mathewhe/aqua_rat huggingface dataset:
Question: In a function they are distributing noble prize. In how many ways can 3 prizes be distributed among 6 boys when a boy gets any no. of prizes?
(A) 216
(B) 218
(C) 230
(D) 340
(E) 453
Rationale: Ans.(A)
Sol. In this case, repetitions are allowed, so all the three prizes can be given in 6 ways, i.e. (6 x 6 x 6) ways = 63 ways = 216 ways Or nr ways = 63 ways = 216 ways
Answer: (A) 216
Question: Pavel has to visit his aunt, who lives exactly eight blocks north and six blocks east of his current location. If Pavel travels only along streets and does not travel diagonally, the shortest possible route connecting the two points is exactly 14 blocks. How many different 14-block routes may Pavel take to travel the shortest possible distance to his aunt’s house?
(A) 14
(B) (14!)/(8!6!)
(C) (22!)/(14!8!)
(D) 8!6!
(E) 14!8!6!
Rationale: for simplification, you can draw a box/rectangle with eight vertical and 6 horizontal lines...
the Q asks u how can u travel from one vertex to opposite vertex along these lines..
And the shortest route will consist of 8 vertical and 6 horizontal moves..
so total ways are 14! out of which 8 are one kind and 6 of the other...
ways= 14!/(8!6!)
ANSWER:B
Answer: (B) (14!)/(8!6!)
Question: if a four-digit number is selected at random from the integers 1000 to 9999, inclusive, what is the probability that the first digit and the last digit of the integer will both be exactly two less than the middle two same digit?
(A)  1:900
(B)  7:900
(C)  7:9000
(D)  1:100
(E)  7:100
Rationale: You are asked about all 3 digit numbers that conform to the follow type: ABA , where A= B-2.
There are 900 numbers between 100 and 999 (inclusive).
Numbers of the form ABA are: 1331, 2442,3553,4664,5775,6886,7997 = total 7
Thus the probability asked = 7/9000
B is the correct answer.
Answer: (B)  7:900
Question: There are twenty players on a rugby team. If the average weight of the players is 180 pounds, what will be the new average height if a 210 pound player will join the team?
(A) 185
(B) 183.22
(C) 184.96
(D) 181.43
(E) 182.78
Rationale: (sum of the 20 weights)/20 = 180
sum of the 20 weights = 3600
new sum = 3600 + 210 = 3810
new average = 3810/21 = 181.43
ans: D
Answer: (D) 181.43
Question: Find large number from below 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
(A) 1235
(B) 1346
(C) 1378
(D) 1635
(E) 1489
Rationale: Let the smaller number be x. Then larger number = (x + 1365).
x + 1365 = 6x + 15
5x = 1350
x = 270
Large number = 270+1365 = 1635
D
Answer: (D) 1635
Question: In a dairy farm, 40 cows eat 40 bags of husk in 40 days. In how many days one cow will eat one bag of husk?
(A) 1
(B) 1/40
(C) 40
(D) 80
(E) 1/80
Rationale: Assume that in x days, one cow will eat one bag of husk.
More cows, less days (Indirect proportion)
More bags, more days (direct proportion)
Hence we can write as
CowsBags40:11:40⎫⎭⎬::x:40
⇒40×1×40=1×40×x
⇒x=40
ANSWER:C
Answer: (C) 40
Question: The number of diagonals of a polygon of n sides is given by the formula c=n(n-3)/2. If a polygon has twice as many diagonals as sides, how many sides does it have?
(A)  3
(B)  5
(C)  6
(D)  7
(E)  8
Rationale: c=n(n-3)
c=2*n
2n=n(n-3)
=>2=n-3
=>n=5
Answer B
Answer: (B)  5
Question: A policeman noticed a criminal from a distance of 240 km. The criminal starts running and the policeman chases him. The criminal and the policeman run at the rate of 8 km and 9 km per hour respectively. What is the distance between them after 3 minutes ?
(A) 100 m
(B) 120 m
(C) 190 m
(D) 150 m
(E) None of these
Rationale: Explanation :
Solution: Relative speed = (9 - 8) = 1 km/hr.
