's work = 1/12
(A +B)'s 1 day's work = 1/6 + 1/12 = 2 + 1/12 = 1/4
A and B together will make 100 baskets in 4 days.

15. (C); Samir's age = x years
His father's age = 4x years
Reema's age = 3/2x years

Required ratio = x : 3x/2 : 4x = 2: 3 : 8

Quant Quiz

Directions (Q. 1-5): Each question below is followed by two statements A and B.

You have to decide whether the data given in the statements are sufficient for answering the questions.

Read both the statement and give answer :

1) If the statement A alone is sufficient to answer the question but the statement B alone is not sufficient.

2) If the statement B alone is sufficient to answer the question but the statement A alone is not sufficient.

3) If both statements A and B together are needed to answer the question.

4) If either the statement A alone or statement B alone is sufficient to answer the question.

5) If the data even in both statements A and B together are not sufficient to answer the question.

1. What is the profit earned by selling a pen for Rs. 120 ?

A) The cost price of 5 such pens is equal to selling price of 4 such pens.

B) 25% profit is earned by selling each pen.

2. What is the salary of C, in a group of A, B, C, D and E, whose average salary is Rs. 12000 ?

A) C's salary is 2.5 times B's salary.

B) Average salary of A and B is Rs. 4000.

3. What is the area of the circle ?

A) The breadth of a rectangle is 3/4th radius of circle.

B) The radius of the circle is equal to the side of a square of area 169 sq m.

4. What is the three digit number ?

A) 3/5 of a number is less by 90 of that number.

B) 1/4 of a number is 25% of that number.

5. What is the speed of the car ?

A) The car covers a distance 120 km in 4 hours.

B) The car covers a distance 210 km in 7 hours.

6. If 6x^2 + 5x + 1 < 0 then the value of x satisfies which inequality are ?

1) -1/2 < x < -1/3

2) x < -1/2 and x > -1/3

3) x ≥ -1/2

4) x ≤ 1/2

5) None of these

Directions (Q. 7-8): In each of these questions, two equations I and II with variable ‘x’ and ‘y’ are given.

You have to solve both the equations to find the value x and y and give answer:

1) If x < y

2) If x ≤ y

3) If x = y

4) If x ≥ y

5) If x > y

I. x^2 = 9

II. y^2 + 8y + 16 = 0

I. 4x^2 + 10x – 6 = 0

II. y^2 – 5y + 6 = 0

9. The radius of a copper sphere is 6 cm. The sphere is melted and drawn into a long wire of uniform circular cross section.

If the length of the wire is 72 cm, then the radius of wire is ?

1) 4 cm

2) 4.2 cm

3) 2 cm

4) 3 cm

5) None of these

10. The ratio of length of rhombus is 3 : 4. Then, the ratio of the area of the rhombus to the square of the shorter diagonal is?

1) 3 : 2

2) 3 : 8

3) 1 : 2

4) 4 : 3

5) None of these

ANSWERS:

1. 4

Using statements A

Profit % = (5 - 4)/4 * 100 = 25%

Cost price = 125 * 100/125 = Rs. 96

Profit = 120 – 96 = Rs. 24

Similarly, we can find profit by using statement B.

2. 5

From statement A salary of C = 2.5 B

From statement B, A + B = 2 × 4000 = Rs. 8000

3. 2

From statement B, radius of circle = sq. root (169) m = 13m

Required area = π r^2

= 22/7 * (13)^2

4. 1

From statement A, 3/5 * x = x - 90

2/5x = 90

From B, x/4 = x/4 we can't determine the value of x

5. 4

Since, speed of car = Distance covered by it/ Time taken by it

6. 1

5x^2 + 6x + 1 < 0

6x^2 + 3x + 2x + 1 < 0

(2x + 1) (3x + 1) < 0

(x + 1/2) (x + 1/3) <0

- 1/2 < x < -1/3

7. 5

From equation I:

x^2 = 9

x = +/-3

From II:

