RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: If you spend 1/4 of your salary during the first week of the month and 20% of it during each of the coming 3 weeks, what part(fraction) of your salary will leave unspent at the end of the month?
A.2/20
B.3/20
C.4/20
D.5/20
Answer: B.3/20
Explanation: Solution:
1/4+3(20/100)=1/4+3/5=5+12/20=17/20
The sallary that will be spent = 17/20
Unspend will be = 1−17/20 =20−17/20 =3/20
Answer B
Question: A set of football matches is to be organized in a "round-robin" fashion, i.e., every
participating team plays a match against every other team once and only once. If 2
matches are totally played, how many teams participated?
A.4
B.5
C.6
D.2
Answer: D.2
Explanation: 2 ways to solve this problem..
summation(x)=n(n-1)/2
n(n-1)/2=2;
n^2-n-4=0
Ans : 2
ANSWER:D
Question: The length of a rectangular plot is thrice its width. If the area of the rectangular plot is 432 sq meters, then what is the width (in meters) of the rectangular plot?
A.10
B.11
C.12
D.13
Answer: C.12
Explanation: Area = L*W = 3W^2 = 432
W^2 = 144
W = 12
The answer is C.
Question: The total number of digits used in numbering the pages of a book having 360 pages is
A.972
B.990
C.1098
D.1305
Answer: A.972
Explanation: Total number of digits
= (No. of digits in 1- digit page nos. + No. of digits in 2-digit page nos. + No. of digits in 3- digit page nos.)
= (1 x 9 + 2 x 90 + 3 x 261) = (9 + 180 + 783) = 972.
ANSWER:A
Question: Gold is 19 times as heavy as water and copper is 9 times as heavy as water. In what ratio should these be mixed to get an alloy 12 times as heavy as water?
A.1:2
B.3:7
C.4:1
D.5:2
Answer: B.3:7
Explanation: G = 19W
C = 9W
Let 1gm of gold mixed with x gm of copper to get 1+x gm of the alloy
1gm gold + x gm copper = x+1 gm of alloy
19W+9Wx = x+1 * 12W
19+9x = 12(x+1)
x = 7/3
Ratio of gold with copper = 1:7/3 = 3:7
Answer is B
Question: The sum of two numbers is 20 and the sum of their squares is 140. Find the product of the two numbers.
A.130
B.140
C.120
D.145
Answer: A.130
Explanation: Let a and b be the two numbers(a+b)^2=a^2+2ab+b^2Given (a+b)=20 a^2+b^2=140So, 20^2=140+2ab2ab=400-1402ab=260ab=130Ans A
Question: A river 4m deep and 22 m wide is flowing at the rate of 2 kmph the amount of water that runs into the sea per minute is?
A.4500
B.2678
C.2933
D.2761
Answer: C.2933
Explanation: (2000 * 4 *22 )/60
= 2933 M3
Answer:C
Question: An amount of Rs.1560 was divided among A, B and C in the ratio 1/2:1/3:1/4. Find the share of C?
A.Rs.367
B.Rs.386
C.Rs.369
D.Rs.360
Answer: D.Rs.360
Explanation: Let the shares of A, B and C be a, b and c respectively.
a:b:c = 1/2:1/3:1/4
a:b:c = 6/12:4/12:3:12 = 6:4:3
Share of C = 3/13 * 1560 = Rs.360.
Answer:D
Question: In how many ways can five members be selected from a group of twelve members?
A.12C5
B.12C8
C.12C4
D.11C3
Answer: A.12C5
Explanation: five members can be selected from twelve members in
12C5
= 12C5 ways.
Answer: A
Question: Sum of products of three numbers taken two at a time is 131. Sum of squares of the three numbers is 138. What is the sum of the three numbers?
A.20
B.88
C.26
D.18
Answer: A.20
Explanation: Explanation:
All the data given in the question points to the equation mentioned below:
Considering the three numbers to be a,b and c:
(a+b+c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca
Accordingly, substitute for a, b and c and solve:
=> a2+b2+c2= 138, ab+bc+ac = 131. Thus, 2(ab+bc+ac)= 2*131= 262
(a+b+c)2= 138+262= 400.
