mathewhe/aqua_rat huggingface dataset:
Question: A box contains 10 tablets of medicine A and 14 tablets of medicine B. What is the least number of tablets that should be taken from the box to ensure that at least two tablets of each kind are among the extracted.
(A) 12
(B) 16
(C) 17
(D) 19
(E) 21
Rationale: The worst case scenario will be if we remove all 14 tablets of medicine B first. The next 2 tablets we remove have to be of medicine A, so to guarantee that at least two tablets of each kind will be taken we should remove minimum of 14+2=16 tablets.
Answer: B.
Answer: (B) 16
Question: Find the value of a/b + b/a, if a and b are the roots of the quadratic equation x2 + 8x + 4 = 0?
(A) 15
(B) 14
(C) 13
(D) 12
(E) 11
Rationale: a/b + b/a = (a2]/ab
a + b = + b2)/ab = (a2 + b2 + a + b)/ab
= [(a + b)2 - 2ab -8/1 = -8
ab = 4/1 = 4
Hence a/b + b/a = [(-8)2 - 2(4)]/4 = 56/4 = 14.
ANSWER:B
Answer: (B) 14
Question: The area of a square field is 7201 sq m. How long will a lady take to cross the field diagonally at the rate of 2.4 km/hr?
(A) 2 min
(B) 3 min
(C) 4 min
(D) 5 min
(E) 6 min
Rationale: Area of a square field = 7201 sq m
Let the side of square = a
a^2 = 7201
=> a = 84.86
Diagonal = (2)^(1/2) * a
= 1.414 * 84.86
=120
Speed of lady = 2.4 km / hour
= 2400 m / hour
= 40 m / min
Time taken by lady to cross the field diagonally = 120/40 = 3 min
Answer B
Answer: (B) 3 min
Question: The radius of the two circular fields is in the ratio 3: 5 the area of the first field is what percent less than the area of the second?
(A) 29
(B) 27
(C) 29
(D) 64
(E) 99
Rationale: r = 3 πr2 = 9
r = 5 πr2 = 25
25 π – 16 π
100 ---- ? => 64% Answer: D
Answer: (D) 64
Question: In a shop, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, find out approximately what percentage of the selling price is the profit?
(A) 20%
(B) 30%
(C) 40%
(D) 50%
(E) 70%
Rationale: Let cost price =100
Then, profit =320
selling price =100+320=420
new cost price =125
profit =420-125=295
Required percentage
=295*100/420 =70 %
Answer : E
Answer: (E) 70%
Question: We made a down payment of $50 and borrowed the balance on a new oven which cost $300. The balance with interest was paid in 23 monthly payments of $11 each and a final payment of $27. The amount of interest paid was what percent of the amount borrowed?
(A) 10%
(B) 12%
(C) 14%
(D) 16%
(E) 18%
Rationale: We borrowed $250.
To pay back this loan, we paid 23*$11 + $27=$280.
The interest was $280-$250=$30.
The percentage was $30/$250=0.12=12%.
The answer is B.
Answer: (B) 12%
Question: The jogging track in a sports complex is 726 meters in circumference. Deepak and his wife start from the same point and walk in opposite directions at 4.5 km/hr and 3.75 km/hr respectively. They will meet for the first time in?
(A) 450min
(B) 528min
(C) 610min
(D) 714min
(E) 359min
Rationale: Clearly, the two will meet when they are 726m apart
To be 4.5+3.75 = 8.25 km apart, they take 1 hour
To be 726 m apart, they take 100/825 * 726/1000 = 242/2750 * 60 = 528 min.
Answer is B
Answer: (B) 528min
Question: A man sitting in a train which is travelling at 50 kmph observes that a goods train travelling in a opposite direction, takes 9seconds to pass him. If the goods train is 280 m long, find its speed.
(A) 58
(B) 62
(C) 74
(D) 81
(E) 65
Rationale: Relative speed = (280/9)m/s = (280/9)*(18/5) = 112 kmph
speed of goods train = 112-50 = 62 kmph
Answer is B
Answer: (B) 62
Question: If 12 men can reap 120 acres of land in 36 days, how many acres of land can 44 men reap in 54 days?
