mathewhe/aqua_rat huggingface dataset:
Question: Fresh grapes contain 80% by weight while dried grapes contain 20% water by weight. What is the weight of dry grapes available from 40 kg of fresh grapes?
(A) 10 kg
(B) 12 kg
(C) 15 kg
(D) 16 kg
(E) 20 kg
Rationale: From the question we know: 40kg * 80% = 32kg of water in the fresh grapes
40kg - 32kg of water = 8kg of non-water mass
We are looking for the weight of the dry grapes (X).
Since the question tells us that 20% of the weight of the dry graps is water and we know that 8kg is non-water mass we can set up the following equation:
X = 1/5(X) + 8kg
4/5(X) = 8kg
X = 10 kg
Answer- A
Answer: (A) 10 kg
Question: The water from one outlet, flowing at a constant rate, can fill a swimming pool in 16 hours. The water from a second outlet, flowing at a constant rate, can fill the same pool in 12 hours. If both outlets are used at the same time, approximately what is the number of hours required to fill the pool?
(A)  0.22
(B)  0.31
(C)  2.50
(D)  3.21
(E)  6.85
Rationale: Always remember RT=W i.e Rate*Time = Work
Also remember that rate can be added or subtracted. For e.g if A do a work in 2 day and B do a work in 2 day.
They both of them together will do a work in 1 day.
So now your question first determine both outlets rate.
1st outlet rate = 1/16 (R=W/T here W=1 work, T = 16hrs)
2nd outlet rate = 1/12 (R=W/T here W=1 work, T = 12hrs)
Both of them working together rate = 1st outlet rate + 2nd outlet rate = 1/16+1/12 = 7/48
again apply the formula RT=W
T = W/R = 1/7/48 = 48/7 =6.85
Answer is E.
Answer: (E)  6.85
Question: In how many ways can the letters of the word RECPECT be arranged?
(A) 2580
(B) 2500
(C) 2000
(D) 2520
(E) 3420
Rationale: RECPECT has 7 words, but E is repeated two times. Thus ways = 7! / 2! = 2520 ways
C
Answer: (C) 2000
Question: Janet has to pay back her bank loan over 8 months following the below sequence.
$50, $55, $65, $80, $85, $95, $110, ?
How much will she pay back on the eigthmonth?
(A) $115
(B) $145
(C) $135
(D) $125
(E) $130
Rationale: The sequence progresses +5, +10, +15 repeated; The amount to pay back on the 8th Month is $115
Ans A
Answer: (A) $115
Question: Can you find the missing number in the sequence?
7 12 37 ? 9142
(A) 1262
(B) 2189
(C) 1132
(D) 1214
(E) 3256
Rationale: A
1262
Sequence is based on formula:
Next = (1st Number)^2 - (2nd number)
7 12 37 ? 9142
7^2 - 12 = 37
12^2 - 37 = 107
37^2 - 107 = 1262 (Answer)
102^2 - 1262 = 9142
Answer: (A) 1262
Question: In a multiple choice test comprising 5 Questions, each with 4 choices, what is the probability of a student getting 3 or more questions correct? Each question has only one correct answer and the student is equally likely to choose any of the four choices.
(A) 24/256
(B) 53/512
(C) 105/512
(D) 459/512
(E) 47/256
Rationale: Probability for choosing correct answer is 1/4 and incorrect answer is 3/4
For 3 correct answers,
C(5,3)*(1/4)^3*(3/4)^2=90/(4^5)
For 4 correct answers,
C(5,4)*(1/4)^4*(3/4)^1=15/(4^5)
For 5 correct answers,
C(5,5)*(1/4)^5*(3/4)^0=1/(4^5)
So total probability
=106/1024
=53/512
Ans B
Answer: (B) 53/512
Question: The average price of three items of furniture is Rs. 30000. If their prices are in the ratio 3:5:7, the price of the cheapest item is?
(A) 2379
(B) 2889
(C) 9288
(D) 9000
(E) 6000
Rationale: Let their prices be 3x, 5x and 7x.
Then, 3x + 5x + 7x = (15000 * 3) or x = 2000.
Cost of cheapest item = 3x = Rs. 6000.
