divelab/Sys2Bench huggingface dataset:
Question: George baked a total of 75 pizzas for 7 straight days, beginning on Saturday. He baked 3/5 of the pizzas the first day, and 3/5 of the remaining pizzas the second day. If each successive day he baked fewer pizzas than the previous day, what is the maximum number of pizzas he could have baked on Wednesday?
Options:
A)5
B)4
C)2
D)6
E)7
Rationale: 3/5 of the 75 pizzas cooked on Saturday = 45 pizzas
3/5 of the remaining pizzas on Sunday = 18 pizzas
We're left with (75-45-18) =12 pizzas for the remaining 5 days. The prompt tells us that each day has FEWER pizzas than the day before it, so we can't have duplicate numbers.
M T W TH F
5 4 2 1 0 =12
W=2
C
Answer: C
Question: A wheel has a diameter of x inches and a second wheel has a diameter of y inches. The second wheel covers a distance of d feet in 400 revolutions. How many revolutions does the first wheel make in covering d feet?
Options:
A)400xy
B)400y - x
C)400x - y
D)400y/x
E)400x/y
Rationale: second Wheel with diameter x inches ----> So the circumference = x*pi --------- (1)
first Wheel with diameter y inches ----> So the circumference = y*pi --------- (2)
Revolutions = distance/circumference
So, from equation (1)
400 = d/(x*pi)
d = 400 * x * pi ---------- (3)
From equation (2)
Revolutions = d/(y*pi) = (400 * x * pi) / (y*pi) = 400x/y
Answer (E)
Answer: E
Question: One half of the people at the game wore the team colors. Two thirds of those people wore team
hats as well. One fourth of those with team colors and team hats had banners to wave.
Twenty five people had team colors and banners, but no hats. One hundred people had only
banners. If there were 1824 people at the game, how many had banners?
Options:
A)177
B)277
C)377
D)477
E)577
Rationale: 1/2 x 1824 = 912 with team colors
2/3 x 912 = 608 with hats and colors
1/4 x 608 = 152 with hats, colors, and banners
152 + 100 + 25 = 277 with banners
correct answer B
Answer: B
Question: Dany bought a total of 20 game cards some of which cost $0.25 each and some of which cost $0.15 each. If Dany spent $4.2 to buy these cards, how many cards of each type did he buy?
Options:
A)4
B)10
C)7
D)8
E)12
Rationale: Let X be the number of cards that cost $0.25 each and Y the number of cards that cost $0.15 each. The total number of cards is 20. Hence
X + Y = 20
If X is the number of cards at $0.25, then the X cards cost
0.25 X
If Y is the number of cards at $0.15, then the Y cards cost
0.15 Y
The total cost of the X cards and the the Y cards is known to be $4.2 and also given by
0.25 X + 0.15 Y = 4.2
We now need to solve the system of equations
X + Y = 20
0.25 X + 0.15 Y = 4.2
The first equation gives Y = 20 - X. Substitute y by 20 - x in the second equation and solve
0.25 X + 0.15 (20 - X) = 4.2
X(0.25 - 0.15) + 3 = 4.2
0.1 X = 1.2
X = 12 and Y = 20 - 12 = 8
correct answer D
Answer: D
Question: 36 men can complete a piece of work in 18 days.In how days will 27 men can complete the work?
Options:
A)18
B)20
C)17
D)24
E)21
Rationale: Let the required number of days be x
Less men,more days(indirect proportion)
27:36::18:x
27x=36*18
x=(36*18)/27
x=24 days
option is D
Answer: D
Question: Kunal electronic services assemble computers. Over a period of time the engineers made the following observation regarding the two vital components - the USB port and CD drive. The probability that USB port is defective is 0.1, that both the USB port and CD drive are defective is 0.02, while the probability that only the CD drive is defective is 0.03 . The probability that the USB port is defective when the CD drive has been found to be defective is?