(A) 820 acres
(B) 660 acres
(C) 620 acres
(D) 720 acres
(E) 920 acres
Rationale: 12 men 120 acres 36 days
44 men ? 54 days
120 * 44/12 * 54/36
10 * 44 * 3/2
44 * 15 = 660
ANSWER:B
Answer: (B) 660 acres
Question: Mudit's age 18 years hence will be thrice his age four years ago. Find Mudit's present age?
(A) 12
(B) 19
(C) 27
(D) 18
(E) 15
Rationale: Explanation:
Let Mudit's present age be 'm' years.
m + 18 = 3(m - 4)
=> 2m = 30 => m = 15 years.
Answer:E
Answer: (E) 15
Question: A certainno. when divided by 35leaves a remainder 25, what is the remainder if the same no.be divided by 15?
(A) 4
(B) 5
(C) 6
(D) 8
(E) 9
Rationale: Explanation:
35 + 25 = 60/15 = 4 (Remainder)
A
Answer: (A) 4
Question: What is the place value of 0 in the numeral 2074?
(A) 3
(B) 2
(C) 5
(D) 0
(E) 1
Rationale: Note : The place value of zero (0) is always 0. It may hold any place in a number,
its value is always 0.
D)
Answer: (D) 0
Question: Nine men went to a hotel. Eight of them spent Rs.3 each over their meals and the ninth spent Rs.2 more than the average expenditure of all the nine. Determine the total money spent by them?
(A) 29.25
(B) 29.29
(C) 29.12
(D) 29.98
(E) 79.12
Rationale: Average of 9 = x
9x = 8 * 3 + x * 2 x = 3.25
Total = 9 * 3.25 = 29.25
Answer:A
Answer: (A) 29.25
Question: If one-third of one-fourth of a number is 15, then three-tenth of that number is :
(A) 35
(B) 36
(C) 45
(D) 54
(E) 30
Rationale: Let the number be x. Then, 1/3 of 1/4 of x=15
13of14ofx=15
<=> x = 15 * 12 = 180.
So, required number =
((3/10)∗180)=54.
Answer :D
Answer: (D) 54
Question: Three machines operating independently, simultaneously, and at the same constant rate can fill a certain production order in 48 hours. If one additional machine were used under the same operating conditions, in how manyfewerhours of simultaneous operation could the production order be fulfilled?
(A) 6
(B) 9
(C) 12
(D) 27
(E) 48
Rationale: If 3 Machines can do the work in 48 hr then 4 Machines can do the work in 3/4*48 = 36 Hrs. hence time saved will be 12hr
option C is the correct answer
Answer: (C) 12
Question: Two pipes A and B can fill a tank in 24 hours and 36 hours respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank?
(A) 20 hours
(B) 15 hours
(C) 14 2/5 hours
(D) 12 hours
(E) 8 hours
Rationale: Part filled by A in 1 hour = 1/24
Part filled by B in 1 hour = 1/36
Part filled by (A+B) in 1 hour = 1/24 + 1/36 = 5/72
Both the pipes together fill the tank in 72/5 = 14 2/5 hours
Answer is C
Answer: (C) 14 2/5 hours
Question: The average waight of A,B,C is 45 Kg. The avgwgt of A & B be 40Kg & that of B,C be 43Kg. Find the wgt of B.
(A) 23kg
(B) 16kg
(C) 29kg
(D) 31kg
(E) 52kg
Rationale: Let A,B,c represent their individual wgts.
Then,
A+B+C=(45*3)Kg=135Kg
A+B=(40*2)Kg=80Kg & B+C=(43*2)Kg=86Kg
B=(A+B)+(B+C)-(A+B+C)
=(80+86-135)Kg
=31Kg.