Answer: E
Answer: (E) 6000
Question: There are 10 women and 8 men in a certain club. If the club is to select a committee of 2 women and 2 men, how many different such committees are possible?
(A) 1040
(B) 1260
(C) 1480
(D) 1620
(E) 1850
Rationale: 10C2 * 8C2 = 45*28 = 1260
The answer is B.
Answer: (B) 1260
Question: Given that 0 < a < b < c < d, which of the following the largest ?
(A) (c+d) / (a+b)
(B) (c+d) / (a+c)
(C) (c+d) / (a+q)
(D) (c+d) / (a+o)
(E) (c+d) / (a+f)
Rationale: Explanation: Take a = 1, b = 2, c = 3, d = 4. option A is clearly true.
Sol: A
Answer: (A) (c+d) / (a+b)
Question: if a@b = a * b^(1/2) then 2@25 = ?
self made
(A) 2
(B) 6
(C) 10
(D) 8
(E) 4
Rationale: 2* (25)^1/2= 2*5= 10
C is the answer
Answer: (C) 10
Question: At a tanning salon, customers are charged $10 for their first visit in a calendar month and $7 for each visit after that in the same calendar month. In the last calendar month, 100 customers visited the salon, of which 30 made a second visit, and 10 made a third visit. All other customers made only one visit. If those visits were the only source of revenue for the salon, what was the revenue for the last calendar month at the salon?
(A) $1220
(B) $1280
(C) $1300
(D) $1340
(E) $1880
Rationale: I get B. This question seems too straightforward for 600+. Am I missing something?
100 first-time visits --> 100(10) = $1000
30 + 10 = 40 subsequent visits --> 40(7) = $280
Total revenue: 1000+ 280 = $1280
The answer is B.
Answer: (B) $1280
Question: The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 1250 resolutions?
(A) 1277 m
(B) 1760 m
(C) 1278 m
(D) 1288 m
(E) 1378V
Rationale: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 1250 resolutions.
= 1250 * 2 * 22/7 * 22.4 = 176000 cm
= 1760 m
Answer: B
Answer: (B) 1760 m
Question: The average height of 35 boys in a class was calculated as 183cm. It has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm. Find the actual average height of the boys in the class (Round off your answer to two decimal places?
(A) 187.89 cm
(B) 181.29 cm
(C) 123.98 cm
(D) 149.98 cm
(E) 146.89 cm
Rationale: Calculated average height of 35 boys = 183 cm.
Wrong total height of 35 boys = 183 * 35 cm. This was as a result of an actual height of 106 cm being wrongly written as 166 cm. Correct total height of 35 boys = 183 cm - (166 cm - 106 cm)/35
= 183 cm - 60 /35 cm
= 183 cm - 1.71 cm = 181.29 cm.
Answer: B
Answer: (B) 181.29 cm
Question: A sum of Rs. 2743 is lent into two parts so that the interest on the first part for 8 years at 3% per annum may be equal to the interest on the second part for 3 years at 5% per annum. Find the second sum?
(A) 1642
(B) 1640
(C) 1632
(D) 1688
(E) 6386
Rationale: (x*8*3)/100 = ((2743 - x)*3*5)/100
24x/100 = 41145/100 - 15x/100
39x = 41145 => x = 1055
Second sum = 2743 – 1055
=1688
Answer:D
Answer: (D) 1688
Question: A bank offers 5% compound interest calculated on half-yearly basis. A customer deposits $ 1600 each on 1stJanuary and 1st July of a year. At the end of the year, the amount he would have gained by way of interest is:
(A) $120
(B) $121
(C) $122
(D) $123
(E) $124
Rationale: Amount	= $ 1600 x 1 +	5 2	+ 1600 x 1 +	5
2 x 100 2 x 100
= $ 1600 x	41	x	41	+ 1600 x	41
40 40 40
= $ 1600 x	41 41	+ 1
40 40
= $ 1600 x 41 x 81
40 x 40
= $ 3321.
C.I. = $. (3321 - 3200) = $ 121
ANSWER : B $ 121
Answer: (B) $121
Question: India has a run rate of 3.2 in the first 10 overs. What should be the run rate in remaining 40 overs to win a game of 282 runs?
