divelab/Sys2Bench huggingface dataset:
Question: COMPLETE THE SERIES..
1, 3, 7, 11, 13,... ?
Options:
A)16
B)17
C)18
D)19
E)20
Rationale: i think in this series we need to divide series in two parts i.e in terms of even place term and odd place term.i.e
1,7,13 so in odd term you see a difference of 6.
and in even terms there is difference of 8
3,11 so next term will be 11+8=19.
so series is like this
1,3,7,11,13,19.
ANSWER:D
Answer: D
Question: Pipes A and B can fill a tank in 2 and 3 hours. Pipe C can empty it in 15 hours. If all pipes are opened together, then the tank will be filled in?
Options:
A)60/17 hr
B)13/12 hr
C)42/11 hr
D)6 hr
E)30/23 hr
Rationale: Net part filled in 1 hour = 1/2 + 1/3 - 1/15 = 23/30
The tank will be full in 30/23 hr
Answer is E
Answer: E
Question: The average of ten numbers is 7 .If each number is multiplied by 12 , then the average of new set of numbers is
Options:
A)28
B)236
C)288
D)84
E)26
Rationale: Explanation:
If each number is multiplied by K, then the new average increases by K times. So new average = 84
Answer:D
Answer: D
Question: The closest approximation of (69.28 × 0.004)/0.03 is
Options:
A)0.092
B)0.92
C)9.2
D)92
E)920
Rationale: (69.28 × 0.004)/0.03
1. 0.004 = 4 × 10^(-3)
2. 0.03 = 3 × 10^(-2)
3. (a × b)/c = a × (b/c)
4. 0.004/0.03 = 4 × 10^(-3)/ (3 × 10^(-2)) = 4 × 10^( -3 - (-2))/3 = 4 × 10^(-1) / 3 = (4/3) × 10^(-1) = 1.333 × 10^(-1)
Therefore,
(69.28 × 0.004)/0.03 = 69.28 × (0.004/0.03) = 69.28 × 1.33 × 10^(-1) = 69.28 × 1.33/10 = 6.928*1.33
Now,
7 × 2 = 14
7 × 1 = 7
or better:
6.9 × 1 = 6.9
6.9 × 2 = 13.8
hence,
6.9 <6.928 × 1.33 < 13.8
9.2 is the only answer that satisfies this condition.
ANSWER:C
Answer: C
Question: A sum of Rs. 2665 is lent into two parts so that the interest on the first part for 8 years at 3% per annum may be equal to the interest on the second part for 3 years at 5% per annum. Find the second sum?
Options:
A)1888
B)1640
C)2768
D)2976
E)2691
Rationale: (x*8*3)/100 = ((2665 - x)*3*5)/100
24x/100 = 39975/100 - 15x/100
39x = 39975 => x = 1025
Second sum = 2665 – 1025
= 1640
Answer: B
Answer: B
Question: Two trains starting at the same time from two stations 200 km apart and going in opposite directions cross each other at a distance of 110 km from one of the stations. What is the ratio of their speeds?
Options:
A)21 : 9
B)11 : 9
C)71 : 9
D)91 : 9
E)21 : 2
Rationale: Explanation:
In the same time, they cover 110 km and 90 km respectively.
{\color{Blue} \therefore } Ratio of their speeds = 110 : 90 = 11 : 9
Answer: B
Answer: B
Question: If 0 < x ≤ 3, then which one of the following is the maximum value of (x – 1)^2 + x ?
Options:
A)–2
B)–1
C)7
D)1
E)2
Rationale: the maximum value of (x – 1)^2 + x for 0 < x ≤ 3 is when x=3 --> (x – 1)^2 + x =7
Answer C
Answer: C
Question: If 42/330 = 0.1272, what is the 32nd digit to the right of the decimal point of the fraction?
Options:
A)1
B)4
C)5
D)7
E)2
Rationale: we are not concerned what 42/330 means..
we have to look at the decimal..
