mathewhe/aqua_rat huggingface dataset:
Question: In 1937, the ship of the great sailor SINBAD left an Egyptian port heading Ivory coast at E mile/month .
One month later another ship of the greatest pirate ever CHENG I SAO was 5000 miles due south of the same Egyptian port and heading due north at Y miles/month. Six months later after the leaving of Sinbad’s ship from Egyptian port, how far apart were the ships? [Ivory coast is in the west of Egypt]
(A) { (6E)^2 + (5000-5y)^2 }^1/2
(B) { (36x)^2 + (5000-7y)^2 }^1/2
(C) { (16x)^2 + (5000-7y)^2 }^1/2
(D) { (7x)^2 + (5200-7y)^2 }^1/2
(E) { (2x)^2 + (300-7y)^2 }^1/2
Rationale: The chinese ship sailed for 5 months i.e. 5Y miles @Y miles/month, therefore distance from Egyptian port is 5000-5Y. Since A is the only option with this value ...therefore A is the answer
Answer: (A) { (6E)^2 + (5000-5y)^2 }^1/2
Question: 3889 + 12.808 - ? = 3854.002
(A) A)47.095
(B) B)47.752
(C) C)47.806
(D) D)47.95
(E) of the above
Rationale: Let 3889 + 12.808 - x = 3854.002.
Then x = (3889 + 12.808) - 3854.002
= 3901.808 - 3854.002
= 47.806.
Answer = C
Answer: (C) C)47.806
Question: What is the units' digit of the following expression (13)^5*(19)^5*(17)^5?
(A) 0
(B) 1
(C) 3
(D) 5
(E) 9
Rationale: We do not have to do any calculations or find units digit of remaining numbers...
all three terms - 13,19,17 - are ODD and since the PRODUCT contains 9, the units digit of the product will remain 9
E
Answer: (E) 9
Question: Nitin ranks 24th in a class of 58 students. What is rank from the last ?
(A) 33
(B) 34
(C) 32
(D) 28
(E) 19
Rationale: Explanation:
Number students behind the nitin in rank = (58 - 24) = 34
Nitin is 34nd from the last
Answer: B) 34
Answer: (B) 34
Question: The captain of a cricket team of 11 members is 24 years old and the wicket keeper is 7 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?
(A) 21
(B) 22
(C) 23
(D) 24
(E) 25
Rationale: Let the average age of the whole team be x years.
11x - (24 + 31) = 9 (x - 1)
11x - 9x = 46
2x = 46
x = 23.
The average age of the team is 23 years.
The answer is C.
Answer: (C) 23
Question: Train A and Train B began traveling towards each other from opposite ends of a 540-mile long track at 1:00 PM. If Train A traveled at 35 miles per hour and Train B traveled at 25 miles per hour, at what time did the trains meet?
(A) 5:40 PM
(B) 10:00 PM
(C) 7:20 PM
(D) 8:00 PM
(E) 9:20 PM
Rationale: This question tests your concepts of relative speed:
If two trains are moving in opposite direction, then distance will reduce at a rate of (Speed of 1 + Speed of 2)
If two trains are moving in same direction, then distance will reduce at a rate of (Speed of 1 - Speed of 2)
Here the trains are moving towards each other, hence in opposite direction.
Trains will cover the 500 mile track in a time of 500/(25 + 35) = 540/60 = 9 hours
Trains started at 1:00 PM, there they will meet at 10:00 PM
Option B
Answer: (B) 10:00 PM
Question: If n and k are integers whose product is 1600, which of the following statements must be true?
(A) n+k>0
(B) n does not equal k
(C) Either n or k is a multiple of 10
(D) If n is even, then k is odd
(E) If n is odd, then k is even
Rationale: If n is odd and k is odd, then the product is odd.
The answer is E.
Answer: (E) If n is odd, then k is even
Question: In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the rate in the remaining 40 overs to reach the target of 272 runs?