Therefore, a+b+c= 20
ANSWER: A
Question: A jar full of whiskey contains 40% alcohol. A part of this whisky is replaced by another containing 19% alcohol and now the percentage of alcohol was found to be 26%. The quantity of whisky replaced is
A.1/3
B.2/3
C.2/5
D.1/4
Answer: B.2/3
Explanation: 1 st jar (alchohol) = 40%
2nd jar = 19%
after mix = 26%
mean = 7:14=1:2=>2/1+2=2/3
ANSWER B
Question: It takes Greg 6 minutes to run a mile, and it takes Pete 8 minutes. If Greg and Pete both begin running at exactly 8:30 a.m. without pausing, when is the first time at which they will finish running a mile simultaneously?
A.8:36 am
B.8:38 am
C.8:48 am
D.8:54 am
Answer: D.8:54 am
Explanation: Since Greg will run s miles after s × 6 minutes and Pete will run c miles after c × 8 minutes, they both will finish running a mile at the same time when s × 6 = c × 8. Since s and c must be integers (they represent the number of miles finished) this question is asking you to find a common multiple of 6 and 8. The question asks for the first time they will finish running a mile simultaneously, so you must find the least common multiple. The least common multiple of 6 and 8 is 24, so in the context of the question, this would be 24 minutes. Therefore, the first time they will finish running a mile at the same time is 8:30 + 24 minutes, or 8:54 a.m. The answer is (D).
Question: The greatest number of four digits which is divisible by 15, 25, 40 and 75 is:
A.9000
B.9400
C.9600
D.9800
Answer: C.9600
Explanation: Greatest number of 4-digits is 9999.
L.C.M. of 15, 25, 40 and 75 is 600.
On dividing 9999 by 600, the remainder is 399.
Required number (9999 - 399) = 9600.
Answer: Option C
Question: If the man walks at the rate of 5 kmph, he misses a train by 7 minutes. However, if he walks at the rate of 6 kmph, he reaches the station 5 minutes before the arrival of the train. Find the distance covered by him to reach the station.
A.4
B.5
C.6
D.7
Answer: C.6
Explanation: Let the distance be x
Difference Between time = 12 min, which is 12/60 in hour which is 1/5
Now x/5-x/6 = 1/5
6x-5x/30 = 1/5
x/30 = 1/5
x = 30/5
x=6 So the required distance = 6
ANSWER:C
Question: 85% of a number is added to 24, the result is the same number. Find the number?
A.257
B.267
C.187
D.one hundred sixty (160)
Answer: D.one hundred sixty (160)
Explanation: (85/100) * X + 24 = X
3X = 480
X = 160
Answer:D
Question: A person has to cover a distance of 6 km in 45 minutes. If he covers one-half of the distance in two-thirds of the total time; to cover the remaining distance in the remaining time, what should be his speed in km/hr?
A.12 km/hr
B.14 km/hr
C.10 km/hr
D.8 km/hr
Answer: A.12 km/hr
Explanation: Explanation:
The person needs to cover 6 km in 45 minutes
Given that he covers one-half of the distance in two-thirds of the total time
=> He covers half of 6 km in two-thirds of 45 minutes
=> He covers 3 km in 30 minutes
Hence, now heneed to cover the remaining 3 km in the remaining 15 minutes
Distance = 3 km
Time = 15 minutes = 1/4 hour
Required Speed=Distance/Time = 3/(1/4) = 12 km/hr
Answer: Option A
Question: The units digit of (3)^(44) + (10)^(46) is:
A.2
B.4
C.1
D.8
Answer: C.1
Explanation: any power of anything ending in zero always has a units digit of 0. So the first term has a units digit of 0.
The period is 4. This means, 3 to the power of any multiple of 4 will have a units digit of 1.
3^44 has a units digit of 1
.
Of course 0 + 1 = 1
C
Question: What is the greatest prime factor of 1+2+3+。。。+22?