0..1272 means 0.1272727...
so leaving first digit to the right of decimal, all ODD numbered are 7 and all EVEn numbered are 2.
here 32 is EVEN, so ans is 2
Answer is E
Answer: E
Question: In Township K, 1/5 of the housing units are equiped with cable Tv. If 1/10 of the housing units, including 1/6 of those that are equiped with cable tv, are equipped with videocassette recorders, what fraction of the housing units have neither cable tv nor videocassette recorders?
Options:
A)23/30
B)11/15
C)7/10
D)1/6
E)2/15
Rationale: 1/5 -- cable TV (This includes some data from video cassette recorder)
1/10 -- video cassette recorder including 1/6(equiped with cable tv) i.e. 1/6(1/5) = 1/30
therefore only video cassette recorder = 1/10 - 1/30 = 1/15
Total = 1/5+1/15+neither cable tv nor videocassette recorders
1 = 4/15 + neither cable tv nor videocassette recorders
therefore neither cable tv nor videocassette recorders = 1-4/15 = 11/15
Hence B.
Answer: B
Question: A sock drawer contains seven socks, each one a different solid color. The colors of the socks are orange, yellow, green, blue, indigo, and violet. A person reaches into the drawer, pulls out two socks, and puts a single sock on each foot. If each sock can fit either the left or the right foot, and if it matters whether a particular sock is on the left or the right foot, how many different sock fashion combinations could the person make from the six socks?
Options:
A)12
B)15
C)21
D)36
E)30
Rationale: It's a question of permutation since order matters here ....
It can be deduced to-
6P2 = 6!/4! = 6*5 = 30 .........Answer is - E
Answer: E
Question: In how many ways can a Chief Minister and a Vice Minister be elected from a team of 14 members?
Options:
A)132
B)144
C)158
D)170
E)182
Rationale: There are 14 choices for the Chief Minister.
Then there are 13 choices for the Vice Minister.
The total number of ways is 14*13 = 182.
The answer is E.
Answer: E
Question: A room has both an entrance and an exit door. The room can fill up with people in 5 hours. The room can be empty of people in 15 hours. If it is desired that the room should be filled, from empty, exactly 6 hours after people begin entering the room at 9:30am, then at what time should people begin exiting the room?
Options:
A)10:00am
B)10:45am
C)12:00pm
D)12:30pm
E)1:30pm
Rationale: In 6 hours the entrance door is opened to fill the room equal to 6*1/5 = 6/5 of the room. So, 1/5 more than necessary, which should be compensated by people using the exit door. To empty out 1/5 of the people, the exit door needs 15/5 = 3 hours.
Therefore, the exit door should be used at 9:30am + 6 hours - 3 hours = 12:30pm.
Answer: D.
Answer: D
Question: The dimensions of each book in an encyclopedia set measures 8 in x 4 in x 12 in. (l x w x h). Each shelf (i.e. each divider) has a surface area of 848 sq in., where the thickness is 1 in and the width is 16 in. Assuming there is enough space in between shelves, how many shelves are needed to fit all of the books?
Options:
A)7
B)12
C)13
D)5
E)26
Rationale: Surface area of each shelf= 2ab + 2ac + 2bc
848 = 2 x 1 x 16 + 2 x 1 x c + 2 x 16 x c
848 = 32 + 2c + 32c
816 = 34c
c = 24 in. (i.e. the length of each shelf)
Each book is 4 in thick
24/4 = 6 books per shelf
26/6 = 4.333=5 shelves
Answer is D
Answer: D
Question: From a Group of 8 People, Including Timo and Gary, 3 people are to be selected at random to work on a certain project. What is the probability that 3 people selected will include Timo but not Gary
Options:
A)5/56
B)9/56
C)15/56
D)21/56
E)25/56
Rationale: Number of ways of selecting 3 people out of 8 people = 8C3
In the three members Timo will always be there in the team. At this step we have vacancy for 2 more members and 7 members are available. Gary cannot be there in the team. So 2 members have to be selected and the number of available members = 7 -Gary = 6
Number of ways to form a 3 member team that includes Timo and excludes Gary = 6C2
Probability = 6C2/8C3 = 15/56
Answer: C
Answer: C
Question: The price of a car and AC are in the ratio 3:2. If the scooter costs $500 more than the AC. then the price of the AC?