(A) 6.25
(B) 6.22
(C) 6.29
(D) 6.39
(E) 6.0
Rationale: Required run rate
= [272 - (3.2 * 10)]/40
= 240/40
= 6.00
Answer: E
Answer: (E) 6.0
Question: Think of a number, divide it by 5 and add 10 to it. The result is 21. What is the number thought of?
(A) 24
(B) 55
(C) 297
(D) 267
(E) 29
Rationale: Explanation :
21-10 = 11
11 x 5 = 55
Answer : B
Answer: (B) 55
Question: Ajay and Sasi start walking towards each other at 6am at speed of 4kmph and 5kmph. They were initially 20km apart. At what time do they meet?
(A) 6am
(B) 8am
(C) 10am
(D) 9am
(E) 12pm
Rationale: Time of meeting = distance / relative speed = 20/6+4 = 20/10 = 2 hrs after 6am = 8am
Answer is B
Answer: (B) 8am
Question: A bought 100kg of rice for Rs 1100 and sold it at a loss of as much money as he received for 2o kg of rice. At what price did he sell the rice?
(A) 800
(B) 880
(C) 900
(D) 920
(E) 940
Rationale: 100Kg of rice for 1100/-
then 1kg rice cost must be 1100/100=11
then 20kg rice cost is 20*11=220/---------------->this is loss
1100-220=880
then sell price=880
ANSWER:B
Answer: (B) 880
Question: March 11, 2003 is a Tuesday. What will be the day on which march 11 2004 comes??
(A) Thursday
(B) wednesday
(C) friday
(D) sunday
(E) monday
Rationale: 2004 is a leap year that means 29 days in feb.
so march 11,2003 to march 11, 2004 will be 366 days.
366/7=52 weeks + 2 days. Hence Thursday
ANSWER:A
Answer: (A) Thursday
Question: If two sides of a triangle are 3 and 12, respectively, which of the following could NOT be the area of this triangle?
(A) 1
(B) 6
(C) 17
(D) 29
(E) 16
Rationale: For this question it would be helpful to know the largest area that this triangle could be, given the two sides of 3 and 12.
We know that the area of a triangle will be maximized when two sides are perpendicular to each other (consult Bunuel's drawing above). Thus we have a max area being equal to one half the base times the height, either (.5)12 * 3 -or- (.5)3 * 12 will result in a maximum area of 18 for the triangle; therefore, the triangle could never have an area of 29.
D
Answer: (D) 29
Question: The measure of the side of a square is doubled. If x represents the perimeter of the original square, what is the value of the new perimeter?
(A) 2x
(B) 4x
(C) 9x
(D) 12x
(E) 27x
Rationale: Original perimeter = x
Hence original side = x/4
New side = 2x/4
New perimeter = 4*2x/4 = 2x
Correct Option: A
Answer: (A) 2x
Question: 3 pig’s and 10 goats are brought for Rs.1100. If the average price of a goat be Rs.50. What is the average price of a pig.
(A) 275
(B) 300
(C) 200
(D) 250
(E) 225
Rationale: Explanation:
Average price of a goat = Rs.50
total price of 10 goats = 10*50 = Rs.500
But total price of 3 pigs and 10 goats = Rs. 1100
Total price of 3 pigs is = 1100 - 500
= 600
Average price of a pig = 600/3
= Rs. 200
Answer: C
Answer: (C) 200
Question: If a man buys 10 lollipops for $80 and sold them for $3 dollars determine his loss.
(A) 50
(B) 60
(C) 70
(D) 80
(E) 90
Rationale: Cost of 10 lollipops = $80
Sold each lollipop for $3
So he sold 10 lollipops for $(10 × 3) = $30
Loss = $(80 – 30) = $50
answer :A
Therefore, loss = $ 50.
Answer: (A) 50
Question: 12.1212+17.0005 - 9.1104 = ?