Options:
A)0.2
B)0.3
C)0.25
D)0.4
E)0.6
Rationale: Explanation :
USB Defective	USB OK	Total
CD Defective	0.02	0.03	(0.05)
CD OK	(0.08)	(0.87)
(0.95)
Total	0.1	(0.9)
The figures enclosed in brackets follow as conclusions. The probability that USB part is defective, when the CD drive is found to be defective is 0.02/0.02+0.03 = 2/5 = 0.40
Answer : D
Answer: D
Question: In a simultaneous throw of a pair of dice, find the probability of getting a total more than 4
Options:
A)1/2
B)7/12
C)5/13
D)5/12
E)1/3
Rationale: Total number of cases = 3*3 = 9
Favourable cases = [(2,3),(3,2),(3,3)] = 3
So Probability = 3/9 = 1/3
Answer is E
Answer: E
Question: At an elementary school, 70% of the faculty members are women and 60% of the faculty members are married. If 2⁄3 of the men are single, what fraction of the men are married?
Options:
A)5⁄7
B)7⁄10
C)1⁄3
D)7⁄30
E)5⁄70
Rationale: --------------------M------W--------Total
Marrried----------10-----50---------60
Not married-----20-----20---------40
Total-------------30-----70--------100
need married man/total man, so 10/30=1/3
C
Answer: C
Question: Find out the wrong number in the series.
6, 12, 48, 94, 384, 768, 3072
Options:
A)768
B)384
C)94
D)488
E)12
Rationale: Each even term of the series is obtained by multiplying the previous term by 2.
2nd term = (1st term) x 2 = 6 x 2 = 12
4th term = (3rd term) x 2 = 48 x 2 = 96.
6th term = (5th term) x 2 = 384 x 2 =768.
4th term should be 96 instead of 94.
ANSWER:C
Answer: C
Question: A team bought a total of 472 balls. If each player on the team bought at least 19 balls, then what is the greatest possible number of players on the team?
Options:
A)21
B)22
C)23
D)24
E)25
Rationale: 472/19=24 plus remainder.
The answer is D.
Answer: D
Question: What percent of 12.4 kg is 20 gms ?
Options:
A)25
B)16
C)18
D)19
E)17
Rationale: Explanation:
Required percentage = (20/12400 * 100)% = 4/25% = 0.16%
Answer: B) .16%
Answer: B
Question: A cube of side one meter length is cut into small cubes of side 10 cm each. How many such small cubes can be obtained?
Options:
A)10
B)100
C)1000
D)10000
E)None of these
Rationale: Along one edge, the number of small cubes that can be cut
= 100/10 = 10
Along each edge 10 cubes can be cut. (Along length, breadth and height). Total number of small cubes that can be cut = 10 * 10 * 10 = 1000
ANSWER:C
Answer: C
Question: Of the following, which is greater than Â½ ?
Indicate ALL such fractions.
Options:
A)4/0
B)4/7
C)4/2
D)4/1
E)4/8
Rationale: Explanation:
One way to deal with fractions is to convert them all to decimals.
In this case all you would need to do is to see which is greater than 0.5.
Otherwise to see which is greater than Â½, double the numerator and see if the result is greater than the denominator. In B doubling the numerator gives us 8, which is bigger than 7.
Answer: B
Answer: B
Question: Find the simple interest on Rs.350 for 10 months at 5 paisa per month?
Options:
A)277
B)175
C)288
D)266
E)121
Rationale: I = (350*10*5)/100 = 175
Answer: B
Answer: B
Question: The average of four positive integers is 69. The highest integer is 93 and the least integer is 39. The difference between the remaining two integers is 28. Which of the following integers is the higher of the remaining two integers?
Options:
A)76
B)86
C)56
D)45
E)17
Rationale: Let the four integers be A, B, C and D where A > B > C > D.
(A + B + C + D)/4 = 69 => A + B + C + D = 276 ---> (1)
A = 93, D = 39 and B - C = 28
(1) => B + C = 276 - (A + D) = 276 - 132 = 144.
B + B -28 = 144
B = (144 + 28)/2 = 86
Answer: B
Answer: B
Question: A train having a length of 240 m passes a post in 24 seconds. How long will it take to pass a platform having a length of 620 m?