Options:
A)1500
B)200
C)1700
D)2000
E)2500
Rationale: Let the price of the Car and AC is 3x and 2x
3x-2x = 500
x = 500
Price of AC = 3*500 = $1500
Answer is A
Answer: A
Question: The difference between the ages of two persons is 10 years.Fifteen years ago ,the elder one was twice as old as the younger one.The present age of the elder person is :
Options:
A)25 years
B)35 years
C)45 years
D)55 years
E)75 years
Rationale: Solution
Let their ages be x year and (x + 10) years respectively.
Then,(x + 10) - 15 = 2 (x - 15) ⇔ x-5 = 2x-30 ⇔ x =25.
∴ Present age of the elder person =(x + 10) =35 years. Answer B
Answer: B
Question: A dog takes 4 leaps for every 5 leaps of a hare but 3 leaps of a dog are equal to 4 leaps of the hare. Compare their speeds?
Options:
A)4:5
B)16:15
C)9:13
D)5:15
E)9:17
Rationale: Let the distance covered in 1 leap of the dog be x and that covered in 1 leap of the hare be y
Then 3x = 4y
x = 4/3 y
4x = 16/3 y
Ratio of speeds of dog and hare = Ratio of distances covered by them in the same time
= 4x:5y = 16/3 y : 5 = 16:15
Answer is B
Answer: B
Question: The mean of 50 observations was 36. It was found later that an observation 48 was wrongly taken as 47. The corrected new mean is?
Options:
A)36.7
B)36.1
C)36.5
D)36.02
E)36.3
Rationale: Correct sum
= (36 * 50 + 48 - 47)
= 1801.
Correct mean = 1801/50
= 36.02
Answer:D
Answer: D
Question: If a equals the sum of the even integers from 2 to 20, inclusive, and b equals the sum of the odd integers from 1 to 19, inclusive, what is the value of a - b ?
Options:
A)1
B)10
C)19
D)20
E)21
Rationale: Sum of consecutive odd or even integers = (no. of odd or even ints) * (first int + last int) / 2
Here A = sum of even ints from 2 to 20, inclusive
number of even ints = 10,
first int + last int = 2+20 = 22
A = 10*22 / 2 = 110
B = sum of odd ints from 1 to 19, inclusive
number of odd ints = 10,
first int + last int = 1+19 = 20
A = 10*20 / 2 = 100
A-B = 110 - 100 = 10
ANSWER:C
Answer: C
Question: The length of the longest tape in cm which can be used to measure exactly, the length 6m; 5m ; and 12m is:
Options:
A)200
B)100
C)50
D)1200
E)500
Rationale: The three lengths in cm are 600,500 & 1200.
HCF of 600, 500 & 1200 is 100
Hence, the answer is 100 cm.
ANSWER:B
Answer: B
Question: Find the numbers which are in the ratio 3:2:4 such that the sum of the first and the second added to the difference of the third and the second is 21.
Options:
A)9, 6, 16
B)9, 6, 19
C)9, 6, 16
D)9, 6, 12
E)9, 6, 11
Rationale: Let the numbers be a, b and c.
a:b:c = 3:2:4
Given, (a + b) + (c - b) = 21
=> a + c = 21
=> 3x + 4x = 21 => x = 3
a, b, c are 3x, 2x, 4x
a, b, c are 9, 6, 12.
Answer: D
Answer: D
Question: A rectangular cube has sides measuring 15 inches long by 12 inches wide by 2 inches high. If the surface area of the rectangle is the same as a cube, what do the sides/walls of the cube measure? Round to the nearest whole number.