(A) 20.0015
(B) 20.0105
(C) 20.0113
(D) 20.1015
(E) None
Rationale: Solution
Given expression
=(12.1212+17.0005)-9.1104
= (29.1217 - 9.1104)
=20.0113.
Answer C
Answer: (C) 20.0113
Question: A thief goes away with a SANTRO car at a speed of 50 kmph. The theft has been discovered after half an hour and the owner sets off in a bike at 60 kmph when will the owner over take the thief from the start?
(A) A)2
(B) B)5
(C) C)7
(D) D)5
(E) E)8
Rationale: Explanation:
|-----------20--------------------|
60 50
D = 20
RS = 60 – 50 = 10
T = 20/10 = 2 hours
Answer: Option A
Answer: (A) A)2
Question: If you roll a fair-sided die twice, what is the probability of getting 1 ,1 ?
(A) 1/3!
(B) 1/36
(C) 1/18
(D) 1/24
(E) 1/12
Rationale: total no. in two dice (1,1) ,(2,2) .....(6,)
Total number of events= 6*6
Total events of getting same pair(1, 1) = 6
Probability= 6/6*6= 1/6=1/3!
A
Answer: (A) 1/3!
Question: A cone of height 9 cm with diameter of its base 18 cm is carved out from a wooden solid sphere of radius 9 cm. The percentage of the wood wasted is :
(A) 45%
(B) 56%
(C) 67%
(D) 75%
(E) None of these
Rationale: Explanation:
We will first subtract the cone volume from wood volume to get the wood wasted.
Then we can calculate its percentage.
Sphere Volume =4/3πr3
Cone Volume =1/3πr2h
Volume of wood wasted =(4/3π∗9∗9∗9)−(1/3π∗9∗9∗9)=π∗9∗9∗9cm3
Required Percentage =π∗9∗9∗9 /4/3π∗9∗9∗9∗100%=3/4∗100%=75%
Option D
Answer: (D) 75%
Question: The length of the bridge, which a train 130 metres long and travelling at 108 km/hr can cross in 30 seconds, is:
(A) 200 m
(B) 225 m
(C) 245 m
(D) 170 m
(E) 240 m
Rationale: Speed = [108 X 5/18] m/sec = 30 m/sec
Time = 10 sec
Let the length of bridge be x metres.
Then, (130 + x)/30 = 10 => 130 + x = 300 => x = 170 m.
ANSWER:D
Answer: (D) 170 m
Question: The speed of a car is 90 km in the first hour and 50 km in the second hour. What is the average speed of the car?
(A) 70
(B) 75
(C) 88
(D) 54
(E) 15
Rationale: S = (90 + 50)/2
= 70 kmph
Answer: A
Answer: (A) 70
Question: A man can row upstream at 26 kmph and downstream at 30 kmph, and then find the speed of the man in still water?
(A) 29
(B) 28
(C) 30
(D) 32
(E) 23
Rationale: US = 26
DS = 30
M = (30 + 26)/2 = 28
Answer:B
Answer: (B) 28
Question: A train 520 meters long is running with a speed of 52 kmph. The time taken by it to cross a tunnel 160 meters long is?
(A) 287 sec
(B) 288 sec
(C) 47 sec
(D) 16 sec
(E) 17 sec
Rationale: D = 520 + 160 = 680
S = 52 * 5/18 = 14.4 mps
T = 680/14.4 = 47 sec
Answer: C
Answer: (C) 47 sec
Question: If Rs. 782 be divided into three parts, proportional to 1/2:2/3:3/4, then the second part is?
(A) A)426
(B) B)526
(C) C)207
(D) D)204
(E) E)272
Rationale: Given ratio
= 1/2:2/3:3/4 = 6:8:9
1st part = 782 * 8/23
= Rs. 272
Answer:E
Answer: (E) E)272
Question: A jogger running at 9 km/hr along side a railway track is 240 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?
(A) 33
(B) 299
(C) 36
(D) 88
(E) 21
Rationale: Speed of train relative to jogger = 45 - 9 = 36 km/hr.