Distance covered in 3 minutes = (1 * 3/60) km = 1/20 km = 50 m.
.'. Distance between the criminal and policeman = (240 - 50) m = 190 m.
Answer : C
Answer: (C) 190 m
Question: Ramya sells an article at three- fourth of its list price and makes a loss of 10%. Find the profit percentage if she sells at the list price.
(A) 20%
(B) 25%
(C) 15%
(D) 35%
(E) None of these
Rationale: Let the list price be x,
S.P =3/4X, S.P = (100 – loss%) /100*C.P = 0.9 C.P
3/4x =0.9C.P, C.P =3X/3.6
If S.P = X, Profit % = (x- 3x/3.6 ) / ( 3x/3.6 ) *100= 60/3 = 20%
ANSWER:A
Answer: (A) 20%
Question: A car drives 60 miles on local roads at 30 mph, and 65 miles on the highway at 65 mph, what is the average speed of the entire trip?
(A) 36 mph
(B) 40 mph
(C) 44 mph
(D) 42 mph
(E) 58 mph
Rationale: So The Answer is Plainly D....
we have a general relation for speed , time and distance : v (velocity) * t ( time)= d (distance)
for first part we have d=60 miles , and v= 30 mph so we can obtain time : 30*t = 60 Or t= 60/30 = 2 hours the needed time to cover 60 miles
in the same way we should divide 65 by 65 to find the needed time to cover 65 miles ,so t= 1 hours
so the total time for covering total distance would be 2+1 = 3 hours and total distance is 60+65= 125 miles
Final stage : average speed is total distance divide to total time : 125/3 = 41.6 miles per hour that rounds up to 42....
Answer: (D) 42 mph
Question: A certain no. when divided by 110 leaves a remainder 25, what is the remainder if the same no.be divided by 15?
(A) 2
(B) 4
(C) 7
(D) 8
(E) 9
Rationale: Explanation:
110 + 25 = 135/15 = 9 (Remainder)
E
Answer: (E) 9
Question: What is the rate percent when the simple interest on Rs.800 amount to Rs.160 in 3 Years?
(A) 5%
(B) 6.6%
(C) 9%
(D) 2%
(E) 4%
Rationale: 160 = (800*3*R)/100
R = 6.6%
Answer: B
Answer: (B) 6.6%
Question: In year Y imported machine tools accounted for 25 percent of total machine - tool sales in the United States, and Japanese imports accounted for 40 percent of the sales of imported machine tools. If the total sales of machine tools imported Japan that year was x billion dollars, then the total sales of all machine tools in the United States was how many billion dollars?
(A) 9X/80
(B) 13X/20
(C) 80/9X
(D) 10X/1
(E) 80X/9
Rationale: IMT = 0.25T
JI = 0.40 IMT
0.40 IMT = $x b
IMT = $x/(0.40) b
T = 4*IMT = 4x/0.40 = 4x*100/40 = 10x/1
Ans: "D"
Answer: (D) 10X/1
Question: What is the probability that Company R's advertisement will be one of the first two be shown during the first commercial break?
(A)  1/ 225
(B)  1 / 30
(C)  1 /15
(D)  2 / 15
(E)  4 /15
Rationale: R 1/15 + (14/15) * 1/14 = 2/15 D
Answer: (D)  2 / 15
Question: A shopkeeper buys mangoes at the rate of 4 a rupee and sells them at 3 a rupee. Find his net profit or loss percent?
(A) 73 1/3 %
(B) 13 1/3 %
(C) 33 1/3 %
(D) 23 1/3 %
(E) 93 1/3 %
Rationale: Explanation:
The total number of mangoes bought by the shopkeeper be 12.
If he buys 4 a rupee, his CP = 3
He selling at 3 a rupee, his SP = 4
Profit = SP - CP = 4 - 3 = 1
Profit Percent = 1/3 * 100 = 33 1/3 %
Answer:C
Answer: (C) 33 1/3 %
Question: Among all sales staff at Listco Corporation, college graduates and those without college degrees are equally represented . Each sales staff member is either a level-1 or level-2 employee. Level-1 college graduates account for 10% of Listco's sales staff. Listco employs 72 level-1 employees, 30 of whom are college graduates. How many sales staff members without college degrees are level-2 employees ?
