mathewhe/aqua_rat huggingface dataset:
Question: The volume of a cube is 2197 cc. Find its surface.
(A) 864
(B) 1014
(C) 1299
(D) 1268
(E) 1191
Rationale: a3 = 2197 => a = 136a2 = 6 * 13 * 13 = 1014Answer: B
Answer: (B) 1014
Question: 2, 4, 3, 6, ?, ?, 9, 18, ?, ?, 33.
(A) 16,31
(B) 16,32
(C) 15,30
(D) 15,32
(E) 15,31
Rationale: 2, 4, 3, 6, ?, ?, 9, 18, ?, ?, 33.
ans: 2, 4, 3, 6, 4, 8, 9, 18, 16, 32, 33.
ANSWER:B
Answer: (B) 16,32
Question: An error 4% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is:
(A) 4.16
(B) 5.16
(C) 7.16
(D) 8.16
(E) 9.16
Rationale: Explanation:
100 cm is read as 104 cm.
A1 =(100 × 100)cm2 = 10000
and A2= (104 × 104)cm2= 10816
(A2 - A1) = 10816-10000 = 816
=> 816/10000*100 =8.16
Answer : D
Answer: (D) 8.16
Question: If k^3 is divisible by 1620, what is the least possible value of integer k?
(A) 12
(B) 30
(C) 60
(D) 90
(E) 120
Rationale: 1620 = 2^2*3^4*5
Therefore k must include at least 2 * 3^2 * 5 = 90.
The answer is D.
Answer: (D) 90
Question: What is the sum of the greatest common factor and the lowest common multiple of 48 and 72?
(A) 192
(B) 120
(C) 168
(D) 160
(E) 184
Rationale: Prime factorization of the given numbers
72= 2^3 * 3^2
48= 2^4 *3
Greatest common factor = 2^3*3 = 24
Lowest common multiple = 2^4*3^2 =144
Sum = 24+ 144 = 168
Answer C
Answer: (C) 168
Question: 40 % of 2 is equal to
(A) 0.2
(B) 0.8
(C) 0.6
(D) 0.7
(E) 0.9
Rationale: 40 % of 2 = (40 / 100) * 2 = 0.8
Answer: Option B
Answer: (B) 0.8
Question: What will come in place of the x in the following Number series? 73205, 6655, 605, 55, x
(A) 67900
(B) 73205
(C) 73789
(D) 87654
(E) 98555
Rationale: (B)
5 x 11 = 55, 55 x 11 = 605, 605 x 11 = 6655, 6655 x 11 = 73205
Answer: (B) 73205
Question: 0.8 x 0.35=?
(A) 3.15e-05
(B) 0.000315
(C) 0.28
(D) 0.028
(E) 0.0028
Rationale: 8 x 35 = 280
Sum of decimal places =3
Therefore, 0.007 x 0.45 = 0.280
Answer is C.
Answer: (C) 0.28
Question: In a class, there are 24 boys whose ages is decreased by 4 months, when one boy aged 20 years is replaced by a new boy. Find the age of the new boy.
(A) 9 YEARS
(B) 10 YEARS
(C) 12 YEARS
(D) 14 YEARS
(E) 15 YEARS
Rationale: Let age of the new boy was X.
Age decreased = 4 months = 4/12 = 1/3 years
Now, we have formula for this type of questions,
Number of members in the Group * age decreased = difference in ages of boy in and boy out.
24 * (1/3) = 20 -X
X = 12 years.
ANSWER : OPTION C
Answer: (C) 12 YEARS
Question: Acording to a military code, SYSTEM is SYSMET and NEARER is AENRER. What is the code for FRACTION ?
(A) CARFTINO
(B) CARFTION
(C) ARFCNOIT
(D) CARFNOIT
(E) SUIIQQWE
Rationale: Explanation:
The letter is the first half and the letter half of the word are separately reversed to obtain the code.
Answer: D
Answer: (D) CARFNOIT
Question: The price of pulses has fallen by 30%. How many quintals can be bought for the same amount which was sufficient to buy 12 quintals at the higher price?