= 36 * 5/18 = 10 m/sec.
Distance to be covered = 240 + 120 = 360 m.
Time taken = 360/10 = 36 sec.
Answer:C
Answer: (C) 36
Question: A number when divided by 221 gives a remainder 43, what remainder will be obtained by dividing the same number 17?
(A) 9
(B) 11
(C) 15
(D) 5
(E) 20
Rationale: 221 + 43 = 264/17 = 9
ANSWER A
Answer: (A) 9
Question: what is the next number of following series
1,5,5,3,10,10,5,6,...
(A) 11
(B) 12
(C) 13
(D) 14
(E) 15
Rationale: 1^2=1
1+2^2=5
5+3^2=14=>1+4=5
14+4^2=30=>3+0=3
30+5^2=55=>5+5=10
55+36=>91=>9+1=10
91+49=140=>5
14)+64=204=6
so
204+81=285=>15
ANSWER:E
Answer: (E) 15
Question: The total cost of a vacation was divided among 3 people. If the total cost of the vacation had been divided equally among 4 people, the cost per person would have been $60 less. What was the total cost cost of the vacation?
(A) $200
(B) $300
(C) $400
(D) $720
(E) $600
Rationale: C for cost.
P price per person.
C= 3*P
C=4*P-240
Substituting the value of P from the first equation onto the second we get P = 240.
Plugging in the value of P in the first equation, we get C= 720. Which leads us to answer choice D
Answer: (D) $720
Question: Out of first 20 natural numbers, one number is selected at random. The probability that it is either an even number or a prime number is?
(A) 17/26
(B) 17/21
(C) 17/92
(D) 17/20
(E) 17/18
Rationale: n(S) = 20
n(Even no) = 10 = n(E)
n(Prime no) = 8 = n(P)
P(EᴜP) = 10/20 + 8/20 - 1/20
= 17/20
Answer:D
Answer: (D) 17/20
Question: The average (arithmetic mean) of 20, 40, and 60 is 4 more than the average of 10, 70, and what number?
(A) 28
(B) 25
(C) 35
(D) 45
(E) 55
Rationale: a1 = 120/3 = 40
a2 = a1 -4 = 36
sum of second list = 36*3 = 108
therefore the number = 108 -80 = 28
ANSWER:A
Answer: (A) 28
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. 3200. They completed the work in 3 days with the help of C. How much is to be paid to C?
(A) Rs. 380
(B) Rs. 600
(C) Rs. 420
(D) Rs. 400
(E) Rs. 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 = 3200 × (1/8) = 400
Answer : Option D
Answer: (D) Rs. 400
Question: Boy sells a book for Rs. 720 he gets a loss of 10 %, To gain 10%, what should be the SP?
(A) 430
(B) 880
(C) 550
(D) 590
(E) 600
Rationale: Cost price = 720/90 x 100 = 800
To gain 10% = 800 x 10/100 = 80
SP = CP + gain = 800 + 80 = 880
Answer : B
Answer: (B) 880
Question: What Least number should be added to 1056,so that the sum is completely divisible by 23?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: That is 1056/23=45
Remainder=21
=>21+2=23
Hence 2 should be added to 1056 so that the sum will be divisible by 23
Answer is option B
Answer: (B) 2
Question: Pipe A fills a tank of capacity 900 liters at the rate of 40 liters a minute. Another pipe B fills the same tank at the rate of 30 liters a minute. A pipe at the bottom of the tank drains the tank at the rate of 20 liters a minute. If pipe A is kept open for a minute and then closed and pipe B is open for a minute and then closed and then pipe C is open for a minute and then closed and the cycle is repeated, when will the tank be full?
(A) 42 minutes
(B) 14 minutes
(C) 54 minutes
(D) 40 minutes 20 seconds
(E) None of these
Rationale: In one cycle they fill 40+30-20 = 50 liters
900 = 50*n => n = 18
here n = number of cycles.
total time = 18*3 = 54 as in one cycle there are 3 minutes.
thus 54 minutes
ANSWER:C
Answer: (C) 54 minutes
Question: For any positive x, y and z if x is n% of y and z is m% of y then what percentage W must x be of z?