y^2 + 8y + (4)^2 = 0

(y + 4)^2 = 0

y = - 4

x > y

8. 1

I: 4x^2 + 12x - 2x - 6 = 0

4x (x + 3) - 2 (x + 3) = 0

(4x - 2) ( x + 3) = 0

x = -3 or 1/2

II:

y^2 - 5y + 6 = 0

(y -3)(y - 2) = 0

y = 3 or 2

y > x

9. 3

___r^2 * 72 = 4/3 π * (6)^3

r^2 = 4

r = 2 cm

10. 5

Area of rhombus = 1/2 * 3x * 4x = 6x^2

Square of the shorter diagonal = 3x^2 = 9x^2

Req. Ratio = 6x^2/9x^2 = 2/3

Data Interpretation

Directions (1-5): Study the following table carefully and answer the questions given below it:

Number of candidates from different locations appeared and passed in a competitive examination over the years

Year	Rural		Semi urban		State capitals		Metropolitan
Year	App.	Pass.	App.	Pass.	App.	Pass.	App.	Pass.
2001	2153	932	8139	2468	7164	3248	9695	6328
2002	4915	1658	9784	4015	8529	3628	12518	6038
2003	1652	208	9432	3528	11725	4526	9538	3214
2004	5628	2392	7894	2513	5054	1468	10158	4018
2005	1839	317	9969	4263	8258	3159	11247	5158
2006	5032	1798	8562	2933	9015	4311	13624	6419

Note: App. → Appeared, Pass. → Passed

Q1. In 2005, what was the average number of failed candidates from all locations ?

(a) 4436

(b) 4894

(d) 4604

(e) None of these

Q2. What percentage of candidates passed from semi-urban location in all the 6 years ?

(a) 41.94

(b) 36.67

(d) 33.67

(e) 38.24

Q3. The total number of failed candidates in 2004, 2005 and 2006 from state-capital location is what percent more/less than failed candidates in 2001, 2002 and 2003 from Rural location ?

(a) 126.09% more

(b) 93.07% more

(d) 112.35% more

(e) 22.32% more

Q4. In which year, percentage of failed candidates was least from metropolitan location ?

(a) 2004

(b) 2006

(d) 2005

(e) 2002

Q5. What is approximate ratio of passed candidates in 2003 from rural location to the percentage of passed candidates in 2006 from state-capital location ?

(a) 53 : 173

(b) 131 : 237

(d) 61 : 39

(e) 63 : 239

Directions (6-10): Read the following information carefully and answer the questions based on it :

In 6 years, number of students taking admission and leaving from five different schools are given below:–

School →	A		B		C		D		E
Years↓	Ad.	L	Ad.	L	Ad.	L	Ad.	L	Ad.	L
1994	1025	—	950	—	1100	—	1500	—	1450	—
1995	230	120	350	150	320	130	340	150	250	125
1996	190	110	225	115	300	150	300	160	280	130
1997	245	100	185	110	260	125	295	120	310	120
1998	280	150	200	90	240	140	320	125	340	110
1999	250	130	240	120	310	180	360	140	325	115

Note: Ad→ admitted,

L → Left

Q6. What is the average number of student studying in all the five schools in 1996 ?

(a) 1278

(b) 1494

(d) 1452

(e) None of these

Q7. What is the number of students studying in school D in 1998 ?

(a) 2200

(b) 2600

(d) 2250

(e) None of these

Q8. Number of students leaving school C from the year 1994-1999 is approximately what percentage of students taking admission in same school in same years ?

(a) 27.87 %

(b) 26.39 %

(d) 28.65 %

(e) 29.34 %

Q9. Number of students taking admission between years 1995-1999 in school D is approximately what percent more/less than student admitted in school B in same years ?

(a) 29.13% less

(b) 35.50% more

(d) 33.73% less

(e) 34.58% more

Q10. What is ratio of number of students in C in 1999 and number of students in E in 1998 ?

(a) 429 : 123

(b) 123 : 127

(d) 17 : 97

(e) None of these

Directions (11-15): What will come in place of the question mark (?) in the following question ?