(A) 20
(B) 22.5
(C) 17
(D) 30
(E) 32.5
Rationale: 80% of original price can buy = 12 quintals.
Therefore, he can buy ( 12 x 100 )/ 70 = 17 quintals at the lower price.
ANSWER:C
Answer: (C) 17
Question: A dog takes 3 leaps for every 7 leaps of a hare. If one leap of the dog is equal to 3 leaps of the hare, the ratio of the speed of the dog to that of the hare is :
(A) 9:7
(B) 9:9
(C) 9:6
(D) 9:1
(E) 9:2
Rationale: Explanation:
Dog : Hare = (3*3) leaps of hare : 7 leaps of hare = 9 : 7.
Answer: A) 9:7
Answer: (A) 9:7
Question: Vijay lent out an amount Rs. 10000 into two parts, one at 8% p.a. and the remaining at 10% p.a. both on simple interest. At the end of the year he received Rs. 890 as total interest. What was the amount he lent out at 8% pa.a?
(A) 5529
(B) 5500
(C) 5520
(D) 5521
(E) 5192
Rationale: Let the amount lent out at 8% p.a. be Rs. A
=> (A * 8)/100 + [(10000 - A) * 10]/100
= 890
=> A = Rs.5500.
Answer:B
Answer: (B) 5500
Question: A juice manufacturer organized taste-testing sessions featuring four brands of orange juice, A, B, C and D. All customers who participated told the organizer which variety they thought was the most similar to freshly-squeezed orange juice. 61% preferred brand A and exactly half as many preferred brand B. Only 45 chose brand C. Which of the following could be the number of customers who preferred brand D?
(A)  1
(B)  8
(C)  14
(D)  20
(E)  27
Rationale: I get D, but I'm not sure that my method is sound.
You have A + B + C + D = total testers. Stating the variety they think is most similar to freshly squeezed orange juice means each person should get 1 vote.
x = total number of testers
A + B + C + D
.61x + (.5)(.61x) + 65 + D = x
.61x + .305x + 65 + D = x
I took total testers = 1000 because that gives me nice numbers to deal with. Also, if I use 200 total testers, that gives me A = 122, B = 61, C = 65...that's over 200 without considering D.
x = 400
A = 244, B = 122, C = 65..also over 400
x = 600
A = 366, B = 183 C = 65....also over 600
x = 800
A = 488, B = 244, C = 65...D = 3...not an option on the list.
x = 1000
A = 610 B = 305 C = 65 D = 14....the first time I get an answer that is an option in the question.
C
Answer: (C)  14
Question: If John has earned 350 dollars by working 2 hrs/day a week at a constant daily rate for 5 weeks, which of the following represents his daily wage?
(A) 1
(B) 2
(C) 5
(D) 4
(E) 3
Rationale: John total earning = 350
No days he worked = 2 * 7 = 14
Rate = 5 week
Daily wage = total / (Rate * days)
= 350/(5*7*2)
= 5
C is correct answer...
Answer: (C) 5
Question: In an increasing sequence of 10 consecutive integers, the sum of the first 5 integers is 545. What is the sum of the last 5 integers in the sequence?
(A)  585
(B)  580
(C)  575
(D)  570
(E)  565
Rationale: All 5 integers are 5 numbers larger than in the first sum (eg. 1 becomes 6, 2 7...). 5*5=25+545=570
D
Answer: (D)  570
Question: In the xy-plane the point (-2 -3) is the centre of a circle, the point (-2, 3) lies inside the circle and the point (6,-3) lies outside the circle. If the radius r of the circle r is an integer then r=
(A) 6
(B) 5
(C) 4
(D) 7
(E) 2
Rationale: Can be solved without much calculations.
You are given that (-2,-3) is the center of the circle. Point (6,-3) lies inside the circle ---> the radius is lesser than distance of (-2,-3) from (6,-3) ---> lesser than 8 units but the radius will also be greater than the distance of (-2,-3) from (-2,3) ----> greater than 6 units.
Thus the radius is >6 but <8and as it is an integer, the only possible value of radius = 7 units.
D is the correct answer.
Answer: (D) 7
Question: If the sides of a triangle are 4 cm, 9 cm and 13 cm, what is its area?