Options:
A)120 sec
B)99 sec
C)89 sec
D)86 sec
E)85 sec
Rationale: Explanation:
v = 240/24 (where v is the speed of the train) = 10 m/s
t = (240+620)/10 = 86 seconds
Answer: Option D
Answer: D
Question: How many integers between 1 and 1,400 are divisible by 25, and 35?
Options:
A)4
B)5
C)6
D)7
E)8
Rationale: LCM of the given numbers
=175
Therefore , number of integers = 1400/175
=8
Answer is Option E
Answer: E
Question: A cistern 8 meters long and 4 meters wide contains water up to a depth of 1 meter 25 cm. What is the total area of the wet surface?
Options:
A)40
B)48
C)54
D)62
E)76
Rationale: Area of the wet surface = [2(lb + bh + lh) - lb]
= 2(bh + lh) + lb
= [2 (4 x 1.25 + 8 x 1.25) + 8 x 4]
= 62
The answer is D.
Answer: D
Question: Anand and Deepak started a business investing Rs. 21,000 and Rs. 35,000 respectively. Out of a total profit of Rs. 13,800, Deepak's share is?
Options:
A)2777
B)2888
C)8625
D)2885
E)2781
Rationale: Ratio of their shares = 21000 : 35000 = 3:5
Deepak's share = 13800 * 5/8 = Rs. 8625.
Answer: C
Answer: C
Question: A coin is tossed six times. What is the probability that there is at the least one tail?
Options:
A)63/64
B)31/64
C)31/67
D)31/64
E)63/31
Rationale: Let P(T) be the probability of getting least one tail when the coin is tossed six times.
= There is not even a single tail.
i.e. all the outcomes are heads.
= 1/64 ; P(T) = 1 - 1/64
= 63/64
Answer: A
Answer: A
Question: Camel and carriage for Rs. 5000. He SP the camel at a gain of 20% and the carriage at a loss of 10%. If he gains 3% on the whole, then find the CP of the camel?
Options:
A)Rs.2166.67
B)Rs.2187.67
C)Rs.2188
D)Rs.2200
E)Rs.2234.7
Rationale: Now, in this numerical, there is no common loss and gain %.
Hence, solve it making equations.
Let cost price of camel be x.
As cost of camel and carriage = Rs 5000
Cost of carriage = Rs. (5000 – x)
After selling camel he gains 20% and on carriage a loss of 10%. But on the whole he gains 3%.
Therefore,
20% of x – 10 % of (5000 – x) = 3 % of 5000
20 × x – 10 × (5000 – x) = 3 × 5000
100 100 100
x – (5000 – x) = 150
5 10
10x – (5000 – x) × 10 = 150 × 10
5 10
2x-5000+x=1500
3x=1500+5000
x=2166.67
The cost of camel = Rs.2166.67
Option (A) is the correct answer
Answer: A
Question: A 60 kg metal bar made of alloy of tin and silver lost 6 kg of its weight in the water. 10 kg of tin loses 1.375 kg in the water; 5 kg of silver loses 0.375 kg. What is the ratio of tin to silver in the bar?
Options:
A)1/4
B)2/5
C)1/2
D)3/5
E)2/3
Rationale: you can simply use this formula to avoid confusion:
w1/w2 = (A2 - Aavg)/(Avg - A1)
Here is how you will find the values of A1 an A2.
We have an overall loss (average loss). The average loss is 6 kg when 60 kg alloy is immersed.
This is a loss of (6/60)*100 = 10%.
This is Aavg
The loss of tin is 1.375 kg for every 10 kg.
This means it loses (1.375/10)*100 = 13.75% of its weight in water.
This is A1.
The loss of silver is .375 kg for every 5 kg.
This means it loses (.375/5)* 100 = 7.5% of its weight in water.
This is A2.
Weight of Tin/Weight of Silver = (Silver's loss - Avg loss)/(Avg loss - Tin's loss)
X/Y = (7.5 - 10)/(10 - 13.75) = 2/3
E
Answer: E
Question: A contractor undertakes to built a walls in 50 days. He employs 50 peoples for the same. However after 25 days he finds that only 40% of the work is complete. How many more man need to be employed to complete the work in time?