(A) 108
(B) 42
(C) 56
(D) 32
(E) 58
Rationale: I'm going in on this one.
So let's say that we have the following
So we know that L1 = 72 and that C and L1 = 0.10X , we should set up a double set matrix btw but anyways, I'm just explaining the point with this problem. Now we are told that 0.10x = 30, therefore the grand total is 300. Now we know that L2 is 300 - 72 = 228. We also learn that C and No C are equally represented thus 150 each. Therefore No C and No L2 will be 150 - 42 = 108.
Thus A is the correct answer choice
Answer: (A) 108
Question: If A can complete the work in x days, b can complete the same piece of work in y days and c can complete the same work in z days. In how many days that they can complete the work simultaneously?
(A) cannot be determined
(B) xyz/(x+y+z)
(C) xyz
(D) x+y+z
(E) (x+y+z)/xyz
Rationale: A's one day work=1/x..similarly b and c's one day work is 1/y and 1/z respectively.
a+b+c=(1/x)+(1/y)+(1/z)=(x+y+z)/xyz(one day work)
Total working days=xyz/(x+y+z).
The option B is the answer.
Answer: (B) xyz/(x+y+z)
Question: Find the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 15 cm?
(A) 288
(B) 276
(C) 285
(D) 299
(E) 261
Rationale: Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them) = 1/2 (20 + 18) * (15)
= 285 cm2
Answer: C
Answer: (C) 285
Question: C individuals pledged to pay equal contributions so that a charity’s goal of $x could be reached. If B of the contributors failed to pay their share, which of the following represents the additional number of dollars that each of the remaining individuals would have to pay in order to allow the charity to reach its goal?
(A) Bx/c
(B) C-B
(C) Bx/C(C - B)
(D) bx
(E) CX
Rationale: Number of individuals = C
Amount paid by each individual = n
Total expected amount = Charity's goal = nC = x
n = x/C
Number of individuals who fail to pay = B
Contribution from individuals who would fail to pay = Bx/C --> Additional amount
Number of individuals who are paying = C - B
Additional amount has to be divided among the (C - B) individuals --> Bx/C(C - B)
C
Answer: (C) Bx/C(C - B)
Question: Two pipes P and Q can fill a tank in 10 hours and 15 hours respectively. If both pipes are opened simultaneously, how much time will be taken to fill the tank?
(A) 4 hours 20 min
(B) 5 hours 49 min
(C) 3 hours 50 min
(D) 6 hours
(E) 3 hours 42 min
Rationale: Explanation:
Part filled by P in 1 hour = 1/10
Part filled by Q in 1 hour = 1/15
Part filled by (P + Q) in 1 hour = ( 1/10 + 1/15) = (5/30) = 1/6
Time taken to fill the tank is (6/1) = 6 hrs
ANSWER D
Answer: (D) 6 hours
Question: A can do a particular work in 6 days . B can do the same work in 8 days. A and B signed to do it for Rs. 2400. They completed the work in 3 days with the help of C. How much is to be paid to C?
(A) s. 300
(B) s. 600
(C) s. 420
(D) s. 400
(E) s. 480
Rationale: Explanation :
Amount of work A can do in 1 day = 1/6
Amount of work B can do in 1 day = 1/8
Amount of work A + B can do in 1 day = 1/6 + 1/8 = 7/24
Amount of work A + B + C can do = 1/3
Amount of work C can do in 1 day = 1/3 - 7/24 = 1/24
work A can do in 1 day: work B can do in 1 day: work C can do in 1 day
= 1/6 : 1/8 : 1/24 = 4 : 3 : 1
Amount to be paid to C = 2400 × (1/8) = 300
Answer : Option A
Answer: (A) s. 300
Question: Which of the following ratios is greatest ?
(A) 7 :15
(B) 15 :23
(C) 17 :25
(D) 21 :29
(E) 22: 29
Rationale: Expl : 7/15 = 0.466, 15/23 = 0.652, 17/25 = 0.68 21/29 = 0.724
Clearly, 0.724 is greatest and therefore, 21 : 29 is greatest
Answer: D
Answer: (D) 21 :29
Question: What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 20%?
