divelab/Sys2Bench huggingface dataset:
Question: if capacity of giving milk of a cow is y litre.from this 1litre is used to make tea.rest amount is multiply by 2 and then divided by 3.calculate the result if y=13 litre.
Options:
A)6
B)5
C)8
D)9
E)4
Rationale: from 13 litre 1 litre used to make tea,rest amount is 12 litre.
12*2=24
now,24/3=8 litre
answer C
Answer: C
Question: Marissa, Keith and Tony all go to Disneyland many times each summer. Together, they have all gone a total of 65 times. Marissa and Keith have gone 55 times total, while Keith and Tony have gone 40 times total. How many times has Keith gone just by himself?
Options:
A)30
B)20
C)25
D)40
E)10
Rationale: Marissa + Keith + Tony = 65
M + K = 55
K + T = 40
Plug these each into the original formula
55 + T = 65
T = 10
Then, M + 40 = 65
M = 25
So, 25 + K + 10 = 65
Subtract 25 and 10 from each side to get Keith's total
K = 30
Answer: A
Answer: A
Question: In game of 500 points there are three participants A, B, and C. A game take place. A gives to B 80 points and to C 101 points. Then how many points can B give to C
Options:
A)15 points
B)25 points
C)35 points
D)45 points
E)55 points
Rationale: In the game of 500 points,
A gives B 80 points that means B got (500-80)=420
A gives B 101 points that means B got (500-101)=399
so, B:C=420:399
so, in the game of 420, B gives "21" (420-399) points to C..
so, in the game of 500, B gives to C as
500*21/420=25 points.
ANSWER:B
Answer: B
Question: Find the ratio in which rice at Rs. 7.20 a kg be mixed with rice at Rs. 5.50 a kg to produce a mixture worth Rs. 6.30 a kg
Options:
A)2:0
B)2:3
C)2:1
D)8:9
E)2:8
Rationale: By the rule of alligation:
Cost of 1 kg rice of 1st kind Cost of 1 kg rice of 2nd kind
Required ratio = 80 : 90 = 8 : 9
Answer: D
Answer: D
Question: What is the sum of all 3 digit numbers that leave a remainder of '2' when divided by 8?
Options:
A)61,600
B)64,850
C)64,749
D)49,700
E)56,720
Rationale: Find the number , Upon Sum of 3 Digits of a number Gives a Reminder 2 when it is Divided by 8
Seeing the Options After Dividing an Finding the Reminder of 2
My Answer was A
Answer: A
Question: (1^3 + 2^3 + 3^3 + ... + 10^3) = x?
Options:
A)360
B)380
C)x=420
D)440
E)450
Rationale: We know that (1^3 + 2^3 + 3^3 + ... + n^3) =	1	2n(n + 1)
6
Putting n = 10, required sum = 1	x 10 x 10 x 21 = 2100/5
420
C
Answer: C
Question: A train 300 m long can cross an electric pole in 20 sec and then find the speed of the train?
Options:
A)17 Kmph
B)54 Kmph
C)72 Kmph
D)18 Kmph
E)19 Kmph
Rationale: Length = Speed * time
Speed = L/T
S = 300/20
S = 15 M/Sec
Speed= 15*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 54 Kmph
Answer: B
Answer: B
Question: With a uniform speed a car covers a distance in 8 hours. Were the speed increased by 4 km/hr the same distance could be covered in 7 1⁄2 hours. What is the distance covered?
Options:
A)640 km
B)480 km
C)420 km
D)Cannot be determined
E)None of these
Rationale: Here D⁄7.5 - D⁄8 = 4
(where D is the distance in km)
⇒ 0.5 D = 4 × 8 × 7.5
⇒ D = 2 × 4 × 8 × 7.5 = 480 km
Answer B
Answer: B
Question: A trader mixes 10 kg of rice at Rs. 20 per kg with 20 kg of rice of other variety at Rs.40 per kg and sells the mixture at Rs. 40 per kg. His profit percent is:
Options:
A)No profit, no loss
B)5%
C)8%
D)20%
E)None of these
Rationale: C.P. of 30 kg rice = Rs. (10 x 20 + 20 x 40) = Rs. 200 + 800 = Rs. 1000.
