mathewhe/aqua_rat huggingface dataset:
Question: Betty worked for three straight hours on her homework questions. If she solved 120 questions in the third hour, which was five times as many as she solved in the second hour, and six times as many questions as she solved in the first hour, how many questions did she solve in total?
(A) 156
(B) 160
(C) 164
(D) 168
(E) 172
Rationale: In the first hour, Betty solved 120/6 = 20 questions.
In the second hour, Betty solved 120/5 = 24 questions.
In the third hour, Betty solved 120 questions.
The total is 20 + 24 + 120 = 164.
The answer is C.
Answer: (C) 164
Question: The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is:
(A) 153600 m^2
(B) 153660 m^2
(C) 153700 m^2
(D) 153800 m^2
(E) 153900 m^2
Rationale: Perimeter = Distance covered in 8 min. = 12000	x 8	m = 1600 m.
60
Let length = 3x metres and breadth = 2x metres.
Then, 2(3x + 2x) = 1600 or x = 160.
Length = 480 m and Breadth = 320 m.
Area = (480 x 320) m2 = 153600 m^2.
A
Answer: (A) 153600 m^2
Question: Rs.280 contained in a box consists of one rupee, 50 paisa and 25 paisa coins in the ratio 4:5:6. What is the number of 25 paisa coins?
(A) 210
(B) 266
(C) 120
(D) 299
(E) 267
Rationale: 4x 5x 6x
100 50 25
400x + 250x + 150x = 28000
x = 35
6x = 210
Answer: A
Answer: (A) 210
Question: A man can row at 6 kmph in still water. If the velocity of current is 1 kmph and it takes him 1 hour to row to a place and come back, how far is the place?
(A) 2.4 km
(B) 2.6 km
(C) 2.9 km
(D) 4.4 km
(E) 5.6 km
Rationale: Explanation:
Speed in still water = 6 kmph
Speed of the current = 1 kmph
Speed downstream = (6+1) = 7 kmph
Speed upstream = (6-1) = 5 kmph
Let the required distance be x km
Total time taken = 1 hour
â‡’ x/7+x/5=1
â‡’5x+7x=35
â‡’12x=35
â‡’x=2.9 km
Answer: Option C
Answer: (C) 2.9 km
Question: 2x<5y<0 which of the following is the greatest?
(A) 6x+3y
(B) -(2x+2y)
(C) -x+4y
(D) 2x+6y
(E) x-2y
Rationale: Plugging in -1 for both x and y we get
A. 6x+3y =-9
B. -(2x+2y) =4
C. -x+4y =-3
D. 2x+6y =-8
E. x-2y =1
Answer: B
Answer: (B) -(2x+2y)
Question: 85% of a number is added to 24, the result is the same number. Find the number?
(A) 150
(B) 140
(C) 130
(D) 160
(E) 170
Rationale: (85/100) * X + 24 = X
3X = 480
X = 160
ANSWER:D
Answer: (D) 160
Question: Working together, Wayne and his son can shovel the entire driveway in three hours. If Wayne can shovel four times as fast as his son can, how many hours would it take for his son to shovel the entire driveway on his own?
(A) 4
(B) 6
(C) 5
(D) 9
(E) 12
Rationale: W: the time for Wyane to do the job
S: the time for his son to do the job
We have 1/W + 1/S = 1/4 and W = 4S
Then we have 1/(4*S) + 1/S = 1/4 <=> 5/(4*S) = 1/4 <=> S = 5
ANS: C
Answer: (C) 5
Question: The banker’s discount of a certain sum of money is Rs. 72 and the true discount on the same sum for the same time is Rs. 60. The sum due is
(A) 210
(B) 280
(C) 360
(D) 450
(E) None
Rationale: Sol.
Sum = B.D. * T.D. / B.D. - T.D. = Rs.[72 * 60 / 72 - 60] = Rs. [72 * 60 / 12] = Rs. 360.
Answer C
Answer: (C) 360
Question: In how many ways can an animal trainer arrange 5 lions and 4 tigers in a row so that no two lions are together?