Options:
A)7
B)5
C)9
D)6
E)4
Rationale: First calculate the surface area of the rectangle by multiplying the length and width of the rectangle together, then multiply by 2 to get both sides of the rectangle. This calculates to 360 inches. Find the surface area of the sides of the rectangular cube. Multiply the height by the length of the rectangle. Multiply the answer by 2 (for the 2 sides on the rectangular cube). This calculates to 60 inches. Then multiply the width of the rectangle by the height. Multiply the answer by 2 (for the 2 sides on the rectangular cube). This calculates to 48 inches. Add the totals together to get the rectangular cube surface area of 468 inches. Since a square cube has 6 sides - divide the surface area by 6. This calculates to 78 inches as the surface area of each side of the cube. The square root of 78 is 8.831. Rounding to the nearest whole number that makes each side of the cube measuring 9 inches. The correct answer is (C).
Answer: C
Question: Each of three investments has a 20% of becoming worthless within a year of purchase, independently of what happens to the other two investments. If Simone invests an equal sum V in each of these three investments on January 1, the approximate chance that by the end of the year, she loses no more than 1/3 of her original investment is
Options:
A)90%
B)80%
C)70%
D)60%
E)40%
Rationale: The problem asks for the approximate chance that no more than 1/3 of the original investment is lost. We can apply the “1 – x” technique: what’s the chance that more than 1/3 of the original investment is lost? There are two outcomes we have to separately measure:
(a) All 3 investments become worthless.
(b) 2 of the 3 investments become worthless, while 1 doesn’t.
Outcome (a): The probability is (0.2)(0.2)(0.2) = 0.008, or a little less than 1%.
Outcome (b): Call the investments X, Y, and Z. The probability that X retains value, while Y and Z become worthless, is (0.8)(0.2)(0.2) = 0.032. Now, we have to do the same thing for the specific scenarios in which Y retains value (while X and Z don’t) and in which Z retains value (while X and Y don’t). Each of those scenarios results in the same math: 0.032. Thus, we can simply multiply 0.032 by 3 to get 0.096, or a little less than 10%.
The sum of these two probabilities is 0.008 + 0.096 = 0.104, or a little more than 10%. Finally, subtracting from 100% and rounding, we find that the probability we were looking for is approximately 90%.
The correct answer is A.
This problem illustrates the power of diversification in financial investments. All else being equal, it’s less risky to hold a third of your money in three uncorrelated (independent) but otherwise equivalent investments than to put all your eggs in one of the baskets. That said, be wary of historical correlations! Housing price changes in different US cities were not so correlated—and then they became highly correlated during the recent housing crisis (they all fell together), fatally undermining spreadsheet models that assumed that these price changes were independent.
Answer: A
Question: A cistern is filled by a tap in 3 1/2 hours. Due to leak in the bottom of the cistern, it takes half an hour longer to fill the cistern. If the cistern is full how long will it take the leak to empty it?
Options:
A)29
B)28
C)99
D)72
E)61
Rationale: 2/7 - 1/x = 1/4
x = 28
Answer: B
Answer: B
Question: A cyclist covers a distance of 90km in 6 hours. Find the speed of the cyclist.
Options:
A)30 km/hr.
B)25 km/hr.
C)20 km/hr.
D)15 km/hr.
E)35 km/hr.
Rationale: Speed of the cyclist =D/T =90/6 =15km/hr. Answer : D
Answer: D
Question: A vendor sells 60 percent of apples he had and throws away 15 percent of the remainder. Next day he sells 50 percent of the remainder and throws away the rest. What percent of his apples does the vendor throw?
Options:
A)17
B)23
C)77
D)26
E)30
Rationale: Explanation :
Let, the number of apples be 100.
On the first day he sells 60% apples i.e.,60 apples. Remaining apples =40.
He throws 15% of the remaining i.e., 15% of 40 = 6.Now he has 40−6=34 apples
The next day he throws 50% of the remaining 34 apples i.e., 17.
Therefore, in total he throws 6+17= 23 apples.
Answer : B
Answer: B
Question: Bucket P has thrice the capacity as bucket Q. It takes 60 turns for bucket P to fill the empty drum. How many turns it will take for both the buckets P and Q, having each turn together to fill the empty drum?