S.P. of 30 kg rice = Rs.30x 40 = Rs. 1200
Gain =200/1000x100% =20%.
Answer: Option D
Answer: D
Question: Three boys are ages 4, 6 and 7 respectively. Three girls are ages 5, 8 and 9, respectively. If two of the boys and two of the girls are randomly selected and the sum of the selected children's ages is z, what is the difference between the probability that z is even and the probability that z is odd?
Options:
A)1/9
B)1/6
C)2/9
D)1/4
E)1/2
Rationale: Age of Boys:4, 6, 7
Sum of ages taken 2 at a time: 10,13,11
Ages of Girls:5, 8, 9
Sum of ages taken 2 at a time: 13,17,14
9 Combinations of sum between sets(10,12,11) & (13,17,14)
=23,27,24- 16,30,17- 24,28,25
Prob(Even)= 5/9
Prob(Odd) =4/9
Answer=5/9 - 4/9 = 1/9
Answer:A
Answer: A
Question: Each Machine of type A has 3 steel parts and 3 chrome parts. Each machine of type B has 6 steel parts and 5 chrome parts. If a certain group of type A and type B machines has a total of 60 steel parts and 44 chrome parts, how many machines are in the group
Options:
A)12
B)13
C)14
D)15
E)16
Rationale: Look at the below representation of the problem:
Steel Chrome total
A 3 3 60 >>no. of type A machines=60/6=10
B 6 5 44 >>no. of type B machines=44/11=4
So the answer is 14 i.e C.
Hope its clear .
Answer: C
Question: When magnified 1,000 times by an electron microscope, the image of a certain circular piece of tissue has a diameter of 2 centimeter. The actual diameter of the tissue, in centimeters, is
Options:
A) 0.005
B) 0.002
C) 0.001
D) 0.0005
E) 0.0002
Rationale: It is very easy if x is the diameter, then the magnified length is 1000x.
ince 1000x=2 then x=2/1000=0.002.
The answer is B
Answer: B
Question: Roja and Pooja start moving in the opposite directions from a pole. They are moving at the speeds of 7 km/hr and 3 km/hr respectively. After 4 hours what will be the distance between them?
Options:
A)22 km
B)40 km
C)65 km
D)18 km
E)16 km
Rationale: Distance = Relative Speed * Time
= (7 + 3) * 4 = 40 km
[ They are travelling in the opposite direction, relative speed
= sum of the speeds].
Answer: B
Answer: B
Question: A cube of edge 5 cm is cut into cubes each of edge 1 cm. The ratio of the total surface area of one of the small cubes to that of the large cube is equal to:
Options:
A)1:25
B)1.225
C)1:52
D)1:522
E)None
Rationale: Sol.
Required ratio = 6 * 1 * 1 / 6 * 5 * 5 = 1/25 = 1:25.
Answer A
Answer: A
Question: A diet contains 400 grams of a mixture of two foods, food X and food Y. Food X contains 10 percent protein and food Y contains 15 percent protein. If a diet provides exactly 48 grams of protein daily, how many grams of food X are in the mixture?
Options:
A)200
B)220
C)240
D)260
E)280
Rationale: Let x be the number of grams of food X in the mixture.
0.1x + 0.15(400-x) = 48
0.05x = 12
x = 240
The answer is C.
Answer: C
Question: From given equation find the value of x: 2x² + 9x − 5
Options:
A)−5
B)-4
C)-6
D)6
E)-4
Rationale: That quadratic is factored as follows:
2x² + 9x − 5 = (2x − 1)(x + 5).
Lesson 17.
Now, it is easy to see that the second factor will be 0 when x = −5.
As for the value of x that will make
2x − 1 = 0,
we must solve that little equation. (Lesson 9.)