(A) 2880
(B) 3000
(C) 3100
(D) 3200
(E) 3400
Rationale: They have to be arranged in the following way:
| L | T | L | T | L | T | L | T | L |
The 5 lions should be arranged in the 5 places marked 'L'.
This can be done in 5! ways.
The 4 tigers should be in the 4 places marked 'T'.
This can be done in 4! ways.
Therefore, the lions and the tigers can be arranged in 5!×4!=5!×4!= 2880 ways
Option is A
Answer: (A) 2880
Question: On increasing the number of lines in a page by 60, they become 240. What is the % of increase in the no. of lines in the page?
(A) 33.3%
(B) 305
(C) 50%
(D) 55%
(E) 60%
Rationale: Explanation : Number of pages increased = 60
Now , the number of pages of book = 240
Number of pages of the books before increase = 240 – 60 = 180
% increase in the number of pages in the book = 60 /180
x 100% = 33.3%
A
Answer: (A) 33.3%
Question: x and y are positive integers. If 1/x + 1/y < 2, which of the following must be true?
(A) x + y > 4
(B) xy>1
(C) x/y + y/x < 1
(D) (x - y)^2 > 0
(E) None of the above
Rationale: since x and y are both +ive int, x*y>1... only exception being x=y=1 as it is not given they are different integers...
however it is given 1/x +1/y<2.. this cannot be true if x=y=1.... so one or both have to be > 1
ANSWER:B
Answer: (B) xy>1
Question: A started a business with an investment of Rs. 70000 and after 6 months B joined him investing Rs. 120000. If the profit at the end of a year is Rs. 26000, then the share of B is?
(A) s.12028
(B) s.12000
(C) s.12003
(D) s.12029
(E) s.24029
Rationale: Ratio of investments of A and B is (70000 * 12) : (120000 * 6) = 7 : 6
Total profit = Rs. 26000
Share of B = 6/13 (26000) = Rs.12000
Answer: B
Answer: (B) s.12000
Question: Two trains of length 100 m and 200 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet?
(A) 18 sec
(B) 15 sec
(C) 21 sec
(D) 20 sec
(E) 19 sec
Rationale: Relative speed = (42 + 30) * 5/18 = 4 * 5
= 20 mps.
Distance covered in passing each other
= 100 + 200 = 300 m.
The time required = d/s
= 300/20
= 15 sec.
Answer: B
Answer: (B) 15 sec
Question: Mr. Smith calculated the average of 10 three digit numbers. But due to a mistake he reversed the digits of a number and thus his average increased by 39.6 The difference between the unit digit and hundreds digit of that number is :
(A) 2
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: Since the average increased by 39.6 and there were a total of 10 numbers, it means the incorrect number was 39.6 greater than the correct number.
Say, the correct number was abc (where a, b and c are the digits of the 3 digit number)
Then the incorrect number was cba.
100c + 10b + a - (100a + 10b + c) = 396
99c - 99a = 99(c - a) = 396
99*4 = 99(c - a)
So c - a = 4
Answer (B)
Answer: (B) 4
Question: A train passes a platform in 32 seconds. The same train passes a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, The length of the platform is
(A) 180 meter
(B) 240 meter
(C) 200 meter
(D) 260 meter
(E) None of these
Rationale: Explanation:
Speed of the train = 54 km/hr = (54×10)/32 m/s = 15 m/s
Length of the train = speed × time taken to cross the man = 15×20 = 300 m
Let the length of the platform = L
Time taken to cross the platform = (300+L)/15
=> (300+L)/15 = 32
=> 300+L = 15×32 =480
=> L = 480-300 = 180 meter
Answer: Option A
Answer: (A) 180 meter
Question: A wooden cube whose edge length is 5 inches is composed of smaller cubes with edge lengths of one inch. The outside surface of the large cube is painted red and then it is split up into its smaller cubes. If one cube is randomly selected from the small cubes, what is the probability that the cube will have at least one red face?