(A) (n/m)%
(B) (m × n)%
(C) (100 / [m × n]) %
(D) (100 × m/n)%
(E) (100 × n/m)%
Rationale: x is n% of y MEANS x= (n/100 )* y------------------------eq1
z is m% of y MEANS z= (m/100 )* y------------------------eq2
Find equation of xz
substitute value of y from 2nd equation into Ist equation
so x= (n/100)*(100z/m)
so x= (n/m)z
or x= (100n/m)z/100
so answer W is 100n/m %.E
Answer: (E) (100 × n/m)%
Question: If a*b*c=195, b*c*d = 65, c*d*e=1000 and d*e*f=250 the (a*f)/(c*d) = ?
(A) 1/2
(B) 1/4
(C) 3/4
(D) 2/3
(E) None of these
Rationale: Explanation :
aâˆ—bâˆ—c/bâˆ—câˆ—d= 195/65 => a/d = 3
dâˆ—eâˆ—f/câˆ—dâˆ—e= 250/1000 => f/c = 1/4
a/d* f/c = 3 * 1/4 = 3/4
Answer : C
Answer: (C) 3/4
Question: A retailer bought a machine at a wholesale price of $80 and later on sold it after a 20% discount of the retail price. If the retailer made a profit equivalent to 20% of the wholesale price, what is the retail price of the machine?
(A) $80
(B) $100
(C) $120
(D) 135
(E) 160
Rationale: The price after the discount was 1.2*80 = $96
Let x be the retail price.
0.8x = $96
x = 96/0.8 = $120
The answer is C.
Answer: (C) $120
Question: A, B, C subscribe Rs. 50,000 for a business. If A subscribes Rs. 4000 more than B and B Rs. 5000 more than C, out of a total profit of Rs. 35,000, what will be the amount A receives?
(A) 14700
(B) 14500
(C) 14900
(D) 14300
(E) 14000
Rationale: Total amount invested = 50000
Assume that investment of C =x.
Then investment of B =5000+x,
Investment of A =4000+5000+x=9000+x
x+5000+x+9000+x=50000
⇒3x+14000=50000
⇒3x=50000–14000=36000
⇒x=36000/3=12000
Investment of C =x=12000
Investment of B =5000+x=17000
Investment of A =9000+x=21000
Ratio of the investment of A, B and C
=21000:17000:12000
=21:17:12
Share of A = Total profit ×21/50
=35000×21/50=700×21=14700
Answer is A.
Answer: (A) 14700
Question: Find the differece between largest and smallest number formerd by the digits 0,1,2,3,5
(A) 41375
(B) 42975
(C) 42775
(D) 43565
(E) 43589
Rationale: Explanation:
53210
01235
---------
41975
Answer: Option B
Answer: (B) 42975
Question: A corporation paid $8 million in federal taxes on its first $50 million of gross profits and then $30 million in federal taxes on the next $150 million in gross profits. By approximately what percent did the ratio of federal taxes to gross profits increase from the first $50 million in profits to the next $150 million in profits?
(A)  6%
(B)  14%
(C)  20%
(D)  23%
(E)  86%
Rationale: Difference in Ratios = (30/150) - (8/50) = (6/50)
% Change = (Change (6/50) / Original ratio (7/50)) *100 = 86%
Answer - E
Answer: (E)  86%
Question: A man can row with a speed of 10 kmph in still water. If the stream flows at 55 kmph, then the speed in downstream is?