A.17
B.29
C.23
D.37
Answer: C.23
Explanation: find the sum from direct formula = n(n+1)/2 = 22(22+1)/2 = 11*23...
23 is a PRIME number, so ans is 23..
C is the answer
Question: Peter invested a certain sum of money in a simple interest bond whose value grew to $400 at the end of 3 years and to $ 600 at the end of another 2 years. What was the rate of interest in which he invested his sum?
A.100%
B.12.5%
C.67%
D.25%
Answer: A.100%
Explanation: Lets assume the Principal Amount (initial amount invested) to be P
rate of interest to beRand time as T. We need to find R
Now After a time of 3years the principal P amounts to $400 and after a time of 5years ( question says after another 5years so 3+2) P becomes $600.
Formulating the above data
Amount (A1) at end of 3years
A1= P(1 + 3R/100) = 400
Amount (A2) at end of 8years
A2 = P(1 + 5R/100) = 600
Dividing A2 by A1 we get
(1 + 5R/100)/(1 + 3R/100) = 6/8
after cross multiplication we are left with R =100
Option: A
Question: Two pipes A and B can fill a cistern in 37 minutes and 45 minutes respectively. Both pipes are opened. The cistern will be filled in just half an hour, if the B is turned off after:
A.9 minutes
B.7
C.6
D.5
Answer: A.9 minutes
Explanation: Let B be turned off after x minutes. Then, Part filled by (A + B) in x min. + Part filled by A in (30 -x) min. = 1. x(2/75 + 1/45) + (30 - x). 2/75 = 1 11x/225 + (60 - 2x)/75 = 1 11x + 180 - 6x = 225. x = 9.
Answer:A
Question: What is 82% of 3/5?
A.6.9
B.0.492
C.0.6845
D.0.6859
Answer: B.0.492
Explanation: 82%*(3/5)=0.82*0.6=0.492
Answer :B
Question: Last year for every 100 million vehicles that travelled on a certain highway, 96 vehicles were involved in accidents. If 3 billion vehicles traveled on the highway last year, hom many of those vehicles were involved in accidents (1 billion=1,000,000,000)?
A.288
B.320
C.2880
D.3200
Answer: B.320
Explanation: Explanation:
If r is halved then it is possible to substitute 1/2r for r in the formula and simplify:
1/(2(1/2r))^3=1/(8(1/8r^3))=1/r^3
Compared to the original where:
V=1/(2r)^3=1/(8r^3), the new value of V is 1/r^3 or
8(1/(8r^3))=8V
When r is halved then V is multiplied by 8.
Answer: Option B
Question: A train 100 m long is running with a speed of 68 kmph. In what time will it pass a man who is running at 8 kmph in the same direction in which the train is going?
A.6 sec.
B.7 sec.
C.9 sec.
D.11 sec.
Answer: A.6 sec.
Explanation: Solution
Speed of the train relative to man	=( 68 - 8 )
= 60 Kmph
= 60 x 5 / 18
=50/3 m/sec.
Time taken by it to cover 100 m at (50 /3)m/sec
= (100 x 3/50)sec
= 6 sec.
Answer A
Question: Running at the same constant rate, 6 identical machines can produce a total of 270 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes?
A.1800
B.900
C.2500
D.2700
Answer: A.1800
Explanation: Explanation :
Let required number of bottles be x
More machines, more bottles(direct proportion)
More minutes, more bottles(direct proportion)
⇒ 6 × 1 × x = 10 × 4 × 270
⇒ x = (10 × 4 × 270)/6 = (10 × 4 × 90)/2 = 10 × 4 × 45 = 1800. Answer : Option A
Question: John had a stock of 800 books in his bookshop. He sold 62 on Monday, 62 on Tuesday, 60 on Wednesday, 48 on Thursday and 40 on Friday. What percentage of the books were not sold?