(A) 6.25
(B) 6.27
(C) 6.22
(D) 6.21
(E) 6.20
Rationale: Explanation:
Runs scored in first 10 overs:
=> Rate*Overs= 3.2*10 = 32 runs
=> Required runs = 282-32 = 250
=> Left overs= 40
Required rate = runs/overs
= 250/40
= 6.25
=> 6.25 runs per over is needed to win the game.
ANSWER: A
Answer: (A) 6.25
Question: In how many ways can 21 books on English and 19 books on Hindi be placed in a row on a shelf so that two books on Hindi may not be together?
(A) 1540
(B) 2314
(C) 5420
(D) 1240
(E) 4512
Rationale: We must place all these books as under:
XEXEX….XEX
There are 21 books on English, 19 books on Hindi
19 places out of 22 can be chosen 22C19=22C3=1540 ways
ANS: A
Answer: (A) 1540
Question: Two trains A and B starting from two points and travelling in opposite directions, reach their destinations 9 hours and 4 hours respectively after meeting each other. If the train A travels at 110kmph, find the rate at which the train B runs.
(A) 40
(B) 165
(C) 120
(D) 80
(E) 100
Rationale: If two objects A and B start simultaneously from opposite points and, after meeting, reach their destinations in ‘a’ and ‘b’ hours respectively (i.e. A takes ‘a hrs’ to travel from the meeting point to his destination and B takes ‘b hrs’ to travel from the meeting point to his destination), then the ratio of their speeds is given by:
Sa/Sb = √(b/a)
i.e. Ratio of speeds is given by the square root of the inverse ratio of time taken.
Sa/Sb = √(4/9) = 2/3
This gives us that the ratio of the speed of A : speed of B as 2:3.
Since speed of A is 110 kmph, speed of B must be 110*(3/2) = 165 kmph
Answer B
Answer: (B) 165
Question: Rs. 800 becomes Rs. 956 in 3 years at a certain rate of simple interest.If the rate of interest is increased by 4% ,What amount will Rs. 800 become in 3 years ?
(A) Rs. 1020.80
(B) Rs. 1025
(C) Rs. 1052
(D) Data inadequate
(E) None of these
Rationale: Solution
S.I. = Rs.(956-800 )=Rs.156
Rate = (100x156/800x3) = 6 1/2%
New rate = (6 1/2 +4)% = 10 1/2%
New S.I. = Rs.(800 x21/2x3/100) Rs. 252.
∴ New amount = Rs.(800+252)= Rs. 1052.
Answer C
Answer: (C) Rs. 1052
Question: A sum of money is put out at compound interest for 2 years at 20%. It would fetch Rs.482 more if the interest were payable half-yearly, then it were pay able yearly. Find the sum.
(A) 3377
(B) 6886
(C) 2788
(D) 2000
(E) 28712
Rationale: P(11/10)4 - P(6/5)2 = 482
P = 2000
Answer:D
Answer: (D) 2000
Question: There stand nine temples in a row in a holy place. All the nine temples have 100 steps climb. A fellow devotee comes to visit the temples. He drops a Re. 1 coin while climbing each of the 100 steps up. Then he offers half of the money he has in his pocket to the god. After that, he again drops Re. 1 coin while climbing down each of the 100 steps of the temple.
If he repeats the same process at each temple, he is left with no money after climbing down the ninth temple. Can you find out the total money he had with him initially?
(A) 143700
(B) 146900
(C) 376190
(D) 248117
(E) 127690
Rationale: B
146900
Whenever you face such type of questions, it is wise to begin from the last thing. Here in this question the last thing will be the 9th temple. He climbed down 100 steps and thus you know, he had Rs. 100 before beginning climbing down. Thus, he must have offered Rs. 100 to the god in that temple too (he offered half of the total amount). Also, he must have dropped Rs. 100 while climbing the steps of the ninth temple. This means that he had Rs. 300 before he begand climbing the steps of the ninth temple.
Now, we will calculate in the similar manner for each of the temples backwards.