Options:
A)25
B)30
C)35
D)20
E)None of these
Rationale: 50 men complete 0.4 work in 25 days.
Applying the work rule, m1 × d1 × w2 = m2 × d2 × w1
we have,
50 × 25 × 0.6 = m2 × 25 × 0.4
or m2 = 50×25×0.6/25×0.4 = 75 men
AnswerA
Answer: A
Question: In how many ways can a committee of 4 people comprising at least 3 boys be formed using a group of 5 boys and 6 girls?
Options:
A)67
B)64
C)65
D)66
E)None of these
Rationale: There are 2 options: the selected groups have no girls or one girls.
-First case: 1 girl + 3 boys: 6C1 * 5C3 = 6*10 = 60
-Second case: 4 boys: 5C4 = 5
So there are 60 + 5 = 65
ANS:C
Answer: C
Question: Avinash is twice as fast as Bharat, and Bharat is one-third as fast as Chandra. If together they can complete a piece of work in 30 days, in how many days can Avinash, Bharat and Chandra do the work respectively?
Options:
A)90,180,60
B)90,180,68
C)90,180,62
D)90,180,69
E)90,180,61
Rationale: Let Chandra do the work in 2x days.
Bharat can do it in 6x days and Avinash can do it in 3x days.
1/(2x) + 1/(6x) + 1/(3x) = 1/30 => (3 + 1 +2)/6x = 1/30 => x = 30
So, the time taken to complete the work by Avinash, Bharat, Chandra is 90, 180, 60 days respectively.
Answer:a
Answer: A
Question: If the wheel is 14 cm then the number of revolutions to cover a distance of 968 cm is?
Options:
A)A)15
B)B)10
C)C)14
D)D)12
E)E)11
Rationale: 2 * 22/7 * 14 * x = 968 => x = 11
ANSWER:E
Answer: E
Question: A man can row with a speed of 15 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is?
Options:
A)87
B)56
C)20
D)67
E)97
Rationale: M = 15
S = 5
DS = 15 + 5 = 20
Answer: C
Answer: C
Question: Find the average of first 35 natural numbers?
Options:
A)21
B)22
C)23
D)18
E)25
Rationale: Sum of first 100 natural numbers = 35*36/2 = 630Required average = 630/35 = 18Answer is D
Answer: D
Question: The average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 43 kg, then the weight of B is:
Options:
A)17 kg
B)20 kg
C)26 kg
D)31 kg
E)None
Rationale: EXPLANATION
Let A, B, C represent their respective weights. Then, we have:
A + B + C = (45 x 3) = 135 …. (i)
A + B = (40 x 2) = 80 …. (ii)
B + C = (43 x 2) = 86 ….(iii)
Adding (ii) and (iii), we get: A + 2B + C = 166 …. (iv)
Subtracting (i) from (iv), we get : B = 31.
B’s weight = 31 kg.
Answer D
Answer: D
Question: a student got 70% in one subject,80% in other.to get overall 75% how much he should get in third subject.
Options:
A)65%
B)75%
C)85%
D)95%
E)88%
Rationale: Already average of two subjects is (70+80)/2 = 75%
To maintain the percentage at 75%, he shouls get 75% marks in third subject
ANSWER:B
Answer: B
Question: A list of measurements in increasing order is 4, 5, 6, 8, 15 and x. If the median of these measurements is 2/3 times their arithmetic mean, what is the value of x?
Options:
A)20
B)22
C)25
D)28
E)30
Rationale: The median is (6+8)/2 = 7
The mean is (4+5+6+8+15+x)/6 = (38+x)/6
(38+x) /6 * 2/3 = 7
x = 63-38 = 25
The answer is C.
Answer: C
Question: How many seconds will a 500 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
Options:
A)25
B)30
C)40
D)45
E)50
Rationale: Speed of train relative to man = 63 - 3 = 60 km/hr.
= 60 * 5/18 = 50/3 m/sec.
Time taken to pass the man = 500 * 3/50 = 30 sec.