We have:
2x = 1
x = 1
2
The solutions are:
x = 1/2 or −5
A
Answer: A
Question: 13 buckets of water fill a tank when the capacity of each bucket is 51 litres. How many buckets will be needed to fill the same tank, if the capacity of each bucket is 17 litres?
Options:
A)39
B)28
C)23
D)12
E)24
Rationale: Capacity of the tank = (13 × 51) litre
Number of buckets required of capacity of each bucket is 17 litre = 13×51/17=13×3=39
Answer is A
Answer: A
Question: The sum of the non-prime numbers between 50 and 60, non-inclusive, is
Options:
A)263
B)293
C)323
D)353
E)383
Rationale: sum of consecutive integers from 51 to 59, inclusive ====> (A1 + An)/2 * # of terms = (51 + 59)/2 * 9 = 55 *9 = 495
sum of non-prime numbers b/w 50 and 60, non inclusive ===> 495 - 112 (i.e., 53 + 59, being the prime #s in the range) =383
Answer: E
Answer: E
Question: The C.P of 10 pens is equal to the S.P of 12 pens. Find his gain % or loss%?
Options:
A)16 2/8%
B)16 6/3%
C)16 2/3%
D)18 2/3%
E)16 25%
Rationale: 10 CP = 12 SP
12 --- 2 CP loss
100 --- ? => 16 2/3%
Answer:C
Answer: C
Question: A person lent a certain sum of money at 4% per annum at simple interest and in 8 years the interest amounted to Rs.340 less than the sum lent. What was the sum lent?
Options:
A)Rs:567
B)Rs:518
C)Rs:519
D)Rs:500
E)Rs:520
Rationale: P - 340 = (P*4*8)/100
P = 500
Answer:D
Answer: D
Question: I. c3 - 988 = 343,
II. d2 - 72 = 49 to solve both the equations to find the values of c and d?
Options:
A)a > b
B)a ≥ b
C)a < b
D)a ≤ b
E)a = b or the relationship between a and b cannot be established.
Rationale: Explanation:
c3 = 1331 => c= 11
d2 = 121 => d= ± 11
c≥ d
B)
Answer: B
Question: In how many ways can a group of 3 people be selected out of 5 men and 7 women, so that 2 of them are of the same gender?
Options:
A)96
B)125
C)155
D)175
E)225
Rationale: Since the question stem asks for 2 members of the same gender we get the following:
1. 2-Men and 1-Woman, hence (2C5)*(1C7) = 5*2*7=70
2. 2-Women and 1-Man, hence (2C7)*(1C5) = 7*3*5 =105
Thus, the total number of ways would be: 70+105=175
ANS:D
Answer: D
Question: A palindrome is a number that reads the same front-to-back as it does back-to-front (e.g. 202, 575, 1991, etc.) p is the smallest integer greater than 800 that is both a prime and a palindrome. What is the sum of the digits of p?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: Given that p is smallest integer greater than 800 - assume there is a 3-digit that satisfies the above conditions. Let the number be xyx ; question asks us the values of 2x+y
We can straight away cross out options A) and D) - sum of digits 3 or 6 implies it is divisible by 3 ---> we know that p is a prime number
Coming to option B) 2x + y = 4 --> only x = 2 and y = 0 satisfy this equation ( x> 2 will never give sum of digits = 4) ; but 202 is divisible by 2 ; we know that p is a prime number
Similarly option C) 2x+y = 5 --> only x = 2 and y = 1 satisfy this equation ( x> 2 will never give sum of digits = 5) ; but 212 is divisible by 2 ; we know that p is a prime number
Therefore answer option should be E ---> can be verified by taking 2x+y = 7 ---> x = 3 and y = 1 ; gives 313
E
Answer: E
Question: The 52nd term of the series a, b , b, c, c, c, d, d, d, d, e, e, e, e, e, .... is
Options:
A)f
B)k
C)l
D)j
E)t
Rationale: a is one time, b,2 times so on...
so 52=n(n+1)/2..