Ans: D
Answer: (D) 31kg
Question: A can do a work in 15 days and B in 20 days. If they work on it together for 6 days, then the fraction of the work that is left is
(A) 8/17
(B) 7/15
(C) 3/10
(D) 8/15
(E) 1/4
Rationale: Person ( A ) ( B ) ( A+B )
Time - ( 15 ) ( 20 ) (-)
Rate - ( 20 ) ( 15 ) ( 35 )
Work -(300) (300) (300)
therefore A+B requires (300/35) days to complete entire work
For 1st 4 days they work 35 * 6 = 210
Remaining work is 300 - 210 = 90
Remaining fraction of work is = 90/300 = 3/10
Answer C
Answer: (C) 3/10
Question: The volumes of two cones are in the ratio 1 : 10 and the radii of the cones are in the ratio of 1 : 2. What is the length of the wire?
(A) 2:5
(B) 2:9
(C) 2:4
(D) 2:7
(E) 2:1
Rationale: The volume of the cone = (1/3)πr2h
Only radius (r) and height (h) are varying.
Hence, (1/3)π may be ignored.
V1/V2 = r12h1/r22h2 => 1/10 = (1)2h1/(2)2h2
=> h1/h2 = 2/5
i.e. h1 : h2 = 2 : 5
Answer: A
Answer: (A) 2:5
Question: Lottery balls numbered consecutively from one through one hundred are placed in a spinner. If one ball is drawn at random, what is the probability that it will have the number 4 on it exactly once?
(A) 9/100
(B) 1/10
(C) 11/100
(D) 18/100
(E) 1/5
Rationale: Probability = No of balls with exactly one 1 / total number of balls
= {4,14,24,34,40,41,42,43,45 to 49,54,64,74,84,94}/100
= 18/100
Answer is D
Answer: (D) 18/100
Question: Ramesh spends 40% of his monthly salary on food, 40% of the remaining on conveyance and clothes and saves 50% of the remaining amount. If his monthly salary is Rs.17,000, how much money does he save every month ?
(A) Rs. 3,400
(B) Rs. 3060
(C) Rs. 2,540
(D) Rs.1,880
(E) None of these
Rationale: Explanation:
Ramesh's monthly income = Rs.17,000
He spends 40% on food.
The total money spent on food = 40/100 * 17000 = Rs. 6800
Now, his monthly remaining income = Rs.17000 – Rs.6800 = Rs. 10200
Out of Rs. 10200, he spends 40% on conveyance and clothes.
The total money spent on conveyance and clothes = 40/100 * 10200 = Rs. 4080
Now, his monthly remaining income = Rs.10200 – Rs.4080 = Rs. 6120
Out of Rs. 6120, he saves 50%.
Amount saved = 50/100 * 6120 = Rs. 3060
ANSWER B
Answer: (B) Rs. 3060
Question: A and B together can complete work in 6 days. A alone starts working and leaves it after working for 4 days completing only half of the work. In how many days it can be completed if the remaining job is undertaken by B?
(A) 4
(B) 12
(C) 5
(D) 6
(E) 7
Rationale: Explanation:
(A+B) one day work =1/6
now A does half of the work in 4 days so A can complete the whole work in 8 days
A’s one day work =1/8
B’s one day work=1/6 - 1/8= 2/48= 1/24
B alone can complete the work in 24 days so half of the work in 12 days
Answer: Option B
Answer: (B) 12
Question: 12 men complete a work in 9 days. After they have worked for 6 days, 6 more
men joined them. How many days will they take to complete the remaining work?
(A) 5
(B) 1
(C) 2
(D) 3
(E) 7
Rationale: 1 man's 1 day work = 1/108
12 men's 6 days work = 6/9 = 2/3
remaining work = 1 – 2/3 = 1/3
18 men's 1 days work = 18/108 = 1/6
1/6 work is done by them in 1 day
therefore, 1/3 work is done by them in 6/3 = 2 days.
ANSWER C
Answer: (C) 2
Question: ASvennumber is defined as a five-digit number which goes according to the following rules: the leftmost digit is even, any digit to the right of an even digit must be an odd digit, and any digit to the right of an odd digit can only be one of the digits 1 or 7. How many different 3-digit numbers areSvennumbers?