(A) 70.6%
(B) 74.5%
(C) 78.4%
(D) 82.1%
(E) 86.9%
Rationale: There are a total of 5*5*5 = 125 cubes.
All the exterior cubes will have at least one face painted red.
The interior is formed by 3*3*3 = 27 cubes.
The number of cubes with at least one side painted red is 125 - 27 = 98 cubes
The probability that a cube has at least one side painted red is 98/125 which is 78.4%
The answer is C.
Answer: (C) 78.4%
Question: In a code language “He gives flower” is written as “nop lui na” , “Bunty gets flower” is written as “dus lap na” and “He gets nothing” is written as “nop lap ugli”. How would “Bunty gets nothing” be written in that code ?
(A) dus lap ugli
(B) dus lap uglJ
(C) dus lap ugl2
(D) Dus lFp ugli
(E) dus ap uglDi
Rationale: Explanation:
He gives flower ---------> nop lui na ---------- (a)
Bunty gets flower -------> dus lap na ----------- (b)
He gets nothing ----------> nop lap ugli --------- (c)
From a and b, we get “flower ===> na”; while from b and c, we get “gets ===> lap”. Hence from b, we get “Bunty ===> dus”. Now from a and c, we get “He ===> nop”.
Hence from c, we get “nothing ===> ugli”. Hence we have “Bunty gets nothing ===> dus lap ugli”.
ANSWER: A
Answer: (A) dus lap ugli
Question: Five family members are seated around their circular dinner table. If only arrangements that are considered distinct are those where family members are seated in different locations relative to each other, and Michael and Bobby insist on sitting next to one another, then how many distinct arrangements around the table are possible?
(A) 10
(B) 12
(C) 14
(D) 16
(E) 18
Rationale: Let's consider Michael and Bobby as one unit.
There are 4! possible arrangements of 4 units.
Around a table, there would be repetitions of each arrangement, so we divide by 4.
Then there are 3! arrangements around a circular table.
For each arrangement, Michael and Bobby can switch places, so we multiply by 2.
The number of arrangements is 3!*2 = 12.
The answer is B.
Answer: (B) 12
Question: If the selling price of 50 articles is equal to the cost price of 35 articles, then the loss or gain percent is:
(A) 45%
(B) 23%
(C) 30%
(D) 60%
(E) 56%
Rationale: C.P. of each article be Re. 1.
Then, C.P. of 50 articles = Rs. 50;
S.P. of 50 articles = Rs. 35.
Loss % = 15/50 * 100 = 30%
ANSWER C
Answer: (C) 30%
Question: In a certain sequence, each term except for the first term is one less than twice the previous term. If the first term is 1.25, then the 3rd term is which of the following?
(A) −1.5
(B) −1
(C) 0
(D) 0.5
(E) 2
Rationale: First = 1.25
Second = 2*1.25-1 = 1.5
Second = 2*1.5-1 = 2
Answer: option E
Answer: (E) 2
Question: If x is 11 percent greater than 70, then x =
(A) 77.7
(B) 91.0
(C) 88.0
(D) 70.9
(E) 71.2
Rationale: 11% of 70 = (70*0.11) = 7.7
11% greater than 70 = 70 + 7.7 = 77.7
Answer is clearly A.
Answer: (A) 77.7
Question: A group of four girls and three boys have tickets for seven adjacent seats in one row of a theater. If the three boys will not sit in three adjacent seats, how many possible different seating arrangements are there for these 7 theatre-goers?
(A)  7! – 2!3!2!
(B)  7! – 4!3!
(C)  7 × 2!3!2!
(D)  7! – 5!3!
(E)  2!3!2!
Rationale: There are 3 boys and 4 girls , we want to calculate the seating arrangements if three boys do not sit together, like MMM.
Let's calculate the # of arrangements when they SIT together and subtract from total # of arrangements of these 7 persons without restriction. Thus we'll get the # of arrangements asked in the question.