Options:
A)30
B)45
C)50
D)25
E)60
Rationale: Let capacity of P be x liters
Then capacity of Q = x/3 liters
capacity of the drum = 60x
Required number of turns = 60x/(x+x/3) = 60x * 3/4x = 45
Answer is B
Answer: B
Question: In how many years does a sum of Rs. 5000 yield a simple interest of Rs. 16500 at 15% p.a.?
Options:
A)22
B)20
C)25
D)30
E)35
Rationale: T = (100 * 16500)/(15 * 5000) = 22 years
ANSWER A
Answer: A
Question: If x= (y-1)(y+2), then what is the least possible value of x?
Options:
A)-9/4
B)9/4
C)7/4
D)2
E)1
Rationale: Answer : A
Answer: A
Question: The area of a triangle is with base 4m and height 5m?
Options:
A)11
B)10
C)99
D)17
E)12
Rationale: 1/2 * 4 * 5 = 10 m2
Answer: B
Answer: B
Question: A call center has two teams. Each member of Team A was able to process 1/5 calls as compared to each member of Team B. If Team A has 5/8 as many number of call center agents as Team B, what fraction of the total calls was processed by Team B?
Options:
A)3/2
B)3/4
C)8/9
D)1/2
E)1/5
Rationale: Let team B has 8 agents, so team A has 5 agents
Let each agent of team B picked up 5 calls, so total calls by team B = 40
So, each agent in Team A picked up 1 calls, so total calls for team A = 5
Fraction for team B = 40/(40+5) = 8/9 = Answer = C
Answer: C
Question: How many multiples of 5 are there between 1 and 89 ?
Options:
A)15
B)20
C)13
D)17
E)22
Rationale: 5 multiples are 5,10,15,---------,80,85
It should be mentioned whether 1 and 89 are inclusive.
the answer is (85-5)/5+1=17
Answer is D
Answer: D
Question: A person takes 20 minutes more to cover a certain distance by decreasing his speed by 20%. What is the time taken to cover the distance at his original speed?
Options:
A)2 hour 20 minutes
B)1 hour 80 minutes
C)1 hour 20 minutes
D)8 hour 20 minutes
E)1 hour 50 minutes
Rationale: Let the distance and original speed be d km and k kmph respectively.
d/0.8k - d/k = 20/60 => 5d/4k - d/k = 1/3
=> (5d - 4d)/4k = 1/3 => d = 4/3 k
Time taken to cover the distance at original speed
= d/k = 4/3 hours = 1 hour 20 minutes.
Answer:C
Answer: C
Question: For every positive integer n, the nth term of sequence is given by an= 1/n - 1/(n+1). What is the sum of the first 90 terms?
Options:
A)0
B)1
C)25
D)89/90
E)90/91
Rationale: a1 = 1 - 1/2
a2 = 1/2 - 1/3
a3 = 1/3 - 1/4
etc...
a90 = 1/90 - 1/91
The sum of these terms is 1-1/91 = 90/91
The answer is E.
Answer: E
Question: Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. In how much time will the trains cross each other?
Options:
A)70/7 sec
B)80/7 sec
C)40/7 sec
D)60/7 sec
E)90/7 sec
Rationale: B
Relative speed = (54 + 72)* 5/18 = 7 * 5 = 35 mps.
The time required = d/s = (100 + 100 + 200)/35
= 400/35 = 80/7 sec.
Answer: B
Question: What is the difference between the place value of 1 in the numeral 7119?
Options:
A)150
B)160
C)180
D)90
E)210
Rationale: 100 - 10 = 90
D
Answer: D
Question: A person incurs 5% loss by selling a watch for $1140. At what price should the watch be sold to earn 5% profit?
Options:
A)$1260
B)$1150
C)$1542
D)$1000
E)$1292
Rationale: Let the new selling price be $x
(100-loss%): (1st S.P.) = (100+gain%):(2nd S.P.)