ANSWER:B
Answer: B
Question: The probability of two events A and B are0.25 and 0.40 respectively. The probability that both A and B occur is 0.15. The probability that neither A nor B occur is _________
Options:
A)0.45
B)0.4
C)0.5
D)0.05
E)0.6
Rationale: we are apply that formula..............
P(AorB)=P(A)+P(B)-P(A AND B)
=.25+.40-.15
=.50
but the probability of neither A nor B=1-.50
=0.50
ANSWER:C
Answer: C
Question: For any integer n greater than 1, #n denotes the product of all the integers from 1 to n, inclusive. How many prime numbers Q are there between #6 +2 and #6 +6 , inclusive?
Options:
A)None
B)One
C)Two
D)Three
E)Four
Rationale: None is the answer. A.
Because for every k 6! + k :: k, because 6! :: k, since k is between 2 and 6.A
Answer: A
Question: On selling 11 balls at Rs. 720, there is a loss equal to the cost price of 5 balls. The cost price of a ball is:
Options:
A)s. 45
B)s. 50
C)s. 55
D)s. 60
E)s. 120
Rationale: (C.P. of 11 balls) - (S.P. of 11 balls) = (C.P. of 5 balls)
C.P. of 6 balls = S.P. of 11 balls = Rs.720.
C.P. of 1 ball = Rs.720/6	= Rs. 120.
Answer: Option E
Answer: E
Question: A bucket full of nuts was discovered by the crow living in the basement. The crow eats a fifth of the total number of nuts in 6 hours. How many hours in total will it take the crow to finish a quarter of the nuts?
Options:
A)6.5
B)7.0
C)7.5
D)8.0
E)8.5
Rationale: In one hour, the crow eats 1/30 of the nuts.
(1/4) / (1/30) = 7.5 hours
The answer is C.
Answer: C
Question: What is the probability T of randomly selecting an arrangement of the letters of the wordMEDITERRANEANin which the first letter is E and the last letter is R?
Options:
A)1/13
B)1/20
C)1/26
D)1/50
E)1/100
Rationale: Why do you calculate the total combinations and everything, it is much easier to calculate as follows:
3/13 * 1 * 1 * 1 * 1 ..... * 2/12 = 6/156 = 1/26
This is because 3/13 = Probability that first letter will be E and 2/12 = probability that thefirstletter will be R. Between everything else cuts down to 1*1*1... e.g. probability T of the second letter is 11/11 = 1, > we do not care what's in between.C
Answer: C
Question: A, B and C jointly thought of engaging themselves in a business venture. It was agreed that A would invest Rs. 6500 for 6 months, B, Rs. 8400 for 5 months and C, Rs. 10,000 for 3 months. A wants to be the working member for which, he was to receive 5% of the profits. The profit earned was Rs. 7400. What is the share of B in the profit.
Options:
A)2670
B)2560
C)2440
D)2550
E)2660
Rationale: A is a working member and for that, he receives 5% of the profit
= 5% of 7400 =(5×7400)/100=370
Remaining amount =7400−370=7030
Ratio of their investments
=6500×6:8400×5:10000×3=65×6:84×5:100×3=13×6:84:20×3=13×2:28:20=13:14:10
Share of B in the profit
=7030×14/37=190×14=2660
Answer is E.
Answer: E
Question: The sides of right triangle ABC are such that the length of side AC is 1.25 times the length of side AB, which itself is 4 units more than the length of side BC. If side AC = 20 units, what is the area of the triangle?
Options:
A)144
B)69
C)120
D)160
E)96
Rationale: AC=1.25xAB, 20=1.25xAB, AB=16 units
AB=4+BC, BC=AB-4, BC=16-4=12 units
Area= (AB*BC)/2 = 96
E is the correct option.
Answer: E
Question: Two brothers took the GMAT exam, the higher score is X and the lower one is Y. If the difference between the two scores is 1/3, what is the value of X/Y ?
Options:
A)3.
B)2.
C)1/2.
D)4
E)There isn't enough data to answer the question.
Rationale: Answer is D : 4
X - Y = (X + Y)/2
Solving for X/Y = 4
Answer: D
Question: There are two circles of different radii. The are of a square is 784 sq cm and its side is twice the radius of the larger circle. The radius of the larger circle is seven - third that of the smaller circle. Find the circumference of the smaller circle.