(A) 20%
(B) 28%
(C) 60%
(D) 26%
(E) 30%
Rationale: SP2 = 2/3 SP1
CP = 100
SP2 = 80
2/3 SP1 = 80
SP1 = 120
100 --- 20 => 20%
Answer:A
Answer: (A) 20%
Question: An investment compounds annually at an interest rate of 12% What is the smallest investment period by which time the investment will more than triple in value?
(A) 11/10 ^n
(B) log3/log1.12
(C) (12/10)^n
(D) 1.12^n
(E) 1.12^n
Rationale: Assume initial amount is x
Annual Interest is 34.1% so after 1 year the amount will become x * (100+12)/100 => x*1.12
now we need to find n for x * (1.12)^n = 3x therefor n = log3/log1.12
B
Answer: (B) log3/log1.12
Question: A certain population of bacteria doubles every 10 minutes. If the number of bacteria in the population initially was 10^5, then what was the number in the population 40 minutes later?
(A) 2(10^5)
(B) 4(10^5)
(C) (2^4)(10^5)
(D) (10^4)(10^5)
(E) (10^5)^4
Rationale: Every 10 minutes, the population is double the previous population.
In 40 minutes, the population doubles 4 times.
The population then is 2^4*10^5.
The answer is C.
Answer: (C) (2^4)(10^5)
Question: The mean proportional between 234 and 104 is :
(A) 12
(B) 39
(C) 54
(D) 64
(E) 156
Rationale: Required mean proportion is = (root of 234)(root of 104) = root of(13*9*2*13*18)
= (13*3*4)
= 156
ANSWER:E
Answer: (E) 156
Question: It is the New Year and Mandy has made a resolution to lose weight this year. She plans to exercise and do yoga. For exercise she plans to workout at the gym and ride her bicycle in the ratio of 2:3 everyday. She will also do yoga in the ratio, yoga:exercise = 2:3. If she does yoga for 25 minutes, how much time will she spend in the gym?
(A) 35 min
(B) 5 min
(C) 15 min
(D) 25 min
(E) 20 min
Rationale: The ratio is 2:3 = yoga:exer, so (25)(3/2) = 37.5 minutes for exercise, and 2:3 = gym:ride, and (2/3)(37.5) = 25 minutes in the gym.
Answer: D
Answer: (D) 25 min
Question: Find the simple interest on Rs.422 for 3 months at 2 paisa per month?
(A) s.27.5
(B) s.34
(C) s.26
(D) s.25.28
(E) s.25.32
Rationale: Explanation:
I = (422*3*2)/100 = 25.32
Answer: Option E
Answer: (E) s.25.32
Question: A certain deck of cards contains 2 blue cards, 2 red cards, 2 yellow cards, and 2 green cards. If two cards are randomly drawn from the deck, what is the probability that they will both be not green?
(A) 15/28
(B) 1/4
(C) 9/16
(D) 1/32
(E) 1/16
Rationale: The question asks they will both be not green. Considering that these are draws without replacement there are following possibilities :
draw 1, draw 2
===== =====
1) Not green, green;
2) green, Not green;
3) green, green;
4) Not green, not green;
The answer has to be either P(4) OR all exclusion of the 3 previous conditions i.e. 1- [P(1) + P(2) + P(3)] => neither of the draws are green
P(4) = 6/8*5/7=15/28
1- [P(1) + P(2) + P(3)] = 1 - [ (6/8 * 2/7) + (2/8*6/7) + (2/8*1/7)] = 1 - [26/8*7] = 1 - [13/28] = 15/28
A
Answer: (A) 15/28
Question: Two trains of length 140 m and 280 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) 28
(B) 266
(C) 990
(D) 20
(E) 21
Rationale: Relative speed = (42 + 30) * 5/18 = 4 * 5 = 20 mps.
Distance covered in passing each other = 140 + 280 = 420 m.
The time required = d/s = 420/20 = 21 sec.
