divelab/Sys2Bench huggingface dataset:
Question: Jill has 21 gallons of water stored in quart, half-gallon, and one gallon jars. She has equal numbers of each size jar holding the liquid. What is the total number of water filled jars?
Options:
A)3
B)6
C)9
D)36
E)14
Rationale: Let the number of each size of jar = wthen 1/4w + 1/2w + w = 21 1 3/4w = 21w=12The total number of jars = 3w =36Answer: D
Answer: D
Question: There are 10 magazines lying on a table; 6 are sports magazines and the other 4 are current affairs magazines. If 4 magazines are to be selected at random from the 10 magazines, what is the probability that at least one of the current affairs magazines will be selected?
Options:
A)2/5
B)3/5
C)4/5
D)6/5
E)7/5
Rationale: Total probability=10C4=210
4C4 +4C3*6C1+4C2*6C2+4C1*6C3=1+24+21+80=126
therefore the probability that at least one of the current affairs magazines will be selected= 126/210=3/5
answer is B
Answer: B
Question: 5a=15625. Find 5a-3
Options:
A)125
B)228
C)270
D)778
E)101
Rationale: ANSWER : A
Answer: A
Question: A factory has a fixed cost of $41,000 a month, and a cost of $2.5 for every item produced. If the selling price of a single item is $5, what is the number of items must be sold monthly for the factory to cover its cost exactly?
Options:
A)9,000
B)14,000
C)16,400
D)22,500
E)27,000
Rationale: selling price - Cost price = 2.5 so per unit profit =2.5
cost to recover =41000
no of items required = 41000/2.5 = 16400
Answer: C
Answer: C
Question: You are renting an apartment and you need √729 for each side, how many feet are you looking to measure?
Options:
A)21
B)22
C)23
D)24
E)27
Rationale: Try filling the numbers into the answer y x y =
Find the closest to 729
Answer E
Answer: E
Question: Find the area of trapezium whose parallel sides are 20 cm and 10 cm long, and the distance between them is 10 cm.
Options:
A)187 cm2
B)185 cm2
C)150 cm2
D)185 cm2
E)195 cm2
Rationale: Explanation:
Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them) = 1/2 (20 + 10) * (10) = 150 cm2
Answer: Option C
Answer: C
Question: A cyclist covers a distance of 750 m in 2 min 30 sec. What is the speed in km/hr of the cyclist?
Options:
A)5 km/hr
B)6 km/hr
C)12 km/hr
D)17 km/hr
E)18km/hr
Rationale: Speed = { 750 } m/sec =5 m/sec = { 5 * 18 } km/hr =18km/hr
Ans: E
Answer: E
Question: The perimeter of a rhombus is 68 cm and one of its diagonals is 16 cm. Find its area?
Options:
A)260 cm2
B)240 cm2
C)280 cm2
D)220 cm2
E)250 cm2
Rationale: 4a = 68 => a = 17
172 – 82 = 152
1/2 * 16 * 30 = 240
ANSWER:B
Answer: B
Question: The ratio of investments of A, B and C is 5:6:7. If they share the profit in the ratio of 5:9:14, then find the ratio of their periods of investments.
Options:
A)2:3:4
B)3:5:6
C)3:2:4
D)2:4:3
E)2:5:3
Rationale: The ratio of investments of A, B and C is 5:6:7.
The ratio of shares of A, B and C is 5:9:14.
Therefore, Ratio of their periods of investments is
(5/5) : (9/6) : (14/7) = 1:3/2:2 = 2:3:4.
ANSWER:A
Answer: A
Question: In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected?
Options:
A)159
B)194
C)210
D)209
E)166
Rationale: Out of 10 students 4 children should to be selected.
So the combination will be 10C4.
10C4=10!/6!*4!=10*9*8*7*6!/6!*(4*3*2*1)
10C4=210
There are 210 differect possible ways to select 4 children out of 10 students.
Answer: C
Question: A certain meter records voltage between 0 and 10 volts inclusive. If the average value of 3 recordings on the meter was 9 volts, what was the smallest possible recording in volts?