(A) 20
(B) 60
(C) 160
(D) 220
(E) 250
Rationale: ASvennumber is defined as a five-digit number which goes according to the following rules: the leftmost digit is even, any digit to the right of an even digit must be an odd digit, and any digit to the right of an odd digit can only be one of the digits 1 or 7. How many different 5-digit numbers areSvennumbers?
4/9*5/10*2/10*2/10*2/10=160/9000
B. 60
Answer: (B) 60
Question: In a hostel there were 100 students. To accommodate 20 more students the average is decreased by rupees 5. But total expenditure increased by Rs.400. Find the total expenditure of the hostel now?
(A) 2299
(B) 2777
(C) 5400
(D) 1277
(E) 231
Rationale: 100x + 400 = 12(x – 5)
x = 50
100 * 50 + 400 = 5400.Answer:C
Answer: (C) 5400
Question: Find the invalid no.from the following series 15, 16, 34, 105, 424, 2124, 12756
(A) 1789
(B) 1890
(C) 2100
(D) 2300
(E) 2124
Rationale: 2nd term = (1st term) * 1 + 1 = 15 *1 + 1 = 16.
3rd term = (2nd term) * 2 + 2 = 16 * 2 + 2 = 34
4th term = (3th term) *3 + 3 = 34 * 3 + 3 = 105
5th term = (4th term) * 4 + 4 = 105 * 4 + 4 = 424
6th term = (5th term) * 5 + 5 = 424 * 5 + 5 = 2125
6th term should 2125 instead of 2124.
E
Answer: (E) 2124
Question: Machine A and machine B process the same work at different rates. Machine C processes work as fast as Machines A and B combined. Machine D processes work three times as fast as Machine C; Machine D’s work rate is also exactly four times Machine B’s rate. Assume all four machines work at fixed unchanging rates. If Machine A works alone on a job, it takes 6 hours and 40 minutes. If all four machines work together on the same job simultaneously, how many minutes will it take all of them to complete it?
(A) 18
(B) 18
(C) 20
(D) 22
(E) 24
Rationale: C = A + B
D = 3C = 3(A+B) = 4B
Then B = 3A and C = 4A
The combined rate of the four machines is A + 3A + 4A + 12A = 20A
Machine A can complete the work in 400 minutes, so its rate is 1/400 of the work per minute.
The combined rate is 20/400 = 1/20 so the work will be completed in 20 minutes.
The answer is C.
Answer: (C) 20
Question: Three unbased coins are tossed. the probability of getting at most three head and three tails is ?
(A) 1/2
(B) 1/4
(C) 3/4
(D) 1/5
(E) 2/3
Rationale: S={TTT,TTH,THT,HTT,THH,HTH,HHT,HHH}
E be the event of getting at least two head is {TTT,HHH}
P(E)=n(E)/n(S)=2/8 = 1/4
Answer(B)
Answer: (B) 1/4
Question: If the average (arithmetic mean) of 5 positive temperatures is q degrees Fahrenheit, then the sum of the 3 greatest of these temperatures, in degrees Fahrenheit, could be:
(A) 6q
(B) 4q
(C) 5q/3
(D) 3q/2
(E) 3q/5
Rationale: The sum of three greatest should be more than sum of two lowest.
The total sum is; 5q
A. 6q; 6q is more than 5q. Not possible.
B. 4q; 5q-4q=q(Possible)
C. 5q/3; 10q/3; 10q/3 > 5q/3. Not possible
D. 3q/2; 7q/2; 7q/2 > 3q/2. Not possible
E. 3q/5; 22q/5; 22q/5 > 3q/5. Not possible.
Ans:B
Answer: (B) 4q
Question: A group of students decided to collect as many paise from each member of group as is the number of members. If the total collection amounts to Rs. 77.44, the number of the member is the group is:
(A) 57
(B) 67
(C) 77
(D) 88
(E) 97
Rationale: Money collected = (77.44 x 100) paise = 7744 paise.
Number of members =Square root of 7744 = 88.
Answer: Option D
Answer: (D) 88
Question: Three men " Sam, Cam and Laurie " are married to Carrie, Billy and Tina, but not necessarily in the same order. Sam's wife and Billy's Husband play Carrie and Tina's husband at bridge. No wife partners her husband and Cam does not play bridge. Who is married to Cam?