(100-5)/1140 = (100+5)/x
x = 105*1140/95 = 1260
Answer is A
Answer: A
Question: An unbiased cubic die is thrown.What is the probability of getting a multiple of 2 and 3?
Options:
A)1/6
B)2/6
C)3/6
D)1
E)1/12
Rationale: Here S={1,2,3,4,5,6}
Let E be the event of getting the multiple of 3
then ,E={3,6}
Let F be the event of getting the multiple of 2
then ,E={2,4,6}
Let G be the event of getting the multiple of 2 and 3
then ,G={6}
P(G)=n(G)/n(S)=1/6
answer option A) 1/6.
Answer: A
Question: In a mixture of a, b and c, if a and b are mixed in 3:5 ratio and b and c are mixed in 8:5 ratio and if the final mixture is 35 liters, find the amount of b?
Options:
A)15.73
B)15.79
C)15.77
D)15.72
E)15.71
Rationale: Ans: As b is common in both ratios, we should equate b in both ratios by multiplying suitable numbers.
a:b = 3 : 5 = 24 : 40
b:c = 8 : 5 = 40 : 25
Now a : b : c = 24 : 40 : 25.
Amount of b in the mixture = 4089×354089×35 = 15.73
Answer:
Answer: A
Question: A garden has 50,000 trees. 12% of the trees are guava trees, 15% are orange trees, 10% are coconut trees and the rest are mango trees. Find the number of mango trees.
Options:
A)30000
B)30200
C)30800
D)31200
E)31500
Rationale: Mango Trees = (100 - 12 - 15 - 10) = 63%.
Number of Mango trees = 63% of 50000 = 31,500.
ANSWER : OPTION E
Answer: E
Question: How many numbers with distinct digits are possible product of whose digits is 28?
Options:
A)6
B)4
C)8
D)12
E)14
Rationale: DETAILED SOLUTION
Two digit numbers; The two digits can be 4 and 7: Two possibilities 47 and 74.
Three-digit numbers: The three digits can be 1, 4 and 7: 3! Or 6 possibilities.
We cannot have three digits as (2, 2, 7) as the digits have to be distinct.
We cannot have numbers with 4 digits or more without repeating the digits.
So, there are totally 8 numbers.
Correct Answer: C
Answer: C
Question: A man’s wages were decreased by 50%. Again, the reduced wages were increased by 50%. He has a loss of?
Options:
A)35%
B)25%
C)20%
D)30%
E)none of these
Rationale: Here, x = - 50 and y = 50
Therefore, the net % change in value
= ( x + y + xy/100) %
= [- 50 + 50 + ( -50 x 50)/100]% or - 25%
Since the sign is negative, there is loss of 25%
ANSWER:B
Answer: B
Question: Convert the 13/36 m/s into kilometers per hour?
Options:
A)1.8 kmph
B)1.6 kmph
C)1.3 kmph
D)3.3 kmph
E)1.9 kmph
Rationale: 13/36 m/s
= 13/36 * 18/5
= 13/10
= 1.3 kmph.
Answer:C
Answer: C
Question: A can do a piece of work 60 days. B can do work in 20 days. In how many days they will complete the work together?
Options:
A)12 days
B)16 days
C)15 days
D)17 days
E)18 days
Rationale: LCM = 60, Ratio= 60:20=3:1
No of days= 60/(3 + 1) = 90/4 = 15 days
ANSWER:C
Answer: C
Question: 2, 7, 36, 4, 14, 225, 6, 21, ?
Options:
A)576
B)476
C)376
D)584
E)594
Rationale: 2, 7, 36, 4, 14, 225, 6, 21, ?
2+7=9 and 9-3=6 and 6^2=36
4+14=18 and 18-3=15 and 15^2=225
6+21=27 and 27-3=24 and 24^2=576
ANSWER:A
Answer: A
Question: A person who has a certain amount with him goes to market. He can buy 50 oranges or 40 mangoes. He retains 10% of the amount for taxi fares and buys 20 mangoes and of the balance he purchases oranges. Number of oranges he can purchase is
Options:
A)36
B)40
C)15
D)20
E)10
Rationale: Explanation :
Let the person has x Rs , then price of 50 oranges or 40 mangoes is x Rs.