Options:
A)87∏ cm
B)56∏ cm
C)12∏ cm
D)16∏ cm
E)75∏ cm
Rationale: Let the radii of the larger and the smaller circles be l cm and s cm respectively. Let the side of the square be a cm.
a2 = 784 = (4)(196) = (22).(142)
a = (2)(14) = 28
a = 2l, l = a/2 = 14
l = (7/3)s
Therefore s = (3/7)(l) = 6 Circumference of the smaller circle = 2∏s = 12∏ cm.
Answer:C
Answer: C
Question: There are 600 boys in a hostel. Each plays either hockey or football or both. If 75% play hockey and 60% play football, how many play both?
Options:
A)210
B)150
C)200
D)180
E)160
Rationale: n(A) = 75*600/100 = 450
n(B) = 60*600/100 = 360
n(AUB) = 600
n(AnB) = 450+360-600 = 210
Answer is A
Answer: A
Question: The average age of a husband, wife and their child 4 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is?
Options:
A)2.12 years
B)4.4 years
C)16.63 years
D)15 years
E)14.25 years
Rationale: Sum of the present ages of husband, wife and child
= (23 * 2 + 5 * 2) = 57 years.
Required average
= 57/4
= 14.25 years.
Answer:E
Answer: E
Question: How many odd integers from 1 to 50 (both inclusive) have odd number of factors?
Options:
A)13
B)4
C)5
D)6
E)7
Rationale: Integers having odd number of factors will be perfect squares. Odd numbers will have odd perfect squares. Thus, the possible values for the perfect squares are :
1,9,25,49 and the corresponding integers are 1,3,5,7 (more than 3). Thus B is the correct answer .
Answer: B
Question: Which of the Conclusion is true fof the below statement
Statement : D @ M, M $ B, B ☆ R, R % T
Conclusion:
I. B ☆ D
II. B @ D
III. T ☆ M
Options:
A)Only I is true
B)Only II is true
C)Only III is true
D)Only either I or II is true
E)None is true
Rationale: D=M, M>B, B<R, R>T D=M>=B<R>T
B @ D True
T ☆ M True
Option D
Answer: D
Question: Anu can do a work in 6 days and Binu alone in 9 days. Anu and Binu undertook to do it for Rs.4200. With help of Minu, they completed the work in 3 days. How much is to be paid to Minu and Anu?
Options:
A)s.700, Rs.2100
B)s.2000, Rs.750
C)s.750, Rs.2000
D)s.800, Rs.1250
E)s.1000, Rs.1250
Rationale: Minuâ€™s one dayâ€™s work = 1/3 - 1/6 + 1/9= 1/3 - 5/18 = 1/18
Anuâ€™s wages: Binuâ€™s wages: Minuâ€™s wages = 1/6 : 1/9 : 1/18 = 6: 4: 2
Minuâ€™s share = Rs.4200* 2/12 = Rs.700
Anuâ€™s share = Rs.4200* 6 /12 = Rs.2100
ANSWER:A
Answer: A
Question: A Prototype fuel-efficient car (P-Car) is estimated to get 85% more miles per gallon of gasoline
than does a traditional fuel-efficient car (T-Car). However, the P-Car requires a special type
of gasoline that costs 20% more per gallon than does the gasoline used by a T-Car. If the two
cars are driven the same distance, what percent less than the money spent on gasoline for the
T-Car is the money spent on gasoline for the P-Car?
Options:
A)16 2/3%
B)35.13 %
C)50%
D)60%
E)66 2/3 %
Rationale: Assumption
Miles/Gallon
T = 100
P = 185 ( 85% more)
$/gallon
T = 100
P = 120 (20% more)
Miles
100 for both
Cost = (Miles X $/ Gallon)/ M/gallon
T = 100
P = 64.86
Hence 100 - 64.86 =35.13%
Ans B
Answer: B
Question: A and B start walking towards each other at 1pm at speed of 5kmph and 7kmph. They were initially 24km apart. At what time do they meet?