(A) 18
(B) 20
(C) 22
(D) 26
(E) 28
Rationale: The triangle with sides 4 cm, 9 cm and 13 cm is right angled, where the hypotenuse is 13 cm.
Area of the triangle = 1/2 * 4 * 9 = 18 cm2
Answer: Option A
Answer: (A) 18
Question: A cube has five of its faces painted half red and half white. The other face is completely painted white. What is the ratio between the red painted areas and the white painted areas of the cube?
(A) 6:11
(B) 2:5
(C) 3:4
(D) 5:7
(E) 2:3
Rationale: Let x be the area of each face of the cube.
The area painted red is 5(x/2) = 5x/2
The area painted white is 5(x/2) + x = 7x/2x
The ratio of red to white is 5x/2:7x/2 which is 5:7.
The answer is D.
Answer: (D) 5:7
Question: The smallest value of n, for which n+2 is not a prime number, is
(A) 1,2
(B) 4,6
(C) 2,4
(D) 8,12
(E) 9,6
Rationale: (1 + 2) = 3.
(2 + 2) = 4.
(3 + 2) = 5.
(4 + 2) = 6.
which is not prime , n=2,4.
ANSWER:C
Answer: (C) 2,4
Question: The average age of 40 students in a class is 10years. If teacher's age is also included then average increases 1year then find the teacher's age?
(A) 59
(B) 55
(C) 61
(D) 51
(E) 36
Rationale: Total age of 50 students = 40*10 = 400
Total age of 51 persons = 41*11 = 451
Age of teacher = 451-400 = 51years
Answer is D
Answer: (D) 51
Question: Sequence Q consists of 16 consecutive integers. If -6 is the least integer in sequence Q, what is the range of the positive integers in sequence Q?
(A)  16
(B)  15
(C)  9
(D)  8
(E)  7
Rationale: Since set Q consists of 16 consecutive integers and -6 is the least integer then set Q is consecutive integers from -6 to 9, inclusive: 9-(-6)+1=16.
The range of positive integers in sequence Q is 9-1=8.
Answer: D.
Answer: (D)  8
Question: Robert is travelling on his cycle and has calculated to reach point A at 2 P.M. if he travels at 10 kmph, he will reach there at 12 noon if he travels at 15 kmph. At what speed must he travel to reach A at 1 P.M.?
(A) 8
(B) 12
(C) 11
(D) 16
(E) 18
Rationale: Explanation :
Let the distance travelled by x km.
Then,
=> (x/10) - (x/15) = 2
=> 3x - 2x =60
=> x = 60
=> Time taken to travel 60 km at 10 km/hr = 60/10 = 6 hours.
=> So, Robert started 6 hours before 2 P.M. i.e., at 8 A.M.
Therefore ,
Speed required = (60/5) km/hr
= 12 km/hr
Answer : B
Answer: (B) 12
Question: How many digits 2^400 has?
(A) 31
(B) 35
(C) 50
(D) 99
(E) 121
Rationale: 2^10 = 1.024 * 10^3 => 2^100 = (1.024)^10 * 10^120
therefore 121 digits would be my best guess
E
Answer: (E) 121
Question: The reciprocal of the hcf and lcm of two are 1/14 and 1/312 .if one of the number is 24 then other no. is
(A) 126
(B) 136
(C) 146
(D) 156
(E) 182
Rationale: reciprocal of the hcf and lcm of two are 1/14 and 1/312
so, HCF = 14 , LCM = 312
LCM * HCF = product of two numbers = a*b => b = LCM * HCF / a
so, other = 14*312 / 24 = 182
ANSWER:E
Answer: (E) 182
Question: On a test consisting of 30 questions. No. of wrong answers is 50% less than number of right answers. Each answer was either right or wrong. What is the ratio of right answers to wrong answers?
(A) 1 : 5
(B) 2 : 6
(C) 2 : 1
(D) 3 : 7
(E) 4 : 9
Rationale: Sol. Let the number of wrong answer - x and number of right answer = 30-x x = 50/100 of (30-x) x = 10
Required ratio = 20 : 10 = 2 : 1
C
Answer: (C) 2 : 1
Question: A does a work in 10 days and B does the same work in 15 days. In how many days they together will
do the same work ?