Options:
A)2
B)3
C)4
D)5
E)7
Rationale: if average of 3 is 9 so sum of 3 should be 27
3 recording can be from 0-10 inclusive
to find one smallest other two should be highest
so, lets assume three var are a,b,c
say a is smallest and give b and c greatest readings say 10 and 10
so a has to be 7
E
Answer: E
Question: At Jerri’s Pet Shop, 60 cups of bird seed are used every 5 days to feed 20 parakeets. How many cups of bird seed would be required to feed 10 parakeets for 5 days?
Options:
A)45.6
B)20
C)9
D)30
E)65
Rationale: Let's go step-by-step.
60 cups are used over a 5 day period, which means 12 cups a day. This feeds 20 parakeets, which means each parakeet needs .60 of a cup every day.
For 10 parakeets, we need 10*.60cups = 6 cups a day. Over 5 days, we need 30 cups. Choice D.
Answer: D
Question: Which of the following must be subtracted from 2^48 so that the resulting integer will be a multiple of 3?
Options:
A)2
B)1
C)3
D)4
E)5
Rationale: {4^1} / 3 =4/3 remainder 1
{4^2} / 3 = 16/3 remainder 1
{4^3} / 3 = 64/3 remainder 1
{4^4} / 3 = 256/3 remainder 1
Actually the same remainder keeps repeating .....
Try with a diff no, say 2
{2^1}/3 = remainder 2
{2^2}/3 = remainder 1
{2^3}/3 = remainder 2
{2^4}/3 = remainder 1
Answer : B
Answer: B
Question: Three persons invested Rs.9000 in a joint business. The second person invested Rs.1000 more than the first and the third Rs.1000 more than second. After two years, they gained Rs.5400. How much third person will get?
Options:
A)2400
B)2408
C)2487
D)2429
E)2123
Rationale: First persons investment = x
Second persons investment = x + 1000
Third persons investments = x + 2000
x + x + 1000 + x + 2000 = 9000
3x = 6000
x = 2000
Ratio = 2000 : 3000 : 4000
2:3:4
4/9 * 54000 = 2400
Answer:A
Answer: A
Question: A, B and C start at the same time in the same direction to run around a circular stadium. A completes a round in 252 seconds, B in 308 seconds and c in 198 seconds, all starting at the same point. After what time will they again at the starting point ?
Options:
A)26 minutes and 18 seconds
B)45 minutes
C)42 minutes and 36 seconds
D)46 minutes and 12 seconds
E)48minutes and 15 seconds
Rationale: L.C.M. of 252, 308 and 198 = 2772.
So, A, B and C will again meet at the starting point in 2772 sec. i.e., 46 min. 12 sec.
answer :D
Answer: D
Question: What is the greatest number of four digits which is divisible by 15, 25, 40 and 75 ?
Options:
A)9800
B)9600
C)9400
D)9200
E)9000
Rationale: Greatest number of four digits = 9999
LCM of 15, 25, 40 and 75 = 600
9999 ÷ 600 = 16, remainder = 399
Hence, greatest number of four digits which is divisible by 15, 25, 40 and 75
= 9999 - 399 = 9600
Answer: Option B
Answer: B
Question: If the average (arithmetic mean) of (2a+16) and (3a-8) is 69, what is the value of a?
Options:
A)26
B)30
C)28
D)36
E)42
Rationale: ((2a+16) + (3a-8)) / 2 = (5a+8)/2 = 69
a= 26
The answer is A.
Answer: A
Question: Two trains, each 100 m long, moving in opposite directions, cross other in 5 sec. If one is moving twice as fast the other, then the speed of the faster train is?
Options:
A)22
B)96
C)60
D)88
E)12
Rationale: Let the speed of the slower train be x m/sec.
Then, speed of the train = 2x m/sec.
Relative speed = ( x + 2x) = 3x m/sec.
(100 + 100)/5 = 3x => x = 40/3.
So, speed of the faster train = 80/3 = 80/3 * 18/5 = 96 km/hr.
Answer:B
Answer: B
Question: 1, 0.2, 0.08, 0.48, 0.0384, ____
Options:
A)0.0584
B)0.0484
C)0.0434
D)0.0384
E)None
Rationale: 1, 0.2, 0.08, 0.48, 0.0384, .....