1. Total # of arrangements of 7 is 7!.
2. # of arrangements when 3 boys are seated together, like MMM;
Among themselves these 3 boys can sit in 3! # of ways,
Now consider these 3 boys as one unit like this {MMM}. We'll have total of 5 units: {MMM}{W}{W}{W}{W}. The # of arrangements of these 5 units is 5!.
Hence total # of arrangements when 3 men sit together is: 3!5!.
# of arrangements when 3 boys do not sit together would be: 7!-3!5!.
Answer: D).
Answer: (D)  7! – 5!3!
Question: If each participant of a chess tournament plays exactly one game with each of the remaining participants, then 231 games will be played during the tournament. What is the number of participants?
(A) 16
(B) 18
(C) 20
(D) 22
(E) 24
Rationale: Let n be the number of participants.
The number of games is nC2 = n*(n-1) / 2 = 231
n*(n-1) = 462 = 22*21 (trial and error)
The answer is D.
Answer: (D) 22
Question: A club with a total membership of 30 has formed 3 committees, M, S and R, which have 8, 12 and 7 members respectively. If no members of committee M is on either of the other 2 committees, what is the greatest possible number of members in the club who are on none of the committees?
(A) 5
(B) 7
(C) 8
(D) 10
(E) 12
Rationale: As no member of committee M is on either of the other 2 committees then 30-M=30-8=22 people are on committee S, committee R or on none of the committee. We want to maximize the last group: members in the club who are on none of the committees
General rule for such kind of problems:
to maximize one quantity, minimize the others;
to minimize one quantity, maximize the others.
So we should minimize total # of people who are on committee S and committee R. Now if ALL 5 people who are the members of committee R are also the members of committee S (if R is subset of S) then total # members of committee S and committee R would be minimized and equal to 12. Which means that 22-12=10 is the greatest possible number of members in the club who are on none of the committees.
Answer: D.
Answer: (D) 10
Question: A train 140 m long, running with a speed of 63 km/hr will pass a tree in?
(A) 18 sec
(B) 6 sec
(C) 8 sec
(D) 15 sec
(E) 7 sec
Rationale: Speed = 63 * 5/18 = 35/2 m/sec
Time taken = 140 * 2/35 = 8 sec
Answer:C
Answer: (C) 8 sec
Question: Jenny has recently moved house and is working out her optimal commute. She can take an indirect route which involves taking a bus for 1 mile and then walk 0.75 miles. Or she can take a direct route and walk for 1.5 miles and this takes her 30 minutes. What is the most amount time that the bus journey can take for Jenny to be indifferent between the two routes assuming travel time is her only concern?
(A) 5 minutes
(B) 10 minutes
(C) 15 minutes
(D) 20 minutes
(E) 25 minutes
Rationale: If Jenny can walk 1.5 miles in 30 minutes, then she can talk 0.75 miles in half the time i.e. 15 minutes.
For Jenny to be indifferent between the two routes, the two journeys must have the same travel time.
The direct route has a travel time of 30 minutes (walking).
The indirect route has a travel time of 15 minutes (walking) plus the bus journey.
For the two routes to be the same the bus journey must take 15 minutes (30-15).
ANSWER: C
Answer: (C) 15 minutes
Question: What are the last two digits of (301*402*503*604*646*547*448*348)^2
(A)  86
(B)  76
(C)  56
(D)  36
(E)  16
Rationale: ((301*402*503*604*646)*(547*448*348))^2
If you observe above digits, last digit are: 1,2,3,4,6,7,8,8; 5 is missing; so I have rearranged them so that multiplication will be easy for me as initial 4 digits have last two digits as 01,02,03,04,46 and final three as 47*48*48.
Solving for only last two digits and multiplying them we get:( (06*04*46)(56*48))^2 = (44*88)^2=72^2=84
Hence answer is A
Answer: (A)  86
Question: Find the odd man out
2880, 480, 96, 24, 10, 4, 4
(A) 480
(B) 96
(C) 24
(D) 10
(E) 4
Rationale: from the right side
4*1=4,
4*2=8 but here given 10 so it's not.