(A) 5 days
(B) 6 days
(C) 7 days
(D) 8 days
(E) None of these
Rationale: Explanation:
Firstly we will find 1 day work of both A and B, then by adding we can get collective days for them,
So,
A's 1 day work = 1/10
B's 1 day work = 1/15
(A+B)'s 1 day work =
(110+115)=(3+230)=16
So together they can complete work in 6 days.
Answer: B
Answer: (B) 6 days
Question: If xy not equal 0 and x^2*y^2 -xy =30, which of the following could be y in terms of x?
I. 1/2x
II. -6/x
III. 5/x
(A) I &II
(B) II
(C) II and III
(D) IV
(E) III
Rationale: x2y2 - xy = 30
x2y2-xy-30 = 0
(xy-5)(xy+6)=0
xy = 5 or xy=-6
y = 5/x or y = -6/x
II and III only
C
Answer: (C) II and III
Question: An amount at compound interest sums to Rs.17640/- in 2 years and to Rs.22932/- in 3 years at the same rate of interest. Find the rate percentage?
(A) 5%
(B) 7%
(C) 9%
(D) 11%
(E) 30%
Rationale: Explanation:
The difference of two successive amounts must be the simple interest in 1 year on the lower amount of money.
S.I = 22932/- - 17640/- = Rs. 5292/-
Rate of interest = (5292/22932) × (100/1) => 30%
Answer: Option E
Answer: (E) 30%
Question: A goods train runs at a speed of 72 kmph and crosses a 290 m long platform in 26 seconds.What is the length of the goods train?
(A) 230 m
(B) 240 m
(C) 260 m
(D) 270 m
(E) 250 m
Rationale: s=290+x/t
72*5/18=290+x/26
x=230
ANSWER:A
Answer: (A) 230 m
Question: How many numbers are there between 100 and 1000 such that at least one of their digits is 6?
(A) 648
(B) 252
(C) 900
(D) 1000
(E) None of these
Rationale: Explanation :
numbers between 100 and 1000:=900numbers between 100 and 1000 which do not have digit 6 in any place:=8×9×9=648Unit digit could take any value of the 9 values (0 to 9, except 6)Tens Digit could take any value of the 9 values (0 to 9, except 6)Hundreds digit could take any value of the 8 values (1 to 9, except 6)numbers between 100 and 1000 which have at least one digit as 6:=900−648= 252
Answer : B
Answer: (B) 252
Question: Nancy obtained 66, 75, 52, 68 and 89 marks (out of 100) in American Literature, History, Home Economics, Physical Education and Art. Calculate her average marks ?
(A) 50
(B) 80
(C) 70
(D) 60
(E) 71
Rationale: Explanation:
Average = (66 + 75 + 52 + 68 + 89 )/ 5 = 70.
Answer: C) 70
Answer: (C) 70
Question: The jogging track in a sports complex is 726 m in circumference. Suresh and his wife start from the same point and walk in opposite direction at 4.5 km/hr and 3.75 km/hr respectively. They will meet for the first time in:
(A) 5.5 min.
(B) 6 min.
(C) 4.9 min.
(D) 5.28 min.
(E) 5 min.
Rationale: Let both of them meet after T min
4500 m are covered by Suresh in 60 m.
In T min he will cover 4500T/60
Likewise, In T min Suresh's wife will cover 3750T/60
Given,
(4500T/60)+(3750T/60)=726
T = 5.28 minutes
Answer : D
Answer: (D) 5.28 min.
Question: Rs.100 amounts to Rs.320 in 4 years at simple interest. If the interest is increased by 3%, it would amount to how much?
(A) 246
(B) 650
(C) 110
(D) 240
(E) 360
Rationale: (100*4*3)/100=12
100+ 12 = 112
Answer: C
Answer: (C) 110
Question: A circular ground whose diameter is 40 metres, has a garden of area 1100m^2around it. What is the wide of the path of the garden ?