1*0.2=0.2
0.2*0.4=0.08
0.08*0.6=0.048
0.048*0.8=0.0384
So 0.0384*1=0.0384
ANSWER:D
Answer: D
Question: The weights of three boys are in the ratio 4 : 5 : 6. If the sum of the weights of the heaviest and the lightest boy is 45 kg more than the weight of the third boy, what is the weight of the lightest boy?
Options:
A)32 kg
B)36 kg
C)40 kg
D)44 kg
E)None of these
Rationale: Let the weights of the three boys be 4k, 5k and 6k respectively.
4k + 6k = 5k + 45
=> 5k = 45 => k = 9
Therefore the weight of the lightest boy
= 4k = 4(9) = 36 kg.
ANSWER:B
Answer: B
Question: A set of numbers has the property that for any number t in the set, t + 2 is in the set. If -1 is in the set, which of the following must also be in the set?
I. 1
II. -4
III. 5
Options:
A)I only
B)II only
C)I and III only
D)II and III only
E)I, II, and III
Rationale: The question is which of the following must be in the set, not could be in the set.
If -1 is in the set so must be -1+2=1, as 1 is in the set so must be 1+2=3, as 3 is in the set so must be 3+2=5 and so on. So basically knowing that -1 is in the set we can say that ALL odd numbers more than -1 are also in the set.
Answer: C.
Answer: C
Question: Two vessels P and Q contain 62.5% and 87.5% of alcohol respectively. If 2 litres from vessel P is mixed with 4 litres from vessel Q, the ratio of alcohol and water in the resulting mixture is?
Options:
A)19 : 9
B)19 : 1
C)19 : 2
D)19 : 5
E)19 : 3
Rationale: Explanation:
Quantity of alcohol in vessel P = 62.5/100 * 2 = 5/4 litres
Quantity of alcohol in vessel Q = 87.5/100 * 4 = 7/2 litres
Quantity of alcohol in the mixture formed = 5/4 + 7/2 = 19/4 = 4.75 litres
As 6 litres of mixture is formed, ratio of alcohol and water in the mixture formed = 4.75 : 1.25 = 19 : 5.
Answer:D
Answer: D
Question: A factory has three types of machines, each of which works at its own constant rate. If 7 Machine As and 11 Machine Bs can produce 470 widgets per hour, and if 8 Machine As and 22 Machine Cs can produce 600 widgets per hour, how many widgets could one machine A, one Machine B, and one Machine C produce in one 8-hour day?
Options:
A)400
B)475
C)550
D)560
E)700
Rationale: Let Machine A produce A widgets per hour. B produce B widgets per hour and C produce C widgets per hour.
7A+11B=470 ---(1)
8A+22C=600 ---(2)
Dividing (2) by 2
4A+11C=300.....(3)
Adding (1)(3)
11A+11B+11C = 770
A+B+C=70 per hour
So for eight hrs = 70*8 = 560 = Answer = D
Answer: D
Question: The length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 625 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 8 units?
Options:
A)140 sq.units
B)158 sq.units
C)187 sq.units
D)80 sq.units
E)815 sq.units
Rationale: Given that the area of the square = 625 sq.units
=> Side of square = √625 = 25 units
The radius of the circle = side of the square =25 units
Length of the rectangle = 2/5 * 25 = 10 units
Given that breadth = 8 units
Area of the rectangle = lb = 10 * 8 = 80 sq.units
Answer: D
Answer: D
Question: If the a radio is sold for rs 490 and sold for rs 465.50.find loss%.
Options:
A)2
B)4
C)3
D)5
E)6
Rationale: sol. cp=rs490,sp= 465.50.
loss=rs(490-465.50)=rs 24.50.
loss%=[(24.50/490)*100]%=5%
Option D
Answer: D
Question: 120 liters of a mixture contains milk and water in the ratio 4:2. If 10 liters of this mixture be replaced by 10 liters of milk, the ratio of milk to water in the new mixture would be?
Options:
A)8:6
B)9:3
C)9:4
D)9:6
E)8:2
Rationale: Quantity of milk in 120 liters if mix = 120*4/6 =80 liters
Quantity of milk in 130 liters of new mix = 80+10 = 90liters
Quantity of water in it = 130-90 = 40 liters
Ratio of milk and water in new mix = 90:40 = 9:4
Answer is C
Answer: C
Question: What is the sum of 80 consecutive integers from -39 inclusive, in a increasing order?