8*3=24
24*4=96
96*5=480
480*6=2880
ANSWER:D
Answer: (D) 10
Question: 16 boys or 24 girls can construct the wall in 6 days. the number of days that 8 boys and 12 girls Will take to construct?
(A) 7 days
(B) 14 days
(C) 6 days
(D) 8 days
(E) 9 days
Rationale: Explanation:
16 boys =24 girls, 1 boy = 24/16 girls
1 boy = 6/4 girls
8 boys + 12 girls = 8 × 6/4 + 12 = 12 + 12 = 24 girls
6 days to complete the work
Answer: Option C
Answer: (C) 6 days
Question: If two integers x, y (x>y) are selected from -10 to 4 (inclusive), how many possible cases are there?
(A) 150
(B) 180
(C) 190
(D) 210
(E) 105
Rationale: If two integers x, y (x>y) are selected from -10 to 9 (inclusive), how many possible cases are there?
A. 150
B. 180
C. 190
D. 210
E. 240
--> 15C2=15*14/2=105. Therefore, the answer is E.
Answer: (E) 105
Question: 7 girls buy hand bag cost 70 dollars. On account of Christmas there is 20% discount. They Buy hand mirrors with their savings on bag. what is actual cost of each mirror.
(A) 15.5
(B) 14
(C) 17.5
(D) 15
(E) 19.5
Rationale: Solution: E.70*7 = 490 without off. 490 with 20% of is 392. and total 98 savings and 14 dollars each girl. mirror cost 14 but still Christmas discount applies. so actual cost of mirror is 17.5 dollars
Answer: (C) 17.5
Question: In how many ways can the letters of the word MOUSES be arranged?
(A) 390
(B) 360
(C) 320
(D) 330
(E) 300
Rationale: MOUSES has 6 words, but S is repeated two times. Thus ways = 6! / 2! = 360 ways
B
Answer: (B) 360
Question: A and B can do a job is 16 days and 12 days respectively. 4 days before finishing the job, A joins B. B has started the work alone. Find how many days B has worked alone?
(A) 6 days
(B) 4 days
(C) 5 days
(D) 7 days
(E) None of these
Rationale: A’s one day’s work = 1⁄16 th work
B’s one day’s work 1⁄12 th work
Let B has worked alone = x days. Then,
A’s amount of work + B’s amount of work = 1
⇒ 4(1⁄16) + (x + 4)(1⁄12) = 1
⇒ 1/4+x+4/12 = 1 ⇒ x = 3⁄4 × 12 - 4
⇒ x = 5 days.
Answer C
Answer: (C) 5 days
Question: On July 1 of last year, total employees at company E was decreased by 10 percent. Without any change in the salaries of the remaining employees, the average (arithmetic mean) employee salary was 10 percent more after the decrease in the number of employees than before the decrease. The total of the combined salaries of all the employees at Company E after July 1 last year was what percent Q of thatbeforeJuly 1 last year?
(A) 90%
(B) 99%
(C) 100%
(D) 101%
(E) 110%
Rationale: the total number of employees = n
the average salary = x
total salary to all emplyoees = xn
after
the total number of employees = n - 0.1n = 0.9n
the average salary = x + 10% of x = 1.1x
total salary to all emplyoees = 0.9n (1.1x)
total salary after as a % of total salary before Q= [0.9n (1.1x)]/xn= 0.99 or 99%=B
Answer: (B) 99%
Question: What is the % change in the area of a rectangle when its length increases by 25% and its width decreases by 25%?
(A) 0%
(B) 20% increase
(C) 20% decrease
(D) 6% decrease
(E) Insufficient data
Rationale: (125/10)*(75/10) = 9375/100 ~94 of original area
0.94 is a 6% decrease from 100/100 ->D
Answer: (D) 6% decrease
Question: A certain car averages 20 miles per gallon of gasoline when driven in the city and 40 miles per gallon when driving on the highway. According to these rates, which of the following is closest to the number of miles per gallon that the car averages when it is driven 10 miles in the city and then 50 miles on the highway?