(A) 8.07
(B) 7.07
(C) 6.07
(D) 7.0
(E) 8.5
Rationale: Req. area = Ï€[(20)2 â€“ (r)2]
= 22â„7 Ã— (400- r^2)[since a2 - b2 = (a + b)(a - b)]
ie)22/7(400-r^2)=1100 , ie) r^2=50, r=7.07m
Answer B
Answer: (B) 7.07
Question: what is rate of interest if principal.amount be 400,simple interest 140 and time 2year.
(A) 10
(B) 17.5
(C) 25
(D) 12
(E) 14.5
Rationale: s.i=(p*r*t)/100
140=800r/100
r=140/8=17.5%
answer B
Answer: (B) 17.5
Question: A prize of $400 is to be distributed among 20 winners, each of whom must be awarded at least $20. If 2/5 of the prize will be distributed to 3/5 of the winners, what is the greatest possible individual award?
(A) $100
(B) $220
(C) $280
(D) $300
(E) $360
Rationale: Total value of the prize =$400
Number of people = 20
2/5 of 400 (=$160) should be distributed among 3/5 of 20 (=12 people ) with each getting $20 each. Remaining money = 400-160 = $240. Now in order to 'maximize' 1 prize, we need to minimise the others and we have been given that each should get $20. Thus, minimising the remaining 7 people (=20-12-1. '-1' to exclude 1 that needs to be maximised) = 7*20=140.
Thus the maximum award can be = 240-140 = $100, hence A is the correct answer.
Answer: (A) $100
Question: For an integer n greater than 1, n* denotes the product of all the integers from 1 to n inclusive. How many prime numbers are there between 6*+3 and 6*+6, inclusive ?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: Given that n* denotes the product of all the integers from 1 to n, inclusive so, 6* + 3 = 6! + 3 and 6* + 6 = 6! + 6.
Now, notice that we can factor out 3 our of 6! + 3 so it cannot be a prime number, we can factor out 4 our of 6! + 4 so it cannot be a prime number, ... The same way for all numbers between 6! + 3 and 6! +6, inclusive. Which means that there are no primes in this range.
Answer: A.
Answer: (A) 0
Question: Two trains, each 120 m long, moving in opposite directions, cross other in 8 sec. If one is moving twice as fast the other, then the speed of the faster train is?
(A) 72 km/hr
(B) 17 km/hr
(C) 60 km/hr
(D) 77 km/hr
(E) 46 km/hr
Rationale: Let the speed of the slower train be x m/sec.
Then, speed of the train = 2x m/sec.
Relative speed = ( x + 2x) = 3x m/sec.
(120 + 120)/8 = 3x => x = 10.
So, speed of the faster train = 20 = 20 * 18/5
= 72 km/hr.
Answer:A
Answer: (A) 72 km/hr
Question: Three unbiased coins are tossed, what is the probability of geƫng at least 2 tails ?
(A) 1/3
(B) 1/6
(C) 1/2
(D) 1/8
(E) None of these
Rationale: Explanation:
Total cases are = 2*2*2 = 8, which are as follows
[TTT, HHH, TTH, THT, HTT, THH, HTH, HHT]
Favoured cases are = [TTH, THT, HTT, TTT] = 4
So required probability = 4/8 = 1/2
Answer: C
Answer: (C) 1/2
Question: In a neighborhood having 90 households, 11 did not have either a car or a bike. If 20 households had a both a car and a bike and 44 had a car, how many had bike only?
(A) 30
(B) 35
(C) 20
(D) 18
(E) 10
Rationale: {Total}={Car}+{Bike}-{Both}+{Neither} --> 90=44+{Bike}-20+11 --> {Bike}=55 --> # those who have bike only is {Bike}-{Both}=55-20=35.
Answer: B.
Answer: (B) 35
Question: Find the sum of the local value and absolute value of 4 in 564823
(A) 4004
(B) 8000
(C) 16000
(D) 12000
(E) 18000
Rationale: Explanation:
Place value = Local value
Face value = Absolute value
The place value of 4 in 564823 is 4 x 1000 = 4000
The face value of 4 in 564823 is nothing but 4.
=> 4000 + 4 = 4004
Answer: Option A
Answer: (A) 4004
Question: A team scored a total of 140 points. If each player on the team scored at least 14 points, then what is the greatest possible number of players on the team?