Therefore, from given information x = (x / 10) + (x / 2) + Amount left.
Hence, the amount left to buy oranges is (2x / 5) , since price of 50 oranges or 40 mangoes is x Rs , hence price of 1 orange, 1 mango is (x / 50), (x / 40) respectively.
Hence, he can buy (2 /5) x 50 = 20 oranges.
Answer : D
Answer: D
Question: Before a salary increase, the weekly salary of a worker for 42 hours in a week was as much as the worker is paid now for 40 hours of work in a week. What is the percent increase in the worker's salary per hour?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: Let x be the original salary per hour.
Let y be the salary per hour after the increase.
40y=42x
y=(42/40)x=1.05x
The salary increased 5%.
The answer is C.
Answer: C
Question: How can a cake(circular) be cut into 8 pieces by making just 3 cuts?
Options:
A)21
B)787
C)37
D)26
E)01
Rationale: Explanation:
Cut the cake using three mutually perpendicular planes. It leaves 8 pieces, one each in each octant.
AnswerA
Answer: A
Question: Kathleen can paint a room in 2 hours, and Anthony can paint an identical room in 7 hours. How many hours would it take Kathleen and Anthony to paint both rooms if they work together at their respective rates?
Options:
A)28/9
B)4/3
C)15/8
D)9/4
E)15/4
Rationale: (1/2 + 1/7)t=2
t=28/9
Answer: A
Answer: A
Question: If a no. when divided by 44, gives 432 as quotient and 0 as remainder. What will be the remainder when dividing the same no. by 34
Options:
A)2
B)3
C)5
D)7
E)9
Rationale: P Ã· 44 = 432
=> P = 432 * 44 = 19008
P / 34 = 19008 / 34 = 559, remainder = 2
A
Answer: A
Question: How should be added in order to make 2345672 this number is divisible by 9?
Options:
A)5
B)6
C)7
D)8
E)9
Rationale: Sum of the numbers 2345672 is 29 which is not multiple of 9
Add 7 which makes the sum 36 which is multiple of 9
So digit becomes 2345679 (as we know that if sum multiple of 9 then it is divisible of 9)
Answer:C
Answer: C
Question: If 8 spiders make 8 webs in 8 days, then 1 spider will make 1 web in how many days?
Options:
A)7
B)6
C)5
D)8
E)3
Rationale: Let the required number days be x.
Less spiders, More days (Indirect Proportion)
Less webs, Less days (Direct Proportion)
spiders 1:8
Webs 8:1
1 x 8 x x = 8 x 1 x 8
=> x= 8
Answer is D
Answer: D
Question: How many multiples of 5 are there between 1 and 36, exclusive?
Options:
A)2
B)5
C)6
D)7
E)9
Rationale: 7
multiples of 5 between 1 and 36 exclusive.
from 5 * 1 upto 5*7, (1,2,3,4,...,7). Hence, 7 multiples !
correct option is D
Answer: D
Question: Stephanie, Regine, and Brian ran a 20 mile race. Stephanie and Regine's combined times exceeded Brian's time by exactly 2 hours. If nobody ran faster than 8 miles per hour, who could have won the race?
I. Regine
II. Stephanie
III. Brian
Options:
A)I only
B)II only
C)III only
D)I or II only
E)II, or III
Rationale: Given that S+R=B+2, where S, R, and B are times in which Stephanie, Regine, and Brian completed the race.
Min time one could complete the race is 20/8=2.5 hours. Let's see if Brian could have won the race: if he ran at the fastest rate, he would complete the race in 2.5 hours, so combined time needed for Stephanie and Regine would be S+R=B+2=4.5 hours, which is not possible as sum of two must be more than or equal the twice the least time: 2*2.5=5. So Brian could not have won the race.
There is no reason to distinguish Stephanie and Regine so if one could have won the race, another also could. So both could have won the race.
Answer: E.
Answer: E