0r n(n+1)= 104... now 10*11=110...9*10<104 so n= 10.. and 10th alphabet is J. ans D
Answer: D
Question: How many minutes does Aditya take to cover a distance of 400 m, if he runs at a speed of 20 km/hr
Options:
A)1 1/5min
B)2 1/5min
C)3 1/5min
D)4 1/5min
E)5 1/5min
Rationale: Explanation:
We know that,
Time=Distance/Speed
Speed=20 km/hr=20∗5/18m/sec=50/9m/sec
Time =(400∗9/50)=72sec=1 1/5min
Option A
Answer: A
Question: A and B invests Rs.6000 and Rs.8000 in a business. After 6 months, A withdraws half of his capital and B withdraws one-fourth of his capital. In what ratio should they share the profits at the end of the year?
Options:
A)13:15
B)9:13
C)9:11
D)13:14
E)9:14
Rationale: A : B
(6000*6)+(3000*6) : (8000*6)+(6000*6)
54000 : 84000
9 : 14
Answer: E
Answer: E
Question: An engineer designed a ball so that when it was dropped, it rose with each bounce exactly one-half as high as it had fallen. The engineer dropped the ball from a 18-meter platform and caught it after it had traveled 53.4 meters. How many times did the ball bounce?
Options:
A)5
B)6
C)7
D)8
E)9
Rationale: Ans: 6
Division of total diatance travelled will be 18+18+9+4.5+2.25+1.125+0.5 ans B
Answer: B
Question: Can anyhow help me with an easy solution for this
3, 4, 49, 5, 3, 64, 7, 6, ?
Options:
A)121
B)169
C)144
D)256
E)225
Rationale: 3, 4, 49, 5, 3, 64, 7, 6, ?
3+4=7 and 7^2=49
5+3=8 and 8^2=64
7+6=13 and 13^2=169
ANSWER:B
Answer: B
Question: There are 4 people of different heights standing in order of increasing height. The difference is 2 inches between the first person and the second person, and also between the second person and the third person. The difference between the third person and the fourth person is 6 inches and the average height is 77. How tall is the fourth person?
Options:
A)79
B)81
C)83
D)85
E)87
Rationale: Let x be the height of the first person.
Then the heights are x, x+2, x+4, and x+10.
4x+16 = 4(77) = 308
x = 73 and the fourth person has a height of 73+10 = 83 inches
The answer is C.
Answer: C
Question: The least number which when divided by 5, 6 , 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder, is:
Options:
A)1677
B)1683
C)2523
D)3363
E)3565
Rationale: L.C.M. of 5, 6, 7, 8 = 840.
Required number is of the form 840k + 3
Least value of k for which (840k + 3) is divisible by 9 is k = 2.
Required number = (840 x 2 + 3) = 1683.
Answer: Option B
Answer: B
Question: The denominator of a fraction is 8 greater than the numerator. If the numerator and the denominator are increased by 5, the resulting fraction is equal to 6â„7. What is the value of the original fraction?
Options:
A)25/33
B)31/39
C)37/45
D)43/51
E)53/61
Rationale: Let the numerator be x.
Then the denominator is x+8.
x+5 / x+13 = 6/7.
7x+35=6x+78.
x=43.
The original fraction is 43/51.
The answer is D.
Answer: D
Question: A group of men decided to do a work in 15days, but 8 of them became absent. If the rest of the group did the work in 18days, Find the original number of men?
Options:
A)15
B)48
C)54
D)33
E)45
Rationale: Original number of men = 8*18 / (18-15) = 48
Answer is B
Answer: B
Question: The elevator in an eleven-story office building travels at the rate of one floor per 1/4 minute, which allows time for picking up and discharging passengers. At the main floor and at the top floor, the operator stops for 1 minute. How many complete trips will an operator make during a 6-hour period?
Options:
A)88
B)56
C)42
D)51
E)64
Rationale: Complete trip = 10 floors up and 10 floors down = 20 floors = 20*1/4 = 5 minutes plus 2 minutes = 7 minutes.
6 hour = 360 minutes.
In 360 minutes operator can make 360/7=51 trips.
Answer: D.