(A) A)6
(B) B)7
(C) C)8
(D) D)9
(E) E)10
Rationale: 140/14=10 plus remainder.
The answer is E.
Answer: (E) E)10
Question: The length of the bridge, which a train 180 meters long and travelling at 48 km/hr can cross in 70 seconds, is:
(A) 245
(B) 276
(C) 987
(D) 168
(E) 1981
Rationale: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (130 + X)/30 = 25/2 ==> 2(130 + X) = 750 ==> X = 245 m.
Answer: A
Answer: (A) 245
Question: When positive integer m is divided by positive integer x, the reminder is 7 and when positive integer n is divided by positive integer y, the reminder is 11. Which of the following Q is a possible value for x + y?
I. 18
II. 19
III. 20
(A) I only
(B) II only
(C) Q=III only
(D) II and III only
(E) None
Rationale: TIP FOR SUCH QUESTIONS:Make Algebraic Equation in the beginning to understand how to proceed further. Then Start thinking the possible values of variables asked about
i.e.When positive integer m is divided by positive integer x, the reminder is 7can be understood as
m = ax +7which means thevalue of x must be greater than 7as the remainder 7 is possible only when the Divisor is bigger than the Remainder 7
i.e. Min Value of x = 8
AND
i.e.When positive integer n is divided by positive integer y, the reminder is 11can be understood as
n = by +11which means thevalue of y must be greater than 11as the remainder 11 is possible only when the Divisor is bigger than the Remainder 11
i.e. Min Value of y = 12
i.e. Minimum Value of x+y = 8+12 = 20
Hence III only can be True
Answer: Option
C
Answer: (C) Q=III only
Question: Two heavily loaded sixteen-wheeler transport trucks are 1025 kilometers apart, sitting at two rest stops on opposite sides of the same highway. Driver A begins heading down the highway driving at an average speed of 90 kilometers per hour. Exactly one hour later, Driver B starts down the highway toward Driver A, maintaining an average speed of 80 kilometers per hour. How many kilometers farther than Driver B, will Driver A have driven when they meet and pass each other on the highway?
(A) 90
(B) 130
(C) 150
(D) 320
(E) 145
Rationale: I've been reading the website for a while and I'm always keen to see different approaches so I would like to share one that works for me:
Short version:
Truck A travels for an hour.
Distance remaining = 1025-90 = 935k
Ratio of speeds 9:8 -> 935/17 = 55
Truck A = 90 + 55*9 = 585
Truck B = 55*8 = 440
Delta = 145km
Answer E
Answer: (E) 145
Question: If x < 0 and 0 < y < 1, which of the following has the greatest value L?
(A) x^2
(B) (xy)^2
(C) (x/y)^2
(D) x^2/y
(E) x^2*y
Rationale: Given, x < 0 and 0 < y < 1
Let, x = -2 and y = 1/2
A. x^2 = (-2)^2 =4
B. (xy)^2 = (-2*1/2)^2 =1
C. (x/y)^2 = {-2/(1/2)}^2 = (-4)^2 =16
D. x^2/y = (-2)^2 / (1/2) = 4*2 =8
E. x^2*y = (-2)^2*(1/2) =2
Answer: option C
Answer: (C) (x/y)^2
Question: The current birth rate per thousand is 52, where as corresponding death rate is 11 per thousand. The net growth rate in terms of population increase in percent is given by?
(A) 4.1%
(B) 3.2%
(C) 3.9%
(D) 4%
(E) 5.1%
Rationale: Net growth on 1000 = 52-11 = 41
Net growth on 100 = 41*100/1000 = 4.1%
Answer is A
Answer: (A) 4.1%
Question: Huey's Hip Pizza sells two sizes of square pizzas: a small pizza that measures 9 inches on a side and costs $10, and a large pizza that measures 14 inches on a side and costs $20. If two friends go to Huey's with $30 apiece, how many more square inches of pizza can they buy if they pool their money than if they each purchase pizza alone?
(A) 5 square inches
(B) 10 square inches
(C) 15 square inches
(D) 25 square inches
(E) 34 square inches
Rationale: In the first case each can buy one pizza of $10 and one pizza of $20.