(A) 28
(B) 30
(C) 34
(D) 36
(E) 38
Rationale: 10*1/20 gpm+50*1/40 gpm=1.75 total gallons
60 total miles/1.75 total gallons=34.3 average mpg
C. 34
Answer: (C) 34
Question: 3 candidates in an election and received 1136, 7636 and 11628 votes respectively. What % of the total votes did the winningcandidate got in that election?
(A) 45%
(B) 50%
(C) 57%
(D) 59%
(E) 62
Rationale: Total number of votes polled = (1136 + 7636 + 11628) = 20400
So, Required percentage = 11628/20400 * 100 = 57%
C
Answer: (C) 57%
Question: The total number of pupils in Class A is 40 out of which 18 are girls, In Class B there are 20 are boys out of total 35 and in Class C there are 16 girls out of total 32. What is the percent of total girls in all the classes.
(A) 33.9%
(B) 43.6%
(C) 32.7%
(D) 62.7%
(E) 22.8%
Rationale: Class A girls = 18
Class B girls = 35-20 = 15
Class C girls = 16
Total percentage = (18+15+16)/(40+35+32) = 35/107 = 0.327
C
Answer: (C) 32.7%
Question: A number Y is chosen at random from the numbers 1, -3, -1, 0, 1, 2, 3. What is the probability that |X|<3?
(A) 1/5
(B) 2/7
(C) 2/9
(D) 3/7
(E) 3/11
Rationale: |X||X| can take 7 values.
To get |X|<2|X|<2 ( i.e., −2<x<+2−2<x
⇒ P(|X|<2)= Favourable CasesTotal CasesP(|X|<2)= Favourable CasesTotal Cases
= 3/7
D
Answer: (D) 3/7
Question: Consider below info to be a table:
AMOUNT OF BACTERIA
TIME - AMOUNT
1PM - 10gms
4PM - x gms
7PM - 22.5 gms
Data for a certain biology experiment are given in the table above. If the amount of bacteria present increased by the same factor during each of the two 3-hour periods shown, how many grams of bacteria were present at 4PM ?
(A) 15.0
(B) 12.1
(C) 12.2
(D) 12.3
(E) 12.4
Rationale: let say the factor is x, the at 7PM quantity = 10 (i.e. quantity @1PM)* x^2 =22.5 => x^2 =2.25 or x = 1.5 => @4PM quantity = 10x =10*1.5 =15.
Answer A
Answer: (A) 15.0
Question: A man spends 10% of his income in house rent, 20% of the rest on his children’s education, 25% of the rest miscellaneous causes. If he now posses Rs. 1944 then his income is?
(A) 3600
(B) 3607
(C) 3606
(D) 3655
(E) 3622
Rationale: X * (90/100) * (80/100) * (75/100) = 1944
X * 0.9 * 0.8 * 0.75
X = 1944/0.54
X = 3600
Answer: A
Answer: (A) 3600
Question: Income and expenditure of a person are in the ratio 5 : 4. If the income of the person is Rs. 16000, then find his savings?
(A) 3600
(B) 3607
(C) 3200
(D) 3602
(E) 3603
Rationale: Let the income and the expenditure of the person be Rs. 5x and Rs. 4x respectively.
Income, 5x = 16000 => x = 3200
Savings = Income - expenditure = 5x - 4x = x
So, savings = Rs. 3200.
Answer:C
Answer: (C) 3200
Question: If p is a natural number and p! ends with g trailing zeros, then the number of zeros that (5p)! ends with will be
(A) a) (p+g) trailing zeros
(B) b) (5p+y) trailing zeros
(C) c) (5p+5y) trailing zeros
(D) d) (p+5y) trailing zeros
(E) e) none of them above
Rationale: Let p = 1. p! = 1! = 1, which means g= 0
(5p)! = 5! = 120, trailing zeros = 1
1 = 1 + 0 = p + g
Answer (A).