(A) Carrie
(B) Billy
(C) Tina
(D) Laurie
(E) none
Rationale: 1 st game:
sam's wife-Tina
VS
Billy'husband-laurie
2 nd game
carrie
VS
tina's husband-sam
Cam is married to carrie
ANSWER:A
Answer: (A) Carrie
Question: How much time will a train of length 200 m moving at a speed of 72 kmph take to cross another train of length 300 m, moving at 36 kmph in the same direction?
(A) 50 sec
(B) 25 sec
(C) 40 sec
(D) 65 sec
(E) 60 sec
Rationale: Explanation:
The distance to be covered = Sum of their lengths = 200 + 300 = 500 m.
Relative speed = 72 -36 = 36 kmph = 36 * 5/18 = 10 mps.
Time required = d/s = 500/10 = 50 sec.
ANSWER IS A
Answer: (A) 50 sec
Question: Mark and Ann together were allocated n boxes of cookies to sell for a club project. Mark sold 11 boxes less than n and Ann sold 2 boxes less than n. If Mark and Ann have each sold at least one box of cookies, but together they have sold less than n boxes, what is the value of n?
(A) 10
(B) 11
(C) 12
(D) 13
(E) 14
Rationale: if n =12
mark sold 1 box
and Ann sold 10 boxes
total 11 < 12
Answer:C
Answer: (C) 12
Question: One hour after Jerry started walking the 60 miles from X to Y, James started walking from X to Y as well. Jerry walks 3 miles per hour and James walks 1 mile per hour faster than Jerry . How far from X will James be when he catches up to Jerry ?
(A) 12 miles
(B) 9 miles
(C) 10 miles
(D) 11 miles
(E) 13 miles
Rationale: One hour after Jerry started walking the 60 miles from X to Y, James started walking from X to Y as well. Jerry walks 3 miles per hour and James walks 1 mile per hour faster than Jerry . How far from X will James be when he catches up to Jerry ?
First, determine how far Jerry has walked in the one hour. he has walked three miles which means she is three miles ahead of James when he sets off. James walks at four miles/hour which means that every hour, james will get one mile closer to Jerry . If he gets one mile closer every hour, it will take him three hours to catch up to her which means he travels 3hours * 4 miles/hour = 12 miles and he travels 4 hours * 3 miles/hour = 12 miles. He will be 12 miles from X when he catches up to her.
A slightly different way to solve...
We don't know how long they will walk before they catch up to one another but we do know that A walks for one hour more than J. J = T and A = T+1. We are looking for the distance at which they meet up which means the distance will be the same. D=r*t so,
r*t (james) = r*t (Jerry )
r*(t) = r*(t+1)
4t = 3t+3
t=3
d=r*t
d=4*3
d=12
answer is A
Answer: (A) 12 miles
Question: A train 108 m long moving at a speed of 50 kmph crosses a train 112 m long coming from opp direction in 6 seconds.The speed of the second train is
(A) 48 kmph
(B) 54 kmph
(C) 66 kmph
(D) 82 kmph
(E) 69 kmph
Rationale: both trains are moving in opposite direction means we need to add their speeds.
i.e: 1st train speed is = 50kmph
let the 2nd train speed = x kmph
relative speed = (50+x) kmph
= (50+x)* 5/18
= (250+5x)/18 m/sec
Distance covered by two trains = 108+112
= 220m
therefore, 220/((250+5x)/18) = 6
=> 250+5x=660
=> x=82km/hr.
ANSWER:D
Answer: (D) 82 kmph
Question: By selling 99 pens, a trader gains the cost of 33 pens. Find his gain percentage?
(A) 33 1/3%
(B) 33 7/3%
(C) 33 1/8%
(D) 32 1/3%
(E) 33 1/5%
Rationale: Let the CP of each pen be Rs. 1.
CP of 99 pens = Rs. 99
Profit = Cost of 33 pens
= Rs. 33
Profit% = 33/99 * 100
= 33 1/3%
Answer: A
Answer: (A) 33 1/3%
Question: If 2|2 –e| = 5, what is the sum of all the possible values for e ?