Options:
A)-29
B)39
C)-30
D)40
E)60
Rationale: From -39 to -1 --> 39 nos.
zero --> 1 number
from +1 to +39 --> 39 nos.
When we add up nos. from -39 to +39 sum will be zero. Total 79 nos will be added.
80th number will be 40.
Sum of these 80 nos. = 40.
D is the answer.
Answer: D
Question: Out of 15 students studying in a class, 7 are from Maharashtra, 5 are from Karnataka and 3 are from Goa. Four students are to be selected at random. What are the chances that at least one is from Karnataka?
Options:
A)12⁄13
B)11⁄13
C)10⁄15
D)1⁄15
E)None of these
Rationale: Total possible ways of selecting 4 students out of 15 students = 15C4 = 15×14×13×12 /1×2×3×4=1365
The no. of ways of selecting 4 students in which no student belongs to Karnataka = 10C4
∴ Hence no. of ways of selecting at least one student from Karnataka = 15C4 – 10C4 = 1155
∴ Probability = 1155⁄1365 = 77⁄91 = 11⁄13
Answer B
Answer: B
Question: In a series of six consecutive even numbers, the sum of the third and sixth numbers is 30. What are the third and sixth number respectively?
Options:
A)10,16
B)8,14
C)16,22
D)14,20
E)12, 18
Rationale: Let the numbers be x, x + 2, x + 4, x + 6, x + 8 and x + 10.
Given (x + 4) + (x + 10) = 30
=> 2x + 14 = 30 => x = 8
The third number = x + 4 = 8 + 4 = 12.
The sixth number = x + 10 = 8 + 10 = 18.
Answer: E
Answer: E
Question: Difference between two numbers is 5, six times of the smaller lacks by 6 from the four times of the greater. Find the numbers?
Options:
A)12,7
B)12,9
C)10,5
D)11,6
E)15,4
Rationale: x â€“ y = 5
4x â€“ 6y = 6
x = 12 y = 7
ANSWER A
Answer: A
Question: In a box, there are 5 blue, 8 white and 3 yellow bulbs. One bulb is picked up randomly. What is the probability that it is neither white nor blue?
Options:
A)3/16
B)5/16
C)8/32
D)2/32
E)9/32
Rationale: Total number of bulbs = (5 + 8 + 3) = 16.
Let E = event that the bulb drawn is neither white nor blue = event that the bulb drawn is yellow.
Therefore, P(E)=3/16
ANSWER:A
Answer: A
Question: Find compound interest on Rs. 8000 at 15% per annum for 2 years 4 months, compounded annually
Options:
A)2109
B)3109
C)4109
D)6109
E)1109
Rationale: Time = 2 years 4 months = 2(4/12) years = 2(1/3) years.
Amount = Rs'. [8000 X (1+(15/100))^2 X (1+((1/3)*15)/100)]
=Rs. [8000 * (23/20) * (23/20) * (21/20)]
= Rs. 11109. .
:. C.I. = Rs. (11109 - 8000) = Rs. 3109. Answer: B
Answer: B
Question: If x is the product of the positive integers from 1 to 8, inclusive, and if i, k, m, and p are positive integers such that x=2^i∗3^k∗5^m∗7^p, then i + k + m + p =
Options:
A)4
B)7
C)8
D)11
E)12
Rationale: Here the idea is to go expressing each factor from one to eight, decomposed into its primes:
1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 = 1 * 2 * 3 *(2*2) * 5 +(2*3) * 7 *(2*2*2) = 2 ^ 7 * 3 ^ 2 * 5 ^ 1 * 7 ^ 1
Then
i = 7
k = 2
m = 1
p = 1
i + k + m + p = 11
Correct answer D
Answer: D
Question: There are 14 points in a given plane, no three of which are on the same line. If one of the points is represented as 'A', then how many triangles can be determined with the 14 points that contain the point A?
Options:
A)78
B)105
C)182
D)210
E)455
Rationale: Any 2 points out 13 points will create triangle with third point A, so the answer is 13C2=78.
Answer: A.
Answer: A
Question: Two trains 121 meters and 165 meters in length respectively are running in opposite directions, one at the rate of 80 km and the other at the rate of 65 kmph. In what time will they be completely clear of each other from the moment they meet?