A.26.5%
B.36.5%
C.71.7%
D.56.5%
Answer: C.71.7%
Explanation: Let N be the total number of books sold. Hence
N = 75 + 50 + 64 + 78 + 135 = 272
Let M be the books NOT sold
M = 960 - N = 960 - 402 = 688
Percentage
Books not sold / total number of books = 688/960= 0.72 = 71.7%
correct answer C
Question: The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder. What is the smaller number ?
A.240
B.270
C.295
D.360
Answer: B.270
Explanation: Explanation:
Let the smaller number be x. Then larger number = (x + 1365).
x + 1365 = 6x + 15
5x = 1350
x = 270
Smaller number = 270.
ANSWER IS B
Question: Valerie buys 3 new dresses on average every year for the last 5 years. In order to increase her average to 4 dresses per year, how many dresses should Valerie buy next year?
A.1
B.5
C.6
D.9
Answer: D.9
Explanation: Solution
Average of 6 years = 4 .
âˆ´ Required number of dresses= (6x4)-(5x3)
= 24- 15
= 9.
Answer D
Question: A contractor undertook to make 15 km of roadway in 40 weeks. In 10 weeks, 3 km was complete by 180 men working 8 hours a day. The men then agreed to work 1 hour a day overtime, And some boys were engaged to assist them, the work was finished in the stipulated time(40 weeks). How many boys were employed, if the work of 3 boys is equal to that of 2 men?
A.48
B.50
C.22
D.27
Answer: B.50
Explanation: Explanation:
Let the capacity of man = 3 units, and boy = 2 units per hour.
Now total work = 3×180×8×7×10 = 3 km. - - - - - - - (1)
Let k boys were recruited. Now total work = (3×180+2×k) ×9×7×30 = 12km. - - - - - - (2)
By dividing 2nd equation by 1st,
⇒ (540+2k)×9×7×303×180×8×7×10=4(540+2k)×9×7×303×180×8×7×10=4
⇒ k = 50
Answer: B
Question: If C + D = 9 and C and D are positive integers, which of the following is a possible value for 5C + 8D?
A.55
B.61
C.69
D.90
Answer: D.90
Explanation: c + d = 11
5c + 8d = 5c + 5d + 3d = 5(c+d) + 3d = 45 + 3d=D=15
D=15
c+d=9=C+15=9=C=9-15=-6
C=-6
5C + 8D=5(-6)+8(15)=-30+120=90
Hence, D is the right answer.
Question: If 20% of certain quantity of work is done by A and the rest 80% by B, the work is completed in 20 days. If 80% of the work is done by A and the remaining 20% by B, then the work is completed in 30 days. How many days are required to complete the work , if A and B work together.
A.11 1/9
B.10 1/9
C.12
D.15
Answer: A.11 1/9
Explanation: 0.2/A + 0.8/B = 20
1/A + 4/B = 100
0.8/A + 0.2/B = 30
4/A+ 1/B = 150
15/B = 250
B = 3/50 work per day
A = 3/100 work per day
Combined rate = 3/40 + 3/100 = 9/100
Time taken when working together = 100/9 = 11(1/9) days
Answer (A)
Question: Sangakara and Ponting select batting by using a dice, but dice is biased. So to resolve,Ponting takes out a coin. What is the probability that coin shows correct option?
A.1/2
B.1/6
C.1/12
D.6/10
Answer: A.1/2
Explanation: as coin has only two faces then probability must be 1/2
ANSWER:A
Question: The average temperature for Monday, Tuesday, Wednesday and Thursday was 48 degrees and for Tuesday, Wednesday, Thursday and Friday was 46 degrees. If the temperature on Monday was 42 degrees. Find the temperature on Friday ?
A.34
B.66
C.25
D.18
Answer: A.34
Explanation: Explanation:
M + Tu + W + Th = 4 x 48 = 192
Tu + W + Th + F = 4 x 46 = 184
M = 42
Tu + W + Th = 192 - 42 = 150
F = 184 â€“ 150 = 34
Answer: A
Question: A certain party consists of four different group of people - 30 students, 35 politicians, 20 actors and 27 leaders. On a particular function day, the total cost spent on party members was Rs.9000. It was found that 6 students spent as much as 7 politicians, 15 politicians spent as much as 12 actors and 10 actors spent as much as 9 leaders. How much did students spent?