Answer: D
Question: Rohan spends 40% of his salary on food, 20% on house rent, 10% on entertainment and 10% on conveyance. If his savings at the end of a month are Rs. 1000. then his monthly salary is
Options:
A)Rs. 5000
B)Rs. 6000
C)Rs. 4000
D)Rs. 3000
E)Rs. 2000
Rationale: Sol.
Saving = [100 - (40 + 20 + 10 + 10]% = 20%.
Let the monthly salary be Rs. x.
Then, 20% of x = 1000
â‡” 20 / 100x = 1000
â‡” x = 1000 Ã— 5 = 5000.
Answer A
Answer: A
Question: A tradesman by means of his false balance defrauds to the extent of 40%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?
Options:
A)80%
B)96%
C)92%
D)84%
E)86%
Rationale: g% = 40 + 40 + (40*40)/100
= 96%
ANSWER:B
Answer: B
Question: Present ages of X and Y are in the ratio 5:6 respectively. Seven years hence this ratio will become 6:7 respectively. What is X's present age in years?
Options:
A)35 years
B)37 years
C)16 years
D)17 years
E)18 years
Rationale: Let the present ages of X and Y be 5x and 6x years respectively.
Then, (5x + 7)/(6x + 7) = 6/7
7(5x + 7) = 6(6x + 7) => x = 7
X's present age = 5x = 35 years.
Answer: A
Answer: A
Question: What is the average of first 21 multiples of 4 ?
Options:
A)A)44
B)B)77
C)C)79
D)D)81
E)E)82
Rationale: Required average = 7(1+2+....+21) / 21
(4/21)X ( (21x22) / 2 ) (because sum of first 21 natural numbers)
= 44
A
Answer: A
Question: Find the greatest number which on dividing 4351 and 5161, leaves a reminder of 8 and 10 respectively
Options:
A)125
B)111
C)129
D)101
E)141
Rationale: Explanation:
In this type of question, its obvious we need to calculate the HCF, trick is
HCF of (4351 - 8) and (5161 -10)
= HCF (4343, 5151) = 101
Option D
Answer: D
Question: The average age of 10 students in a class is 15 years. If the age of teacher is also included, the average becomes 16 years, find the age of the teacher.
Options:
A)30
B)26
C)28
D)29
E)45
Rationale: Explanation:
If teacher's age is 15 years, there is no change in the average. But teacher has contributed 1 year to all the students along with maintaining his age at 16.
Age of teacher = Average age of all + Total increase in age
= 16 + (1 x 10 ) = 26 years
Answer:B
Answer: B
Question: A man goes to his office from his house at a speed of 3 km/hr and returns at a speed of 2 km/hr. If he takes 5 hours in going and coming, what is the distance between his house and office?
Options:
A)8
B)7
C)4
D)6
E)09
Rationale: If a car covers a certain distance at x kmph and an equal distance at y kmph,the average speed of the whole journey = 2xyx+y kmphHence, average speed = 2×3×22+3=125 km/hrTotal time taken = 5 hours⇒Distance travelled=125×5=12 km⇒Distance between his house and office =122=6 km
Answer : D
Answer: D
Question: Half a number plus 7 is 17.What is the number?
Options:
A)8
B)9
C)10
D)11
E)20
Rationale: Let x be the number. Always replace "is" with an equal sign
(1/2)x + 7 = 17
(1/2)x = 17 - 7
(1/2)x = 20
x = 20
correct answer is E
Answer: E
Question: A bike agent buys 30 bicycles, of which 8 are first grade and the rest are second grade, for Rs 3,150, Find at what price he must sell the first grade bikes so that if he sells the second grade bikes at three quarters of the price, he may make a profit of 40% on his outlay.