Options:
A)7.18
B)7.12
C)7.16
D)7.15
E)7.11
Rationale: T = (121 + 165)/ (80 + 65) * 18/5
T = 7.15
Answer:D
Answer: D
Question: The ratio between the present ages of A and B is 4.5:3 respectively. The ratio between A's age 4 years ago and B's age 4 years hence is 1:1. What is the ratio between A's age 4 years hence and B's age 4 years ago?
Options:
A)3:4
B)3:0
C)3:1
D)7:3
E)3:7
Rationale: Let the present ages of A and B be 4.5x and 3x years respectively.
Then, (4.5x - 4)/(3x + 4) = 1/1
1.5x = 8 => x = 5.33
Required ratio = (5x + 4):(3x - 4) = 28:12 = 7:3.Answer: D
Answer: D
Question: The area of a square is 4225 sq cm. Find the ratio of the breadth and the length of a rectangle whose length is twice the side of the square and breadth is 24 cm less than the side of the square.
Options:
A)5:28
B)5:19
C)5:12
D)5:13
E)41:130
Rationale: Let the length and the breadth of the rectangle be l cm and b cm respectively. Let the side of the square be a cm.
a2 = 4225
a = 65
L = 2a and b = a - 24
b : l = a - 24 : 2a = 41 : 130
Answer:E
Answer: E
Question: In a mixture of milk and water, the proportion of milk by weight was 80%. If, in a 180 gm mixture, 36 gms of pure milk is added, what would be the percentage of milk in the mixture formed?
Options:
A)83.37%
B)83.93%
C)83.38%
D)83.23%
E)83.33%
Rationale: Percentage of milk in the mixture formed
= [80/100 (180) + 36] / (180 + 36) * 100% = (144 + 36)/216 * 100%
= 5/6 * 100% = 83.33%.
Answer:E
Answer: E
Question: The average of 10 numbers is zero. Of them, How many of them may be greater than zero, at the most?
Options:
A)6
B)7
C)10
D)8
E)9
Rationale: Average of 10 numbers = 0
=> Sum of 10 numbers/10=0
=> Sum of 10 numbers = 0
Hence at the most, there can be 9 positive numbers.
(Such that if the sum of these 9 positive numbers is x, 10th number will be -x)
ANSWER:E
Answer: E
Question: By selling an article at Rs.500, a shopkeeper makes a profit of 25%. At what price should he sell the article so as to make a loss of 25%?
Options:
A)s.600
B)s.480
C)s.300
D)s.450
E)s.550
Rationale: SP = 500
Profit = 25%
CP = (SP)*[100/(100+P)]
= 500 * [100/125]
= 400
Loss = 25% = 25% of 400 = Rs.100
SP = CP - Loss = 400 - 100 = Rs.300
ANSWER:C
Answer: C
Question: What percent is 50 gm of 1 kg?
Options:
A)1.5 %
B)0.5 %
C)2.5 %
D)3.5 %
E)5 %
Rationale: 1 kg = 1000 gm
50/1000 × 100 = 5000/1000
=5/1 = 5 %
E)
Answer: E
Question: A certain bus driver is paid a regular rate of $16 per hour for any number of hours that does not exceed 40 hours per week. For any overtime hours worked in excess of 40 hours per week, the bus driver is paid a rate that is 75% higher than his regular rate. If last week the bus driver earned $920 in total compensation, how many total hours did he work that week?
Options:
A)36
B)40
C)44
D)50
E)52
Rationale: For 40 hrs = 40*16=640
Excess = 920-640=280
For extra hours =.75(16)=12+16=28
Number of extra hrs =280/28=70/7=10
Total hrs =40+10=50
Answer D 50
Answer: D
Question: A and B started a business investing Rs. 90,000 and Rs 30,000 respectively. In what ratio the profit earned after 2 years be divided between A and B respectively?
Options:
A)9:2
B)3:1
C)18:20
D)18:4
E)17:4
Rationale: A: B = 90000 : 30000
= 9 : 3
= 3 : 1
ANSWER:B
Answer: B
Question: x varies inversely as square of y. Given that y=3 for x=1. The value of x for y = 4 will be equal to:
Options:
A)3
B)6
C)1/9
D)1/3
E)9/16
Rationale: Explanation :
Solution: Given x = k/y^2, where k is constant. Now, y=3 and x =1 gives k = 9.