Before the devotee climbed the eight temple: (300+100)*2 + 100 = 900
Before the devotee climbed the seventh temple: (900+100)*2 + 100 = 2100
Before the devotee climbed the Sixth temple: (2100+100)*2 + 100 = 4300
Before the devotee climbed the fifth temple: (4300+100)*2 + 100 = 8900
Before the devotee climbed the fourth temple: (8900+100)*2 + 100 = 18100
Before the devotee climbed the third temple: (18100+100)*2 + 100 = 36,500
Before the devotee climbed the second temple: (36500+100)*2 + 100 = 73300
Before the devotee climbed the first temple: (73300+100)*2 + 100 = 146900
Therefore, the devotee had Rs. 146900 with him initially.
Answer: (B) 146900
Question: The average of first 20 natural numbers is?
(A) 10.5
(B) 11.4
(C) 5.3
(D) 5.9
(E) 5.1
Rationale: Sum of 20 natural no. = 420/2 = 210
Average = 210/20 = 10.5
Answer:A
Answer: (A) 10.5
Question: a dog have birth to 12 puppies, 2 female and 10 male. what is the ratio of the female puppies to the male?
(A) 1/5
(B) 1/6
(C) 1/10
(D) 2/12
(E) 1/8
Rationale: If female is 2 and male is 10, then 1/5.
so ratio of female to male is = 2/10 = 1/5
ANSWER:A
Answer: (A) 1/5
Question: A small water pump would take 3 hours to fill an empty tank. A larger pump would take 3/4 hour to fill the same tank. How many hours would it take both pumps, working at their respective constant rates, to fill the empty tank if they began pumping at the same time?
(A) 3/4
(B) 3/5
(C) 5/7
(D) 1/2
(E) 4/5
Rationale: Rate of the small pump is 1/3 tank/hour
Rate of the larger pump is 1/(3/4) or 4/3 tank/hour;
Combined rate of the two pumps is 1/3+4/3=5/3 tank/hour, together they will fill the empty tank in 1/(5/3)) = 3/5 hours (time=job/rate).
Answer: B
Answer: (B) 3/5
Question: P is five times as old as Q, and Q is six years older than R. If R is z years old, what is P’s age in terms of z?
(A) 5z + 6
(B) 5z − 30
(C) 5z + 30
(D) (z + 6)/5
(E) (z − 6)/5
Rationale: P = 5Q
Q = R+6 = z+6
P = 5(z+6) = 5z + 30
The answer is C.
Answer: (C) 5z + 30
Question: A wire in the form of a circle of radius 3.5 m is bent in the form of a rectangule, whose length and breadth are in the ratio of 6 : 5. What is the area of the rectangle?
(A) 54 cm2
(B) 30 cm2
(C) 17 cm2
(D) 26 cm2
(E) 98 cm2
Rationale: The circumference of the circle is equal to the permeter of the rectangle.
Let l = 6x and b = 5x 2(6x + 5x) = 2 * 22/7 * 3.5
=> x = 1
Therefore l = 6 cm and b = 5 cm Area of the rectangle
= 6 * 5
= 30 cm2
Answer: B
Answer: (B) 30 cm2
Question: R=(429)^2 * 237 * (1243)^3 is thrice of ?
(A) 33605 * 31960 * (1243)^2
(B) 33654 * 538219 * (1243)^2
(C) 33891 * 533247 * (1243)^2
(D) 34122 * 532004 * (1243)^2
(E) 34606 * 534572 * (1243)^2
Rationale: R=(429)^2*237*(1243)^3 is an odd number.
Among answer choices only C is an odd number, (so thrice C also will be an odd number).
Answer: C.
Answer: (C) 33891 * 533247 * (1243)^2
Question: The area of the square formed on the diagonal of a rectangle as its side is 108 1/3 % more than the area of the rectangle. If the perimeter of the rectangle is 28 units, find the difference between the sides of the rectangle?
(A) 5
(B) 4
(C) 7
(D) 2
(E) 1
Rationale: Let the sides of the rectangle be l and b respectively.
From the given data,
(√l2 + b2) = (1 + 108 1/3 %)lb
=> l2 + b2 = (1 + 325/3 * 1/100)lb
= (1 + 13/12)lb
= 25/12 lb
=> (l2 + b2)/lb = 25/12
12(l2 + b2) = 25lb
Adding 24lb on both sides
12l2 + 12b2 + 24lb = 49lb
12(l2 + b2 + 2lb) = 49lb
but 2(l + b) = 28 => l + b = 14
12(l + b)2 = 49lb
=> 12(14)2 = 49lb
=> lb = 48
Since l + b = 14, l = 8 and b = 6
l - b = 8 - 6 = 2m.Answer: D
Answer: (D) 2
Question: Expenditures of a Company (in Lakh Rupees) per Annum Over the given Years.