(A) 1/2
(B) 2
(C) 5/2
(D) 4
(E) 5
Rationale: if e<2, then 2-e=5/2; e=-1/2
if e>2 , then e-2=5/2; e=9/2
9/2-1/2=8/2=4=D
Answer: (D) 4
Question: A is the son of C; C and Q are sisters; Z is the mother of Q and P is the son of Z. Which of the following statements is true?
(A) P and A are cousins
(B) P is the maternsl uncle of A
(C) Q is the maternal grandfather of A
(D) C and P are sisters
(E) none
Rationale: P is the maternsl uncle of A
ANSWER:B
Answer: (B) P is the maternsl uncle of A
Question: I have a huge bed-sheet of 1 meter long.
I want to cuts this role into pieces of 20 centimeter long cloth.
How long will it take me to cut the bed sheet if each 20 centimeter cut took me 5 minutes ?
(A) 200 minutes
(B) 245 minutes
(C) 140 minutes
(D) 220 minutes
(E) 324 minutes
Rationale: B
245 minutes
It will take 49 cuts not 50.
so 49*5 => 245 minutes
Answer: (B) 245 minutes
Question: Find large number from below question The difference of two numbers is 1325. On dividing the larger number by the smaller, we get 5 as quotient and the 5 as remainder
(A) 1650
(B) 1324
(C) 1245
(D) 1300
(E) 1635
Rationale: Let the smaller number be x. Then larger number = (x + 1325).
x + 1325 = 5x + 5
4x = 1320
x = 330
Large number = 330+1320 = 1650
Answer : A
Answer: (A) 1650
Question: If two-third of a bucket is filled in 2 minutes then the time taken to fill the bucket completely will be .
(A) 3 minutes
(B) 70 seconds
(C) 60 seconds
(D) 100 seconds
(E) 120 seconds
Rationale: 2/3 filled in 2 mint
1/3 filled in 1 mint
then 2/3+1/3= 2 + 1 = 3 minutes
ANSWER: A
Answer: (A) 3 minutes
Question: A salt solution contains 15 grams of salt per 1000 cubic centimeters of solution. If 25 cubic centimeters of the solution were poured into an empty container, how many grams of salt would be in the container?
(A)  0.550
(B)  0.350
(C)  0.450
(D)  0.700
(E)  0.375
Rationale: We are given that a salt solution contains 15 grams of salt per 1000 cubic centimeters of solution. Since we are dealing with a solution, we know that the grams of salt is proportional to the number of cubic centimeters of solution. Thus, to determine how many grams of salt would be in the container when we have 25 cubic centimeters of solution, we can set up a proportion.
We can say: “15 grams of salt is to 1000 cubic centimeters of solution as x grams of salt is to 25 cubic centimeters of solution.” Let’s now set up the proportion and solve for x.
15/1000 = x/25
When we cross multiply we obtain:
(15)(25) = 1000x
375 = 1000x
0.375 = x
There are 0.375 grams of salt in the solution in the container.
The answer is E.
Answer: (E)  0.375
Question: In a certain animal shelter, the ratio of the number of catsto the number of dogs is 15 to 7. If 12 additional dogs were to be taken in by the shelter, the ratio of the number of cats to the number of dogs would be 15 to 11. How many cats are in the shelter?
(A) 15
(B) 45
(C) 30
(D) 45
(E) 60
Rationale: This ratio question can be solved in a couple of different ways. Here's an Algebraic approach...
We're told that the ratio of the number of cats to the number of dogs is 15:7. We're then told that 12 more dogs are added to this group and the ratio becomes 15:11. We're asked for the number of cats.
Algebraically, since the number of cats is a multiple of 15 and the number of dogs is a multiple of 7, we can write this initial relationship as...
15X/7X
When we add the 12 cats and factor in the 'ending ratio', we have an equation....
15X/(7X+12) = 15/11
Here we have 1 variable and 1 equation, so we can solve for X....