.'. x = 9/y^2
=> x =9 /4^2 = 9/16
Answer : E
Answer: E
Question: The true discount on a bill due 9 months hence at 16% per annum is Rs. 198.The amount of the bill is
Options:
A)Rs. 1386
B)Rs. 1764
C)Rs. 1650
D)Rs. 2268
E)None of these
Rationale: Solution
32.5
Let P.W. be Rs. x.Then,S.I. on Rs.x at 16% for 9 months =Rs.198.
∴ x 16 x9/ 12x 1/100}= 198 or x = 1650.
∴ P.W. = Rs. 1650.
Answer C
Answer: C
Question: What is the next number in the sequence : 14,19,29,40,44,52,59,73 __?
Options:
A)90
B)85
C)81
D)85
E)83
Rationale: next no. = previous + (sum of digits)
14 + (1+4) = 19
19 + (1+9) = 29
29 + (2+9) = 40
40 + (4+0) = 44
44 + (4+4) = 52
52 + (5+2) = 59
59 +(5+9) = 73
73 + (7+3) = 83
ANSWER:E
Answer: E
Question: A person starts writing all 4 digit numbers .How many times had he written the digit 3?
Options:
A)3700
B)3800
C)3900
D)4000
E)4100
Rationale: _ _ _ 3 = 9*10*10
_ _ 3 _ = 9*10*10
_ 3 _ _ = 9*10*10
3 _ _ _ = 10*10*10
900+900+900+1000=3700
ANSWER:A
Answer: A
Question: The salaries of A, B and C are in the ratio 1:3:4. If the salaries are increased by 5%, 10% and 15% respectively, then the increased salaries will be in the ratio
Options:
A)20:66:95
B)21:66:96
C)21:66:92
D)19:66:92
E)None
Rationale: Solution: Let A's Salary = Rs. 100
Then, B's Salary = Rs. 300
And, C's Salary = Rs 400
Salary has given in 1:3:4 ratio.
Now,
5% increase in A's Salary,
A's new Salary = (100 + 5% of 100) = Rs. 105.
B's Salary increases by 10%, Then,
B's new Salary = (300 + 10% of 200) = Rs. 330.
C's Salary increases by 15%,
C's new Salary = (400 + 15% of 400) = Rs. 460.
Then, ratio of increased Salary,
A:B:C = 105:330:460 = 21:66:92.
Alternative
100(A's salary)===5%↑===> 105(A's increased salary);
300 (B's salary)===10%↑===>330 (B's increased salary);
400 (C's salary)===15%↑===> 460 (C's increased salary).
Ratio of their increased salary = 105:330:480 = 21:66:92
Answer: Option C
Answer: C
Question: If the average (arithmetic mean) of a and b is 45 and the average of b and c is 50, what is the value of c âˆ’ a?
Options:
A)25
B)10
C)90
D)14
E)It cannot be determined from the information given
Rationale: the arithmetic mean of a and b =(a+b)/2=45 -- a+b=90 --1
similarly for b+c=100 --2
subtracting 1 from 2 we have
c-a=10;
ANSWER:B
Answer: B
Question: A motorcyclist goes from Bombay to Pune, a distance of 192 kms at an average of 32 kmph speed. Another man starts from Bombay by car 2 ½ hours after the first, and reaches Pune ½ hour earlier. What is the ratio of the speed of the motorcycle and the car?
Options:
A)1:2
B)1:8
C)1:1
D)1:6
E)1:3
Rationale: T = 192/32 = 6 h
T = 6 - 3 = 3
Time Ratio = 6:3 = 2:1
Speed Ratio = 1:2
Answer: A
Answer: A
Question: Find the least value of 'a' so that 365a16 is divisible by 8.
Options:
A)9
B)8
C)0.
D)2
E)1
Rationale: Explanation:
Given, number is divisible by 8 only if 'a16' is divisible by 8.
.: Least value of a is '0'.
Answer: Option C
Answer: C
Question: A mixture contains milk and water in the ratio 5:2. On adding 10 liters of water, the ratio of milk to water becomes 5:3. The quantity of milk in the original mixture is?