Year	Item of Expenditure
Salary	Transport and Fuel	Bonus	Interest on Loans	Taxes
1998	288	98	3.00	23.4	83
1999	342	112	2.52	32.5	108
2000	324	101	3.84	41.6	74
2001	336	133	3.68	36.4	88
2002	420	142	3.96	49.4	98
The total amount spent for transport by the company during the given period is approximately what percent of the total amount of salary paid during this period?
(A) A)0.5%
(B) B)1.24%
(C) C)1%
(D) D)3%
(E) E)4%
Rationale: Required percentage
=	(288 + 342 + 324 + 336 + 420)
=	[	17	x 100	]	%
1710
~= 1%.
Answer : C
Answer: (C) C)1%
Question: The length of the bridge, which a train 150 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
(A) 76 m
(B) 178 m
(C) 225 m
(D) 187 m
(E) 176 m
Rationale: Speed = [45 X 5/18] m/sec
= [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (150 + x)/30 = 25/2
=> 2(150 + x)= 750 => x = 225 m.
Answer: C
Answer: (C) 225 m
Question: If a two-digit positive integer has its digits reversed, the resulting integer differs from the original by 36. By how much do the two digits differ?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: we are given that if the integer N has its digits reversed the resulting integer differs from the original by 25. First let’s express the reversed number in a similar fashion to the way in which we expressed the original integer.
10B + A = reversed integer
Since we know the resulting integer differs from the original by 27 we can say:
10B + A – (10A + B) = 36
10B + A – 10A – B = 36
9B – 9A = 36
B – A = 4
Since B is the tens digit and A is the units digit, we can say that the digits differ by 4.
The answer is B.
Answer: (B) 4
Question: Eighty percent of the lights at Hotel California are on at 8 p.m. a certain evening. However, forty percent of the lights that are supposed to be off are actually on and ten percent of the lights that are supposed to be on are actually off. What percent X of the lights that are on are supposed to be off?
(A) 22(2/9)%
(B) 16(2/3)%
(C) 11(1/9)%
(D) 10%
(E) 5%
Rationale: Is the Answer D.
let me try..
Let the light which are supposed to be OFF = SO
Let the light which are supposed to be ON = SN
Let the light which are ACTUALLY OFF = AO
Let the light which are ACTUALLY ON = AN
Let the total no. of lights be 100,
So ACTUALLY ON lights = 80
And ACTUALLY OFF lights = 20
Also given >> forty percent of the lights that are supposed to off are actually on >>> (40/100)*SO are ACTUALLY ON
it means >>> (60/100)*SO are ACTUALLY OFF
Also given >> ten percent of the lights that are supposed to be on are actually off >>> (10/100)*SN are ACTUALLY OFF
it means >>> (90/100)*SN are ACTUALLY ON
So, Total ACTUALLY ON lights = (40/100)*SO + (90/100)*SN = 80
and Total ACTUALLY OFF lights = (60/100)*SO + (10/100)*SN = 80
From here we get SO = 20
we need to find: What percent of the lights that are on are supposed to be off >>> So light ACTUALLY ON are 80 and light which are ACTUALLY ON, which are supposed to be OFF = (40/100)*SO = 8.
So (8/80)*100 X= 10%.D
Answer: (D) 10%
Question: What is the lowest possible common multiple of 2 distinct integers, each greater than 145?
(A) 146
(B) 147
(C) 292
(D) 146*146
(E) 146*147
Rationale: The least common multiple of two numbers greater than 145 is 2(146) = 292, where the two distinct integers are 146 and 292.
The answer is C.
Answer: (C) 292
Question: Anand and Deepak started a business investing Rs. 500 and Rs. 600 respectively. Out of a total profit of Rs. 420. Deepak's share is?