A.2377.55
B.2477.55
C.2577.55
D.2677.55
Answer: A.2377.55
Explanation: as question says,
30s+35p=20a+27L =9000 say eqn 1
6s=7p , 15p=12a , 10a=9L
or
6s=7p , 7p=(12*7)/15 a =(28/5)a , (28/5)a= (28/50)*9L
OR
6s=7p=(28/5)a=(252/50)L = K
now
s=(k/6), p= (k/7) , a=(.1785k) , L=(.1984k)
put these value in eqn one you will got value of k is 475.511
now 6s=k
hence s=k/6=79.25
there are 30 students hence 79.25*30=2377.55
ANSWER:A
Question: If 40% of a certain number is 160, then what is 30% of that number?
A.270
B.380
C.120
D.360
Answer: C.120
Explanation: Explanation:
40% = 40*4 = 160
30% = 30*4 = 120
Answer: Option C
Question: The instructions state that Cheryl needs 4/9 square yards of one type of material and 2/3 square yards of another type of material for a project. She buys exactly that amount. After finishing the project, however, she has 8/18 square yards left that she did not use. What is the total amount of square yards of material Cheryl used?
A.1/12
B.1/9
C.2/3
D.1 1/9
Answer: C.2/3
Explanation: Total bought = 4/9+2/3
left part 8/18--->4/9
so used part 4/9+2/3-4/9=2/3
ANSWER:C
Question: A train travels from city A to city B. The average speed of the train is 60 miles/hr and it travels the first quarter of the trip at a speed of 90 mi/hr. What is the speed of the train in the remaining trip?
A.30
B.45
C.54
D.72
Answer: C.54
Explanation: Using the RTD chart, with A being the first quarter, B the rest of the trip and All the combinedtrip.
_______R_____T______D
A.........90........3..........270
B.........54.......15.........810
All........60.......18........1080
Let me explain how we fill in the chart:
1) Starting with what we know, we add 90 and 60
2) Picking an easy number for the total distance (6*9=54), so I chose 540. Multiply by 2 to get the whole trip, and we get 1080. Add 1080 for all-distance.
3) 1/4 of the whole distance happened at a Rate of 90. So, 1080/4=270, add 270 under A-D.
4) 2080 - 270 = 810, for the rest of the trip. Add 810 under B-D.
5) Claculate the individual Times for A and All, using T=D/R. Add the results, 3 and 18, under A-T and All-T.
6) 18-3=15, this is the remaining Time for B. Add 15 under B-T.
7) Finally, 15R=810 -->R=810/15 --> R= 54ANS C
Question: Brand X coffee costs twice as much as brand Y coffee. If a certain blend is 1/2 brand X and 1/2 brand Y. what fraction of the cost of the blend is Brand X?
A.a. 1/3
B.b. 2/5
C.3. 2/3
D.4. 1/5
Answer: C.3. 2/3
Explanation: Assume Cost of X= Ca = 200 , Cost of Y = Cb=100
The blend contains 0.5 X and 0.55 Y ---> Cost of the blend = Cbl = 0.5*200+0.5*100= 150
Thus fraction of X in the blend = 0.5*200/150 = 2/3.
Answer : C
Question: For the positive integers q, r, s, and t, the remainder when q is divided by r is 7 and the remainder when s is divided by t is 3. All of the following are possible values for the product rt EXCEPT:
A.32
B.38
C.44
D.52
Answer: B.38
Explanation: Therefore, since the remainder when q is divided by r is 7, then r>7;
Similarly, since the remainder when s is divided by t is 3, then t>3.
Now, all answers, except 38 can be represented as the product of two multiples one of which is greater than 7 and another is greater than 3:
32=8*4
44=11*4
52=13*4
63=9*7
However, 38=1*38 or 19*2, thus rt cannot equal to 38.