Answer: E
Answer: (E) 21
Question: Prints a page 64 pg per min .If the printed for 3 hours except 10 min.Where there
was an paper jam,how many page did it print
(A) 10,880
(B) 12,880
(C) 14,880
(D) 8,880
(E) 18,880
Rationale: 64 pages ------->1 min
3 hrs except 10 mints means=3*60=180-10=170 mints
i.e.,170*64=10,880 pages printed.
ANSWER:A
Answer: (A) 10,880
Question: A car started running at a speed of 30 km/hr and the speed of the car was increased by 2 km/hr at the end of every hour. Find the total distance covered by the car in the first 10 hours of the journey.
(A) 342 km
(B) 390 km
(C) 642 km
(D) 742 km
(E) 382 km
Rationale: The total distance covered by the car in the first 10 hours = 30 + 32 + 34 + 36 + 38 + 40 + 42 + 44 + 46 + 48 = sum of 10 terms in AP whose first term is 30 and last term is 48 = 10/2 [30 + 48] = 390 km.
ANSWER:B
Answer: (B) 390 km
Question: In a school of 800 students, 45% wear blue shirts, 23% wear red shirts, 15% wear green shirts, and the remaining students wear other colors. How many students wear other colors (not blue, not red, not green)?
(A) 120
(B) 128
(C) 136
(D) 144
(E) 152
Rationale: 45 + 23 + 15 = 83%
100 – 83 = 17%
800 * 17/100 = 136
The answer is C.
Answer: (C) 136
Question: The simple interest accrued on an amount of Rs.49500 at he end of three is Rs.17820. What would be the compound interest accured on the same amount at teh same rate in the same period? (Round off your answer to two decimal places)
(A) 20043.94
(B) 20043.95
(C) 20043.92
(D) 20043.57
(E) 20043.12
Rationale: Let the rate of interest be R% p.a.
(49500)(3)(R)/100 = 17820
495R = 5940
R = 12
CI on Rs.49500 at 12% p.a. for three years
= 49500{[1 + 12/100]3 - 1} = 69543.936 - 49500 = Rs.20043.94
when rounded off to two decimal places.Answer: A
Answer: (A) 20043.94
Question: The cost price of 20 articles is the same as the selling price of x articles. If the profit is 25% then determine the value of x.
(A) 14
(B) 15
(C) 16
(D) 17
(E) 18
Rationale: Explanation:
Let the cost price 1 article = Re 1
Cost price of x articles = x
S.P of x articles = 20
Gain = 20 -x
=>25=(20−x/ x∗100)
=>2000−100x=25x
=>x=16
Option C
Answer: (C) 16
Question: Tough and Tricky questions: Word Problems.
If Bill's salary increased by 16 percent, he would earn $812 per month. If instead, his salary were to increase by only 10 percent, how much money R would he earn per month?
(A) $700
(B) $754
(C) $770
(D) $782
(E) $893
Rationale: OFFICIAL SOLUTION:
(C) If Bill’s salary increased by 16% he would earn $812. Algebraically, this can be written as:
$812 = 1.16S, where S is his current salary.
Then S = $812/1.16 = $700.
Now that we know his current salary is $700, we can calculate what his salary would be if it were increased by 10%. We know that 10% of $700 is $70, so his salary would be:
R=$700 + $70 = $770.
The correct answer is choice (C).
Answer: (C) $770
Question: Two trains of equal length are running on parallel lines in the same directions at 46km/hr. and 36km/hr. The faster trains pass the slower train in 36 seconds. The length of each train is:
(A) 82m
(B) 50m
(C) 72m
(D) 80m
(E) None of these
Rationale: Explanation:
The relative speed of train is 46-36 = 10 Km/hr = (10 X 5) / 18 = 25/9 m/s10×518=259m/s
In 36 secs the total distance travelled is 36x25/9 = 100 m.
Therefore the length of each train is = 100/2 = 50 m.
Answer B
Answer: (B) 50m
Question: The cost per unit of electricity during a 4 year period is as follows:
Year 1, $0.75 per unit;
Year 2, $1.50 per unit;
Year 3, $2.25 per unit;
Year 4, $3 per unit.