In square inches that would be (9*9=81) for the small pizza and (14*14=196) for the large pizza. In total sq inches that would be (81+196)*2= 554 sq inches.
In the second case if they pool their money together they can buy 3 large pizzas. In terms of square inches that would be 3*196= 588 sq inches.
Hence, the difference is 34 square inches more (588-554).
The correct answer is E
Answer: (E) 34 square inches
Question: There are 6 girls and 6 boys. If they are to be seated in a row, what is the probability that no two boys sit together?
(A) A)2*6!6!/12!
(B) B)6!5!/12!
(C) C)6!6!/12!
(D) D)6!/12!
(E) E)6!7!/12!
Rationale: If girls are alternate, then only no 2 boys can be together.
So among 12 places, boys can be seated in 6 alternate places in 6! ways.
And girls can be seated in the remaining 6 places in 6! ways.
Therefore total number of ways = 6! * 6!
But there could be 2 such arrangements-->
1. When first place is filled by a girl
2. When first place is filled by a boy
Therefore total number of ways = 2*6! * 6!
Also total number of ways to fill 12 places = 12!
Hence probability =2∗6!6!/12!
Answer:A
Answer: (A) A)2*6!6!/12!
Question: A fill pipe can fill 1/4 of cistern in 16 minutes. In how many minutes, it can fill 3/4 of the cistern?
(A) 24min
(B) 30min
(C) 48min
(D) 26min
(E) 16min
Rationale: Required time = 16*4*3/4 = 48 minutes
Answer is C
Answer: (C) 48min
Question: Find the area of the quadrilateral of one of its diagonals is 20 cm and its off sets 9 cm and 6 cm?
(A) 188 cm2
(B) 150 cm2
(C) 168 cm2
(D) 198 cm2
(E) 987 cm2
Rationale: 1/2 * 20(9 + 6)
= 150 cm2
Answer: B
Answer: (B) 150 cm2
Question: Arun purchased 30 kg of wheat at the rate of Rs. 11.50 per kg and 20 kg of wheat at the rate of 14.25 per kg. He mixed the two and sold the mixture. Approximately what price per kg should be sell the mixture to make 30% profit?
(A) 66.3
(B) 76.3
(C) 86.3
(D) 16.3
(E) 36.3
Rationale: Explanation:
C.P. of 50 kg wheat = (30 * 11.50 + 20 * 14.25) = Rs. 630.
S.P. of 50 kg wheat = 130% of Rs. 630 = 130/100 * 630 = Rs. 819.
S.P. per kg = 819/50 = Rs. 16.38 = 16.30.
Answer: D
Answer: (D) 16.3
Question: Calculate the HCF of 16, 108, 220
(A) 3
(B) 5
(C) 4
(D) 1
(E) 2
Rationale: Explanation:
Lets solve this question by factorization method.
The factors of 16 are: 1, 2, 4, 8, 16
The factors of 108 are: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
The factors of 220 are: 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110, 220
Then the greatest common factor is 4.
Answer: Option C
Answer: (C) 4
Question: Each of the 39 points is placed either inside or on the surface of a perfect sphere. If 72% or fewer of the points touch the surface, what is the maximum number of segments which, if connected from those points to form chords, could be the diameter of the sphere?
(A) 7
(B) 11
(C) 13
(D) 14
(E) 38
Rationale: Maximum number of points on the surface is 72%*39 = 28.08 ... or 28 since it has to be an integer
Now note that if two points form a diameter, they cannot be part of any other diameter.
So in the best case we can pair up the points
We have 28 points, so at best we can form 14 pairs (28).
So, answer is (D)
Answer: (D) 14
Question: Sum of the digits number is 8 and their product is 12. Find the difference between the digits?
(A) 4
(B) 5
(C) 3
(D) 7
(E) 2
Rationale: Explanation:
x + y = 8
xy = 12
(x â€“ y)2 = (x + y)2 â€“ 4xy
(x â€“ y)2 = 64 â€“ 48 => (x â€“ y) = 4
Answer:A
Answer: (A) 4