Answer: (A) a) (p+g) trailing zeros
Question: If Rs. 782 be divided into three parts, proportional to 1/2:2/3:3/4, then the first part is:
(A) Rs. 182
(B) Rs. 190
(C) Rs. 196
(D) Rs. 204
(E) Rs. 210
Rationale: Explanation:
Given ratio =1/2:2/3:3/4=6:8:9
1st part = Rs. 782*6/23=Rs. 204
Answer is D
Answer: (D) Rs. 204
Question: A team bought a total of 466 balls. If each player on the team bought at least 13 balls, then what is the greatest possible number of players on the team?
(A) 21
(B) 22
(C) 23
(D) 24
(E) 35
Rationale: 466/13=35 plus remainder.
The answer is E.
Answer: (E) 35
Question: A and B together can do a piece of work in 8 days. If A alone can do the same work in 12 days, then B alone can do the same work in?
(A) 33
(B) 66
(C) 24
(D) 88
(E) 99
Rationale: B = 1/8 – 1/2 = 1/24 => 24 days
Answer:C
Answer: (C) 24
Question: M = {-6, -5, -4, -3, -2}
T = {-2, -1, 0, 1, 2, 3, 4}
If an integer is to be randomly selected from set M above and an integer is to be randomly selected from set T above, what is the probability that the product of the two integers will be negative?
(A) 0
(B) 11/35
(C) 4/7
(D) 1/2
(E) 3/5
Rationale: Answer C.
Total # of outcomes: 5*7= 35
# of outcomes where Product is -ve : (-6,1) ,(-6,2), (-6,3)... Hence, total: 20
Probability: 4/7
Answer: (C) 4/7
Question: Six bells commence tolling together and toll at intervals of 2, 4, 6, 8 10 and 12 seconds respectively.
In 30 minutes, how many times do they toll together?
(A) 12
(B) 14
(C) 15
(D) 16
(E) 17
Rationale: Explanation :
Here's the simple solution :
Take lcm of 2,4,6,8,10,12 seconds
The outcome is 120seconds.
Convert it into minutes = 120 / 60
= 2 minutes
In 30mins it will rings 15times together
But ,In 0th second all bells rings together
Hence Total number of bell rings is = 15 + 1
= 16
Hence (D) is the correct answer.
Answer : D
Answer: (D) 16
Question: A man whose speed is 4.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey?
(A) 6
(B) 4
(C) 9
(D) 3
(E) 2
Rationale: M = 45
S = 1.5
DS = 6
US = 3
AS = (2 * 6 * 3) /9
= 4
Answer:B
Answer: (B) 4
Question: A random 10-letter code is to be formed using the letters A, B, C, D, E, F, G, H, I and I (only the “I” will be used twice). What is the probability that a code that has the two I’s adjacent to one another will be formed?
(A) 1/10
(B) 1/8
(C) 1/5
(D) 1/4
(E) 1/2
Rationale: Total number of combinations possible = 10!/2!10!/2!
Total favorable combinations = 9!9! - We have considered the two Is as one element. Since we have two Is, they can interchange their positions, without affecting the code.
Probability = 9!/(10!/2!)=9!∗2!/10!=1/59!/(10!/2!)=9!∗2!/10!=1/5
ANS:C
Answer: (C) 1/5
Question: Find the number of square tiles to cover the floor of a room measuring 6 m * 14 m leaving 0.50 m space around the room. A side of square tile is given to be 50 cms?
(A) 271
(B) 260
(C) 277
(D) 200
(E) 212
Rationale: 5 * 13 = 1/2 *1/2* x => x = 260
Answer: B
Answer: (B) 260
Question: The average age of P, Q, R, S five years ago was 45 years. By including T, the present average age of all the five is 49 years. The present age of T is?
(A) 64 years
(B) 48 years
(C) 45 years
(D) 40 years
(E) None of these
Rationale: Present age of P, Q, R, S = 45 x 4 + 20 = 200
Present age of P, Q, R, S and T = 49 x 5 = 245
Hence, the age of T = 245 - 200 = 45 years.
ANSWER:C
Answer: (C) 45 years