If a factory spent equal dollars on electricity each year, what was the average cost of a unit of electricity during the 4 year period?
(A) $1.55
(B) $1.44
(C) $1.66
(D) $1.77
(E) $1.88
Rationale: Let money spent each year = $225
Units bought first year = 300
Units bought second year = 150
Units bought third year = 100
Units bought fourth year = 75
Total number of units = 625
Total money spent = 225*4 = 900
Average = 900/625 = 1.44
Answer : B
Answer: (B) $1.44
Question: A motorist knows six different routes from Bristol to Birmingham. From Birmingham to Sheffield he knows three different routes and from Sheffield to Carlisle he knows two different routes. How many routes does he know from Bristol to Carlisle ?
(A) 4
(B) 8
(C) 12
(D) 24
(E) 36
Rationale: Explanation:
Total number of routes from Bristol to Carlisle = (6 x 3 x 2) = 36.
Answer: E
Answer: (E) 36
Question: In a room with 8 people, 5 people have exactly 1 friend in the room and 4 people have exactly 2 friends in the room (Assuming that friendship is a mutual relationship, i.e. if Jane is Paul's friend, Paul is Jane's friend). If two individuals are selected from the room at random, what is the probability that those two individuals are NOT friends?
(A) 5/21
(B) 3/7
(C) 4/7
(D) 5/7
(E) 25/28
Rationale: (5/8)(6/7) + (4/8)(5/7) if you choose one of the 5 with one other friend, then you have a 6/7 chance of not picking their friend 2nd. If you choose one of the 4 with 2 friends, you have a 5/7 chance of not picking one of their friends second. Add them up.
30/56 + 20/56
50/56=25/28 E. 25/28
Answer: (E) 25/28
Question: At 6′o a clock ticks 6 times. The time between first and last ticks is 25 seconds. How long does it tick at 12′o clock
(A) 47
(B) 55
(C) 28
(D) 66
(E) 11
Rationale: Explanation:
For ticking 6 times, there are 5 intervals.
Each interval has time duration of 25/5 = 5 secs
At 12 o'clock, there are 11 intervals,
So total time for 11 intervals = 11 × 5 = 55 secs.
Answer: B
Answer: (B) 55
Question: A shop owner professes to sell his articles at certain cost price but he uses false weights with which he cheats by 12% while buying and by 20% while selling. What is his percentage profit?
(A) 10.22%
(B) 20.22%
(C) 21.22%
(D) 40%
(E) Can't be calculated
Rationale: The owner buys 100 kg but actually gets 112kg;
The owner sells 100 kg but actually gives 80kg;
Profit: (112-80)/80*100=~40%
Answer: D.
Answer: (D) 40%
Question: An outlet pipe can empty 2/3 rd of a cistern in 12 minutes. In 8 minutes, what part of the cistern will be emptied?
(A) 4/9
(B) 5/8
(C) 4/7
(D) 4/11
(E) 5/9
Rationale: 2/3 ---- 12
? ----- 8 ==> 4/9
ANSWER A
Answer: (A) 4/9
Question: In how many different ways can 5 people be seated in a room with 7 chairs?
(A) 2,520
(B) 181,440
(C) 403,200
(D) 1,814,400
(E) 3,628,800
Rationale: Order doesn't matter
With 7 chairs and only 5 to seat
5!- Number of ways the 5 can seat on the chair
7C2 - Number of ways the 2 empty sits can be vary with the 5 seated
5! * 7C2 = 2,520 Answer - A
Answer: (A) 2,520
Question: Using all the letters of the word "NOKIAS", how many words can be formed, which begin with N and end with A?
(A) 8
(B) 24
(C) 9
(D) 3
(E) 1
Rationale: There are five letters in the given word.
Consider 6 blanks ....
The first blank and last blank must be filled with N and A all the remaining three blanks can be filled with the remaining 3 letters in 4! ways.
The number of words = 4! = 24.
Answer:B
Answer: (B) 24
Question: Chris mixed 5 pounds of raisins with 4 pounds of nuts. If a pound of nuts costs 3 times as much as a pound of raisins, then the total cost of the raisins was what fraction of the total cost of the mixture?