Options:
A)Rs 200
B)Rs 240
C)Rs 180
D)Rs 210
E)Rs 230
Rationale: Suppose the price of first grade bike = Rs X
And the price of second grade bike = Rs Y
Therefore, 8X + 22Y = 3150
Suppose he sells the first grade bike at the rate of Rs Z per cycle
Therefore, 8Z + 22 x 3/4Z = 3150 + 40% of 3150
98Z = 17640 => Z = 180
S.P. of the first grade bike = Rs 180
S.P. of the second grade bike = Rs 135
ANSWER:C
Answer: C
Question: A drawer holds 5 red hats and 5 blue hats. What is the probability of getting exactly three red hats or exactly three blue hats when taking out 8 hats randomly out of the drawer and returning each hat before taking out the next one?
Options:
A)3/4
B)5/8
C)7/16
D)15/32
E)31/64
Rationale: Let's find the probability of getting exactly 3 red hats.
One possible case is red-red-red-blue-blue-blue-blue-blue.
The probability of this is 1/2*1/2*1/2*1/2*1/2*1/2*1/2*1/2 = 1/256
There are 8C3 = 56 such cases so we need to multiply this by 56.
P(exactly 3 red hats) = 56*1/256 = 7/32
Clearly the probability of getting exactly 3 blue hats will also be 7/32.
The sum of the probabilities is 7/32+7/32 = 14/32 = 7/16
The answer is C.
Answer: C
Question: If d is the smallest positive integer such that 3,150 multiplied by d is the square of an integer, then d must be
Options:
A) 2
B) 5
C) 6
D) 7
E) 14
Rationale: Solution:
This problem is testing us on the rule that when we express a perfect square by its unique prime factors, every prime factor's exponent is an even number.
Let’s start by prime factorizing 3,150.
3,150 = 315 x 10 = 5 x 63 x 10 = 5 x 7 x 3 x 3 x 5 x 2
3,150 = 2^1 x 3^2 x 5^2 x 7^1
(Notice that the exponents of both 2 and 7 are not even numbers. This tells us that 3,150 itself is not a perfect square.)
We also are given that 3,150 multiplied by d is the square of an integer. We can write this as:
2^1 x 3^2 x 5^2 x 7^1 x d = square of an integer
According to our rule, we need all unique prime factors' exponents to be even numbers. Thus, we need one more 2 and one more 7. Therefore, d = 7 x 2 = 14
Answer is E.
Answer: E
Question: John takes 6 hrs to print 32 pages. Peter takes 5hrs to print 40 pages. In how many hours they will print 110 pages together ?
Options:
A)8 hours
B)8 hours 15 minutes
C)9 hours 15 minutes
D)11 hours
E)12 hours
Rationale: Ram can type 32/6 pages per hour
Shaam can type 8 pages per hourThey can type 32/6 + 8 = 40/3 pages per hour
So they will take 110/40 × 3 = 33/4 hours or 8 hours 15 minutes
B)
Answer: B
Question: 70,78, 80,85,90,105,105,130,130,130
The list consists of the times in seconds that it took each of the 10 school children to run a distance of 400 mts . If the standard deviation of the 10 running times is 22.4, rounded to the nearest tenth of a second, how many of the 10 running times are more than 1 standard deviation below the mean of the 10 running times.
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: How many of the 10 running times are more than one SD below the meanmeans how many data points from given 10 are less thanmean-1SD.
We are given that SD=22.4, so we should find mean --> mean=100 --> there is only 1 data points below 100-22.4=77.6, namely 70
Answer: A.
Answer: A
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)11%
B)12%
C)12.5%
D)13%
E)14%
Rationale: Quantity X Rate = Price
1 x 1 = 1
0.7 x 1.25 = 0.875
Decrease in price = (0.125/1) × 100 = 12.5%
C
Answer: C
Question: The greatest number of four digits which is divisible by 25, 40, 54 and 75 is:
Options:
A)5000
B)5400
C)5600
D)5800
E)5200
Rationale: Greatest number of 4-digits is 9999.
L.C.M. of 25, 40, 54 and 75 is 600.
On dividing 9999 by 5400, the remainder is 4599.
Required number (9999 - 4599) = 5400.
Answer: Option B
Answer: B
Question: The length of a rectangle is increased to 2 times its original size and its width is increased to 3 times its original size. If the area of the new rectangle is equal to 1800 square meters, what is the area of the original rectangle?