Answer: B.
Question: In a certain business school class, p students are accounting majors, q students are finance majors, r students are marketing majors, and s students are strategy majors. If pqrs = 1365, and if 1< p < q < r < s, how many students in the class are accounting majors?
A.3
B.5
C.8
D.11
Answer: A.3
Explanation: pqrs = 1365 = 3* 5 *7 * 13
Since 1< p < q < r < s, the number of students who are accounting majors is p = 3.
The answer is A.
Question: If the manufacture gains 10%, the wholesale dealers 15% and the retailer 25% then find the cost of production of a table, the retail price of which is $1265 ?
A.$650
B.$800
C.$1200
D.$950
Answer: B.$800
Explanation: Let the cost of production of the table be $x
Then, 125% of 115% of 110% of x = 1265
125/100 * 115/100 * 110/100 * x = 1265
253/160 * x = 1265
x = 1265*160/253 = $800
Answer is B
Question: If a, b, c and d are positive integers less than 4, and 4^a+3^b+2^c+1^d=78 then what is the value of b/c?
A.3
B.2
C.1
D.1/2
Answer: C.1
Explanation: Since a, b and c are positive integers less than 4 we have the following possibilities:
4^a=4,16,or 64
3^b=3,9,or 27
2^c=2,4,or 8
Trial and error gives us quite quick the solution of
4^a=64
3^b=9
2^c=4
64+9+4=77
i.e. c=2 and b=2 ----> b/c=1/1=1
The correct answer is C
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are drawn what is the probability that one is yellow and two are red?
A.12/457
B.12/855
C.12/455
D.12/456
Answer: C.12/455
Explanation: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.
When three marbles are drawn, the probability that one is yellow and two are red
= (2 * 4 * 3 * 3 * 2)/(1 * 2 * 15 * 14 * 13) = 12/455.Answer: C
Question: Arnold and Danny are two twin brothers that are celebrating their birthday. The product of their ages today is smaller by 11 from the product of their ages a year from today. What is their age today?
A.2.
B.4.
C.5.
D.7.
Answer: C.5.
Explanation: ad = (a+1) (d+1) -11
0= a+d-10
a+d = 10
a=d (as they are twin brothers)
a=d=5
C is the answer
Question: What is the remainder when 1201 × 1202 ×1203 × 1207 is divided by 6?
A.0
B.1
C.2
D.3
Answer: A.0
Explanation: The remainders when dividing each number by six are: 1, 2, 3, and 1.
The product is 1*2*3*1 = 6
The remainder when dividing 6 by 6 is 0.
The answer is A.
Question: If f(x) = 7 x +12, what is f-1(x) (the inverse function)?
A.(x-12)/7
B.(x-12)/6
C.(x-12)/5
D.(x-12)/4
Answer: A.(x-12)/7
Explanation: f(x) = 7 x + 12
take both side f-1(x)
f(f-1(x))= 7 f-1(x) + 12
x= 7(f-1(x)) +12
f-1(x) = (x-12)/7
ANSWER:A
Question: In certain code 'TWICE' is written as '34$5δ' and 'WEARS' is written as '4δ29%'. How is 'SEAT' written in that code?
A.22
B.23
C.697
D.66P
Answer: B.23
Explanation: Answer: Option B
Question: A furniture store owner decided to drop the price of her recliners by 20% to spur business. By the end of the week she had sold 60% more recliners. What is the percentage increase of the gross?
A.10%
B.15%
C.20%
D.28%
Answer: D.28%
Explanation: Say a recliner is actually worth $100
If she sells 100 recliners then she earns $10000
After the discount of 20%, she will earn $80 per recliner and she sells 60% more ie.,160 recliners
Hence her sales tields 160*80=$12800
Increase in sales=12800-10000=$2800
So% increase = 2800*100/10000 =28%
D is the answer
Question: In an election only two candidates contested. A candidate secured 70% of the valid votes and won by a majority of 178 votes. Find the total number of valid votes?
A.445
B.570
C.480
D.520
Answer: A.445
Explanation: Let the total number of valid votes be x.