(A)  5/17
(B)  1/5
(C)  1/4
(D)  1/3
(E)  3/7
Rationale: 1 lbs of raisin = $1
5 lbs of raisin = $5
1 lbs of nuts = $3
4 lbs of nuts = $12
Total value of mixture = 12+5 = 17
Fraction of the value of raisin = 5/17 = 1/5
Ans:A
Answer: (A)  5/17
Question: How many prime numbers between 1 and 100 are factors of 7,150 ?
(A) One
(B) Two
(C) Three
(D) Four
(E) Five
Rationale: Make prime factorization of 7,150 --> 7,150=2∗5^2∗11∗13 So, 4 prime numbers between 1 and 100 (namely 2, 5, 11, and 13) are factors of 7,150.
Answer: D.
Answer: (D) Four
Question: Five coins are tossed simultaneously. In how many of the outcomes will the third coin turn up a head?
(A) 2^4
(B) 2^10
(C) 3 * 2^8
(D) 3 * 2^9
(E) 3 * 2^10
Rationale: Fix the third coin as H. The remaining 4 coins have 2^4 outcomes.
A
Answer: (A) 2^4
Question: What is the next number of the following sequence
1,3,4,5,6,1,9,16,25,...
(A) 14
(B) 15
(C) 36
(D) 17
(E) 18
Rationale: (1, 3 ,4,5, 6) (1, 9, 16, 25,x)
square of 1st group gives 2nd group
1^2 = 1
3^2 = 9
4^2 = 16
5^2 =25
6^2 =36
ANSWER:C
Answer: (C) 36
Question: One vessel contains a mixture of 6 parts pure wine and 4 parts soda, whereas the other vessel contains a mixture of 9 parts pure wine and 5 parts soda. Compare the strength of the wine.
(A) 35;36
(B) 7 : 8
(C) 7 : 4
(D) 42 : 45
(E) None of these
Rationale: 6/10 : 9/14
LCM of 5,14 = 70
(6/10)*70 : (9/14)*70
42:45
Answer is D.
Answer: (D) 42 : 45
Question: Three partners A,B,C starts a business. Twice A's capital is equal to thrice B's capital and B's capital is four times C's capital. Out of a total profit of Rs.14000 at the end of the year, B's share is
(A) Rs.4000
(B) Rs.5040
(C) Rs.7500
(D) Rs.6600
(E) None
Rationale: Solution
Let C = x.
Then, B = 4x and 2A = 3x4x = 12x or A = 6x.
âˆ´ A : B : C = 6x : 4x : x	= 6 : 4 : 1.
So B's capital	= Rs(14000 x 4 / 11)
= Rs.5040.
Answer B
Answer: (B) Rs.5040
Question: Which of the following is not a prime number ?
(A) 21
(B) 23
(C) 27
(D) 29
(E) 31
Rationale: 21 is not a prime number. Choice A is the correct answer.
Answer: (A) 21
Question: A reduction of 35% in the price of apples would enable a man to obtain 42 more for Rs.20, what is reduced price per dozen?
(A) 1.7
(B) 3.5
(C) 6.3
(D) 7.1
(E) 10.4
Rationale: A
20*(35/100) = 6 --- 42
? --- 12 => Rs.1.7
Answer: (A) 1.7
Question: A certain sum of money is divided among A, B and C so that for each Rs. A has, B has 65 paisa and C 40 paisa. If C's share is Rs.40, find the sum of money?
(A) 288
(B) 262
(C) 72
(D) 205
(E) 267
Rationale: A:B:C = 100:65:40
= 20:13:8
8 ---- 40
41 ---- ? => Rs.205
Answer: D
Answer: (D) 205
Question: If 15 ≤ x ≤ 25, and 0.2 ≤ y ≤ 0.6, what is the greatest possible value of 3/(x·y)?
(A) 1/3
(B) 0.6
(C) 0.9
(D) 1
(E) 3
Rationale: or greatest possible value of 3/(x·y), x and y should be made minimum
minimum value of x is 15 and minimum value of y is 0.2
so greatest possible value of 3/(15*0.2)= 1
ANSWER:D
Answer: (D) 1