(A) s. 220.01
(B) s. 450.20
(C) s. 845.01
(D) s. 320.01
(E) s. 229.09
Rationale: Ratio of their shares = 500 : 600 = 5 : 6
Deepak's share = Rs. (420* 6/11) = Rs. 229.09 ANSWER "E
Answer: (E) s. 229.09
Question: The numerator of a fraction is increased by 200% and denominator is increased by 250% the resultant fraction is 3/14. What is the original fraction?
(A) 1/2
(B) 3/4
(C) 1/4
(D) 1/8
(E) 3/8
Rationale: if the original fraction is x/y then after increasing numerator by 200% and denomenator by 250% new fraction will become 3x/3.5y
3x/3.5y = 3/14 => x/y = 1/4 , Hence original fraction is 1/4
ANSWER:C
Answer: (C) 1/4
Question: 300 is what percent of 40?
.
(A) 0.2%
(B) 2%
(C) 5%
(D) 20%
(E) 750%
Rationale: 300= x*40/100
x = 750%
Ans; E
Answer: (E) 750%
Question: The least number, which when divided by 12, 15, 20 and 54 leaves in each case a remainder of 8 is:
(A) 504
(B) 536
(C) 544
(D) 548
(E) 568
Rationale: Required number = (L.C.M. of 12, 15, 20, 54) + 8
= 540 + 8
= 548.
Answer: Option D
Answer: (D) 548
Question: The length of the rectangular field is double its width. Inside the field there is square shaped pond 8m long. If the area of the pond is 1/18 of the area of the field. What is the length of the field?
(A) 23
(B) 32
(C) 34
(D) 43
(E) 48
Rationale: Explanation:
A/18 = 8 * 8 => A = 8 * 8 * 18
x * 2x = 8 * 8 * 18
x = 24 => 2x = 48
Answer: Option E
Answer: (E) 48
Question: Which of the following does NOT have a decimal equivalent that is a terminating decimal?
(A) 1/2^25
(B) 5^3/2^7
(C) 3^8/6^10
(D) 3^9/6^7
(E) 6^8/10^10
Rationale: For a fraction to have terminating decimal, it must either have only 2 and/or 5 in the denominator. All other values in the denominator leads to non terminating decimal values
Hence,
1. A has 2 in the denominator, Hence it is terminating
2. B is also terminating
3. 3^8/(6^10) can be written as 3^8/ (2^10 * 3^10) => 1/(2^10 * 3^2). There is 3 in the denominator. Hence it is non terminating decimal
4. 3^9/(2^7 * 3^7) => 3^2/2^7. Hence Terminating
5. Has both 2 & 5 in the denominator. Hence Terminating.
Option C
Answer: (C) 3^8/6^10
Question: In Company J, the total monthly payroll for the 15 factory workers is $30,000 and the total monthly payroll for the 30 office workers is $75,000. By how much does the average (arithmetic mean) monthly salary of an office worker exceed that of a factory worker in this company?
(A) $450
(B) $500
(C) $600
(D) $650
(E) $750
Rationale: The average monthly salary of a factory worker is: $30,000 / 15 = $2000.
The average monthly salary of an office worker is: $75,000 / 30 = $2500.
The difference in average salary is: $2500 - $2000 = $500.
The answer is B.
Answer: (B) $500
Question: The length of the room is 5m and width is 5m. Find the cost of paving the floor by slabs at the rate of Rs.200 per sq meter?
(A) 2000
(B) 3000
(C) 4000
(D) 3500
(E) 5000
Rationale: l=5m w=5m
area of the floor = 5x 5 = 25 sq m
cost of paving = 200 x 25= Rs. 5000
Answer: E
Answer: (E) 5000
Question: There are two numbers. If 50% of the first number is added to the second number, then the second number increases to its five-fourth. Find the ratio of the first number to the second number?
(A) A)1/2
(B) B)5/8
(C) C)6
(D) D)6/7
(E) E)7
Rationale: Let the two numbers be x and y.
50/100 * x + y = 5/4y
=> 1/2 x = 1/4 y => x/y = 1/2
A)
Answer: (A) A)1/2
Question: A family with 1 mother, 1 father, and 3 children sit in a car with 2 front seats and 3 back seats. If the mother drives with a child in the front, and the father sits in the back with the other two children, how many seating arrangements are possible?