Options:
A)30
B)40
C)50
D)60
E)70
Rationale: milk:water = 5:2
5x : 2x + 10 = 5 : 3
3[5x] = 5[2x + 10]
15x = 10x + 50
15x - 10x = 50
x = 10
The quantity of milk in the original mixture is = 5 : 2 = 5 + 2 = 7
7x = 70
Short cut method:
milk:water = 5 :2
after adding 10 liters of water
milk:water = 5 :3
milk is same but water increse 10liters then the water ratio is increse 1 parts
1 part -----> 10 liters
The quantity of milk in the original mixture is = 5 : 2 = 5 + 2 = 7
7 parts -----> 70 liters (Answer is = 70)
Short cut method - 2 : for Only milk problems
milk : water
5 : 2
5 : 3
milk ratio same but water ratio 1 part incress per 10 liters
1 part of ratio -------> 10 liters
7 part of ratio -------> 70 liters
C)
Answer: C
Question: If x,y ,and z are positive real numbers such that x(y+z) = 132, y(z+x) =152 , and z(x+y) = 180, then xyz is
Options:
A)40
B)60
C)160
D)100
E)120
Rationale: xy+xz = 132 --------------------------------------1)
yz+yx = 152---------------------------------------2)
xz+zy = 180---------------------------------------3)
Re-writing equation 3 as follows:
xz+zy = 152 + 28
xz+zy = yz+yx + 28
xz = yx + 28 ............... (4)
Adding (1)(4)
2xz = 160
xz = 80
xyz has to be multiple of 80,only 160 fits in
Answer = C
Answer: C
Question: One-third of Rahul’s savings in National Savings Certificate is equal to one-half of his savings in Public Provident Fund. If he has Rs. 2,00,000 as total savings, how much has he saved in Public Provident Fund ?
Options:
A)Rs. 30,000
B)Rs. 50,000
C)Rs. 80,000
D)Rs. 90,000
E)None
Rationale: EXPLANATION
Let savings in N.S.C and P.P.F. be Rs. x and Rs. (200000 – x) respectively. Then,
1/3x=1/2(200000-x)
=> x/3 + x/2 = 100000
=> 5x/6 = 100000
=> x= 100000 x 6 /5= 120000
Savings in Public Provident Fund = Rs. (200000 – 120000) = Rs. 80000
Answer C
Answer: C
Question: A shop sells floor tiles at Rs 48 per square meter. A building contractor employs a machine that polishes the tiles that damages 10% of the total number of tiles which cannot be used any more. Calculate the amount that needs to be paid by contractor to tile shop owner, if the hall is of a square shape and has a perimeter of 400 meters?
Options:
A)Rs 4,00,000
B)Rs 5,00,000
C)Rs 5,28,000
D)Rs 3,65,000
E)Rs 3,75,000
Rationale: 4 sides of a square then 400/4=100
area of the hall 100*100=10000
10% damaged so 10000*110/100=11000
48 per square meter then 48*11000=528000
ANSWER:C
Answer: C
Question: In what ratio must the rice at Rs.3.20/kg be combined with rice at Rs.2.90/kg so that the combination becomes of worth Rs.3.08/kg ?
Options:
A)3:2
B)5:3
C)7:3
D)7:5
E)8:5
Rationale: Explanation :
Given
i. C.P of a kg quantity of I kind (p) = 3.20
ii. C.P of a kg quantity of II kind (p) = 2.90
iii. Mean rice price (p) = 3.08
iv. d – m = 3.08 – 2.90 = 0.18
v. m – c = 3.20 – 3.08 = 0.12
Therefore, Needed ratio = 0.18 : 0.12 = 3 : 2
Answer : A
Answer: A
Question: 1/3th of the passengers got down at first stop and 30 people got into the bus, 1/4th of the passengers got down at second stop and 12 people got into the bus.In last stop 84 people got down from the bus. What is the initial capacity of the bus?
Options:
A)98
B)99
C)97
D)96
E)95
Rationale: Let x be the no of initial passenger
no of passengr left in 1st stop (2x/3)+30
no of passenger in the 2nd stop 3/4((2x/3)+30) + 12
which is equal to 84 (passngr on last stop)
so final eqn....3/4((2x/3)+30) + 12 = 84
Ans x = 99
ANSWER:B
Answer: B