Options:
A)100 square meters
B)200 square meters
C)300 square meters
D)400 square meters
E)500 square meters
Rationale: If L and W be the original length and width of the rectangle and its area is given by
L ? W
After increase the length becomes 2 L and the width becomes 3 W. The area is then given by (2 L) ? (3 W) and is known. Hence
(2 L) ? (3 W) = 1800
Solve the above equation to find L ? W
6 L ? W = 1800
L ? W = 1800 / 6 = 300 square meters , area of original rectangle
correct answer C
Answer: C
Question: A man invests some money partly in 12% stock at 132 and partly in 10% stock at 80.To obtain equal dividends from both,he must invest the money in the ratio :
Options:
A)3 : 4
B)3 : 5
C)11:8
D)16 : 15
E)None
Rationale: Solution
For an income of Rs. 1 in 12% stock at 132, investment = Rs. (132/12)= Rs. 11 .
For an income of Rs. 1 in 10% stock at 80, investment = Rs.(80/10) = Rs. 8.
∴ Ratio of investments = 11:8 =11:8
Answer C
Answer: C
Question: Working alone, Jerry finishes cleaning half the house in a third of the time it takes Nick to clean the entire house alone. Jerry alone cleans the entire house in 6 hours. How many hours will it take Nick and Jerry to clean the entire house if they work together?
Options:
A)1.5
B)2
C)2.4
D)3
E)3.6
Rationale: Answer is 3.6 hours.
Jerry does the complete house in 6 hours while Nick does it in 9 hours. 1/ (1/6+1/9)= 3.6
answer is E
Answer: E
Question: .008/?= .01
Options:
A).8
B).09
C).009
D).0009
E)None of them
Rationale: Let .008/x = .01;
Then x = .008/.01
= .8/1
= .8
Answer is A
Answer: A
Question: I. a3 - 988 = 343,
II. b2 - 72 = 49 to solve both the equations to find the values of a and b?
Options:
A)a > b
B)a ≥ b
C)a < b
D)a ≤ b
E)a = b or the relationship between a and b cannot be established.
Rationale: Explanation:
a3 = 1331 => a = 11
b2 = 121 => b = ± 11
a ≥ b
B)
Answer: B
Question: Tanks Q and B are each in the shape of a right circular cylinder. The interior of tank Q has a height of 10 meters and a circumference of 8 meters, and the interior of tank B has a height of 8 meters and a circumference of 10 meters. The capacity of tank Q is what percent of the capacity of tank B?
Options:
A)75%
B)80%
C)100%
D)120%
E)125%
Rationale: B.
For Q, r=8/2pi. Its capacity = (4pi)^2 * 10= 160pi
For B, r=10/pi. Its capacity = (5pi)^2 *8 = 200pi
Q/B = 160pi/200pi = 0.8
Answer: B
Question: 4 dice are thrown simultaneously on the board. Find the probability show the same face.
Options:
A)1/115
B)2/113
C)1/216
D)2/121
E)3/114
Rationale: The total number of elementary events associated to the random experiments of throwing four dice simultaneously is:
=6×6×6×6=64=6×6×6×6=64
n(S)=64n(S)=64
Let XX be the event that all dice show the same face.
X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}
n(X)=6n(X)=6
Hence required probability,
=n(X)n(S)=664=n(X)n(S)=664
=1/216
C
Answer: C
Question: 10 men, working 4 hours a day can complete a work in 18 days. How many hours a day must 15 men work to complete the work in 12 days ?
Options:
A)4 hours a day
B)5 hours a day
C)6 hours a day
D)7 hours a day
E)8 hours a day
Rationale: Explanation:
More Men, Less Hours {Indirect Proportion}
Less Days, More Hours {Indirect Proportion}
[men 15 10
days 12 18] ::4:x
=>xâˆ—15âˆ—12=10âˆ—18âˆ—4
=>x=10âˆ—18âˆ—4/ 15âˆ—12
=>x=4
Option A
Answer: A