(A) 3
(B) 4
(C) 6
(D) 12
(E) 18
Rationale: In the front seat we have 3 possibilities of children. (C1 or C2 or C3)
In the back seat we have (2!*1)*3 = 6 possibilities ( C1,C2,F / C2,C1,F / C1,F,C2 / C2,F,C1 / F,C1,C2 / F,C2,C1 -> IF C3 is in front seat)
So, 6*3 = 18 (try to figure out to change the possibilities of sitting back the C3 child in the place of C1 or C2 and do the 6 possibilities again and again).
Or, another way to see:
Looking into the back seat:
( C1,C2,F / C2,C1,F / C1,F,C2 / C2,F,C1 / F,C1,C2 / F,C2,C1) = 6
or +
( C3,C2,F / C2,C3,F / C3,F,C2 / C2,F,C3 / F,C3,C2 / F,C2,C3) = 6
or +
( C1,C3,F / C3,C1,F / C1,F,C3 / C3,F,C1 / F,C1,C3 / F,C3,C1) = 6
-------
ANS : E :18
Answer: (E) 18
Question: A technical support team of 6 agents is chosen from 9 senior-level agents and 5 junior-level agents. The team must have at least 2 seniors and at least 3 juniors. How many ways can this team be created?
(A) 140
(B) 320
(C) 1015
(D) 1020
(E) 2204
Rationale: Solution: We have two possibilities 2S 4J or 3S 3J
(9C2)(5C4)+(9C3)(5C3)=700
D) 1020
Answer: (D) 1020
Question: The least number of complete years in which a sum of money put out at 20% compound interest will be more than doubled is:
(A) 3
(B) 4
(C) 5
(D) 6
(E) None of these
Rationale: Explanation:
P(1 + 20/100)n >2P => (6/5)n >2
Now,(6/5 x 6/5 x 6/5 x	6/5	)>2
So, n = 4 years.
ANSWER IS B
Answer: (B) 4
Question: How many figures are required to number the pages the pages of a book containing 223 pages?
(A) 372
(B) 661
(C) 561
(D) 467
(E) 761
Rationale: 1 to 9 = 9 * 1 = 9
10 to 99 = 90 * 2 = 180
100 to 223 = 124 * 3 = 372
-----------
561
ANSWER:C
Answer: (C) 561
Question: Find L.C.M of 852 and 1491
(A) 5964
(B) 5664
(C) 4964
(D) 4664
(E) 5555
Rationale: 852) 1491 (1
852
639) 852 (1
639
213) 639 (3
639
0
H.C.F of 852 and 1491 is 213
: . L.C.M = 852*1491/213 = 5964
Answer is A.
Answer: (A) 5964
Question: In a set of numbers from 100 to 1000 inclusive, how many integers are odd and do not contain the digit 3?
(A) 180
(B) 288
(C) 286
(D) 284
(E) 324
Rationale: We have to find the total number of 3-digit odd numbers not having 3 as a digit.
Units digits will be among 1,5,7,9
Tenth digits will be among 0,1,2,5,4,6,7,8,9
Hundredth digits will be among 1,2,5,4,6,7,8,9
So total numbers = 4*9*8 =288
Answer : B
Answer: (B) 288
Question: By selling an umbrella for Rs. 300, a shop keeper gains 10%. During a clearance sale, the shopkeeper allows a discount of 5% on the marked price. His gain percent during the sale is?
(A) 5.56%
(B) 2%
(C) 8%
(D) 3%
(E) 4%
Rationale: Marked price = Rs. 300
C.P. = 100/110 * 300 = Rs. 270
Sale price = 95% of Rs. 300 = Rs. 285
Required gain % = 15/270 * 100 =5.56%.
Answer: A
Answer: (A) 5.56%
Question: 3/4 of 1/2 of 2/5 of 5020 = ?
(A) 392
(B) 229
(C) 753
(D) 493
(E) 540
Rationale: C
753
? = 5020 * (2/5) * (1/2) * (3/4) = 753
Answer: (C) 753
Question: Solve(0.76 × 0.76 × 0.76 − 0.008)/(0.76 × 0.76 + 0.76 × 0.2 + 0.04)
(A) 0.56
(B) 0.62
(C) 0.5
(D) 0.48
(E) 0.52
Rationale: 0.56
Option 'A'
Answer: (A) 0.56