Options:
A)4pm
B)6pm
C)3pm
D)10pm
E)5pm
Rationale: Time of meeting = distance / relative speed = 24/7+5 = 24/12 = 2 hrs after 1pm = 3pm
Answer is C
Answer: C
Question: P and Q started a business investing Rs.85,000 and Rs.15,000 respectively. In what ratio the profit earned after 2 years be divided between P and Q respectively?
Options:
A)3 : 4
B)3 : 5
C)15 : 23
D)17 : 3
E)None
Rationale: Solution
P : Q	= 85000 : 15000
=85 : 15
=17 : 3
Answer D
Answer: D
Question: If a = 105 and a^3 = 21 × 25 × 45 × w, what is the value of w?
Options:
A)35
B)42
C)45
D)49
E)54
Rationale: a=105 = 3* 5 *7
a^3 = 21 × 25 × 45 × w
=> a^3 = (7*3) x (5*5) x ( 3^2 * 5) x w
=> a^3 = 3^3 * 5^3 * 7 x w
=>( 3* 5 *7) ^3 = 3^3 * 5^3 * 7 x w
w = 7^2 = 49
Answer D
Answer: D
Question: 6 25 64 81 32 ?
Find The Last Number In the Series ?
Options:
A)5
B)4
C)1
D)2
E)7
Rationale: C
The answer is 1
6 {6^1}
25 {5^2}
64 {4^3}
81 {3^4}
32 {2^5}
1 {1^6}
Answer: C
Question: 2 dice are tossed. What is the probability that the total score is a prime no. is?
Options:
A)3/14
B)5/12
C)5/13
D)7/11
E)7/12
Rationale: 5/12
B
Answer: B
Question: The Shopkeeper increased the price of a product by 25% so that customer finds it difficult to purchase the required amount. But somehow the customer managed to purchase only 70% of the required amount. What is the net difference in the expenditure on that product?
Options:
A)12%
B)12.5%
C)12.9%
D)12.11%
E)13.5%
Rationale: X Rate = Price
1 x 1 = 1
0.7 x 1.25 = 0.875
Decrease in price = (0.125/1) × 100 = 12.5%
B)
Answer: B
Question: A circular rim 14 inches in diameter rotates the same number of inches per second as a circular rim 21 inches in diameter. If the smaller rim makes x revolutions per second, how many revolutions per minute does the larger rim makes in terms of x ?
Options:
A)48pi/x
B)40x
C)48x
D)24x
E)x/75
Rationale: Let's try the explanation. We have two wheels. One with 14pi and the other one with 21pi. They have the same speed. In the smaller wheel it's 14pi*x, which must be equal to the speed of the bigger one (21pi*a number of revolutions).They are asking that number of revolutions (but in minutes, which makes the question even harder).
Anyway, we have 14pi*x=21pi*a.
(14pi*x)/(21pi). As I said, that's in seconds. So, to convert it to minutes we multiply by 60 and we get the result, 40x.
Ans : B
Answer: B
Question: The ratio between the perimeter and the width of a rectangle is 5 : 1. If the area of the rectangle is 150 sq. cm, what is the width of the rectangle?
Options:
A)10 cm
B)12 cm
C)14 cm
D)16 cm
E)18 cm
Rationale: 2L+2W = 5W
L = 3W/2
W*L = 150
3W^2/2 = 150
W^2 = 100
W = 10
The answer is A.
Answer: A
Question: 'a' and 'b' are positive integers such that their LCM is 20 and their HCF is 1. What is the difference between the maximum and minimum possible values of 'a + b'?
Options:
A)0
B)12
C)13
D)9
E)11
Rationale: a = 4, b = 5 as they have to co-primes (HCF being 1 and LCM = 20)
So A+B = 9 is their max and min value
hence Difference = 0
Answer - A
Answer: A
Question: If the average (arithmetic mean) of (2a+16) and (3a-8) is 74, what is the value of a?
Options:
A)25
B)30
C)28
D)36
E)42
Rationale: ((2a+16) + (3a-8)) / 2 = (5a+8)/2 = 74
a= 28
The answer is C.
Answer: C