70% of x = 70/100 * x = 7x/10
Number of votes secured by the other candidate = x - 7x/100 = 3x/10
Given, 7x/10 - 3x/10 = 178 => 4x/10 = 178
=> 4x = 1780 => x = 445.
ANSWER:A
Question: If Jack walked 6 miles in 1 hour and 15 minutes, what was his rate of walking in miles per hour?
A. 4
B. 4.8
C. 6
D. 6.25
Answer: B. 4.8
Explanation: Distance walked in 1 hour and 15 mins = 6 miles
Speed per hour = Distance/Time = 6/(5/4) = 4.8 miles per hour
Answer B
Question: A man has some hens and cows. If the number of heads be 100 and the number of feet equals 180, then the number of hens will be:
A.22
B.23
C.80
D.90
Answer: D.90
Explanation: Explanation:
Let the number of hens be x and the number of cows be y.
Then, x + y = 100 .... (i)
and 2x + 4y = 220 x + 2y = 110 .... (ii)
Solving (i) and (ii) we get: x = 90, y = 10.
The required answer = 90.
Answer: D
Question: A clock loses 10 minutes each hour.
If the clock is set correctly at noon,what time is it when it reads 3 PM ?
A.3:36 PM
B.3:47 PM
C.3:45 PM
D.2:36 PM
Answer: A.3:36 PM
Explanation: A
3:36 PM.
The clock loses 10 minutes each hour,
so it loses 5 minutes every half-hour,
and it loses 1 minute very 6 minutes.
It is 12:50 PM at 1:00 o'clock.
It is 1:40 PM at 2:00 o'clock.
It is 2:30 PM at 3:00 o'clock.
It is 2:55 PM at 3:30 o'clock.
It is 3:00 PM at 3:36 o'clock.
Question: A and B together can complete a piece of work in 4 days. If A alone can complete the same work in 12 days, in how many days can B alone complete that work?
A.22 days
B.4 days
C.13 days
D.6 days
Answer: D.6 days
Explanation: (A + B)'s 1 day's work = (1/4). A's 1 day's work = (1/12).
B's 1 day's work =((1/4)-(1/12))=(1/6)
Hence, B alone can complete the work in 6 days.
Answer is D.
Question: In a function they are distributing noble prize. In how many ways can 3 prizes be distributed among 7 boys when a boy gets any no. of prizes?
A.55
B.58
C.343
D.354
Answer: C.343
Explanation: Ans.(C)
Sol. In this case, repetitions are allowed, so all the three prizes can be given in 4 ways, i.e. (7 x 7 x 7) ways = 73 ways = 343 ways Or nr ways = 73 ways = 343 ways
Question: If S is the sum of the reciprocals of the consecutive integers from 91 to 100, inclusive, which of the following is less than S?
I. 1/10
II. 1/9
III. 1/11
A.None
B.I only
C.III only
D.II and III only
Answer: B.I only
Explanation: Since we summarize the reciprocals from 100 to 91, we can say also that we add ten numbers who are all (with one exception 1/100) greater than 1/100, so that the sum must be greater than 1/10.
On the other side we can say that we add the reciprocals from 91 to 100, so that the sum has to be less than the sum of ten times 1/91.
We can conclude that the sum has to be less than 1/9 but more than 1/10. That leaves us B as the only possible answer.
Question: Eight carpenters can individually complete a particular task in 3, 4, 5, and 7 hours, respectively. What is the maximum fraction of the task that can be completed in forty-five minutes if seven of the carpenters work together at their respective rates ?
A.11/15
B.3/5
C.11/30
D.329/480
Answer: D.329/480
Explanation: Farmer A, B, C, and D
A's rate: 1/3 job/hour
B's rate: 1/4 job/hour
C's rate: 1/5 job/hour
D's rate: 1/7 job/hour
By intuition we know that the three fastest farmers are A B and C.
As such
(1/3 + 1/4 + 1/5)*(7/8) = ?
47/80 or (D)