(15X)(11) = (7X+12)(15)
(X)(11) = (7X+12)(1)
11X = 7X + 12
4X = 12
X = 3
With this X, we can figure out the initial number of dogs and cats...
Initial dogs = 15X = 15(3) = 45
Final Answer: B
Answer: (B) 45
Question: The water level in a reservoir has been dropping at the rate of 14 inches per day. Exactly 4 days ago, the water level was at w inches. What will be the water level exactly 4 days from now if the rate at which the level is dropping remains the same?
(A) w − 126
(B) w − 112
(C) w − 14
(D) w + 14
(E) w + 126
Rationale: Drop=14 inches/day
4 Days ago=w, means now it's equal w-56 and in 4 days = w-56-56=w-112
Answer B
Answer: (B) w − 112
Question: How many integers between 50 and 200 are there such that their unit digit is odd?
(A) 100
(B) 120
(C) 75
(D) 50
(E) 150
Rationale: 150 numbers between - 50 and 200
Out of which half would be even, half odd.
Number of odd unit digit number = 75.
correct option is C
Answer: (C) 75
Question: In how many ways can 5 different candies be distributed in 4 identical baskets?
(A) 120
(B) 51
(C) 24
(D) 5^4
(E) 4^5
Rationale: 5-N-N-N : 5C5 = 1 - OK
4-1-N-N : 5C4 *1C1 = 5 - OK
3-2-N-N : 5C3*2C2 = 10 - OK
3-1-1-N : 5C3*2C1*1C1 = 20 - NO - only 10, once you decide to split the remaining two after choosing the 3 before, no factor of 2 needed
2-2-1-N : 5C2*3C2*1C1 = 30 - NO - it is 15 = 30/2; baskets being identical, doesn't matter which group of 2 you choose first
2-1-1-1 : 5C2*3*2*1 = 60 - NO - only 10, because you only choose those 2 to be placed together, all the other three you put in different baskets, no choices
Total of 1 + 5 + 10 + 10 + 15 + 10 = 51.
Answer B.
Answer: (B) 51
Question: A wheel has a diameter of x inches and a second wheel has a diameter of y inches. The first wheel covers a distance of d feet in 75 revolutions. How many revolutions does the second wheel make in covering d feet?
(A) 75x/y
(B) 75x-y
(C) 25x-y
(D) 25x+y
(E) 75y/x
Rationale: A wheel covers 2πr distance in one revolution. where r= diameter/2
First wheel covers d feet in 75 rev. => d= 75* 2π * (x/2)
Second wheel covers d feet in let's say P revolutions; => d = P* 2π * (y/2)
comparing both equations:-
=> p= (75∗2π∗x/2)/(2π∗y/2)
=> 75x/y
Answer :- A
Answer: (A) 75x/y
Question: Radha remembers that her father's birthday is after 16th but before 21st of March, While her brother Mangesh remembers that his father,s birthday is before 22nd but after 19th of March. On which date is the birthday of their father?
(A) 19th
(B) 20th
(C) 21st
(D) Cannot be determined
(E) None of these
Rationale: before 21st and after 19th they mentioned clearly
so 20th march
ANSWER:B
Answer: (B) 20th
Question: In a TV factory, an average of 60 TVs are produced per day for the fist 25days of the months. A few workers fell ill for the next five days reducing thedaily avg for the month to 58 sets/day . The average production per day for day last 5days is ?
(A) 42
(B) 46
(C) 48
(D) 50
(E) 54
Rationale: Production during these 5 days = Total production in a month - production in first 25 days.
= 30 x 58 - 25 x 60
= 240
∴ Average for last 5 days = 240 / 5
= 48
C
Answer: (C) 48
Question: The sum of three consecutive even numbers is 42. Find the middle number of the three?
(A) 14
(B) 16
(C) 18
(D) 24
(E) 25
Rationale: Explanation:
Three consecutive even numbers (2P - 2), 2P, (2P + 2).
(2P - 2) + 2P + (2P + 2) = 42
6P = 42 => P = 7.
The middle number is: 2P = 14.
ANSWER IS A
Answer: (A) 14