(A) 29
(B) 65
(C) 20
(D) 27
(E) 121
Rationale: M = 10
S = 55
DS = 10 + 55 = 65
Answer: B
Answer: (B) 65
Question: The number of real roots of the equation A2/x + B2/(x-1) = 1, where A and B are real numbers not equal to zero simultaneously is
(A) None
(B) 1
(C) 2
(D) 1 or 2
(E) 3
Rationale: Explanation :
=> A2/x + B2/(x-1) = 1,
=> A2 (x-1) + B2x = x2 - x.
This is a quadratic equation.
Hence, number of roots = 2 or 1 (1 in the case when both roots are equal )
Answer : A
Answer: (A) None
Question: (?) - 19657 - 33994 = 9999
(A) 63650
(B) 63656
(C) 63678
(D) 63628
(E) 63710
Rationale: A
63650
19657+33994=53651
Let x - 53651 = 9999
Then, x = 9999 + 53651 = 63650
Answer: (A) 63650
Question: It costs $4 for the first 1/4 hour to use the laundry machine at the Laundromat. After the first ¼ hour it costs $12 per hour. If a certain customer uses the laundry machine for 3 hours and 25 minutes, how much will it cost him?
(A) $25
(B) $32
(C) $36
(D) $40.
(E) $42.
Rationale: 3 hrs 25 min = 205 min
First 15 min ------> $4
Time left is 190 min...
Now, 60 min costs $ 12
1 min costs $ 12/60
190 min costs $ 12/60*190 => $ 38
So, Total cost will be $38 + $4 => $ 42
Hene answer will be (E) $ 42
Answer: (E) $42.
Question: A student chose a number, multiplied it by 8, then subtracted 138 from the result and got 102. What was the number he chose?
(A) 30
(B) 120
(C) 130
(D) 140
(E) 150
Rationale: Solution:
Let xx be the number he chose, then
8⋅x−138=102
8x=240
x=30
Answer A
Answer: (A) 30
Question: Two trains 120 meters and 165 meters in length respectively are running in opposite directions, one at the rate of 80 km and the other at the rate of 65 kmph. In what time will they be completely clear of each other from the moment they meet?
(A) 7.16
(B) 7.16
(C) 7.07
(D) 7.15
(E) 7.11
Rationale: T = (120 + 165)/ (80 + 65) * 18/5
T = 7.07
Answer: C
Answer: (C) 7.07
Question: How many figures are required to number the pages the pages of a book containing 1210 pages?
(A) 3533
(B) 3833
(C) 3333
(D) 3633
(E) 3733
Rationale: 1 to 9 = 9 * 1 = 9
10 to 99 = 90 * 2 = 180
100 to 999 = 900 * 3 = 2700
1000 to 1210 = 211 * 4 =844
-----------
3733
ANSWER:E
Answer: (E) 3733
Question: Eleven years ago Tina was half as old as Ike will be in 4 years. If Ike is m years old now, how old is Tina now, in terms of m?
(A) 4m - 11
(B) m/2 + 13
(C) 1/(2m - 22)
(D) (4m + 11)/2
(E) 2m-7
Rationale: Ike's current age = m
Ike's age after 4 years = m + 4
Tina age 11 years ago =(m+4)/2
Tina's current age = (m+4)/2 + 11 = (m+4+22)/2= m/2+13
Ans B
Answer: (B) m/2 + 13
Question: If x and y are integers and x + y = 4, which of the following must be true?
(A) x and y are consecutive integers.
(B) Both x and y are even.
(C) If x > 0, then y < 0.
(D) If x < 0, then y > 0.
(E) Both x and y are less than 5.
Rationale: In option C if x > 0,then y<0 means x is +ve and y is -ve
In option B if x < 0, then y>0 means y is +ve and x is -ve, both are same and satisfying x+y = 5.
How option D is right could you explain
Answer: (D) If x < 0, then y > 0.
Question: A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 38 years now, the son's age five years back was:
(A) 14
(B) 67
(C) 56
(D) 89
(E) 34
Rationale: Let the son's present age be x years. Then, (38 - x) = x
2x = 38.
x = 19.
Son's age 5 years back (19 - 5) = 14 years.
Answer:A
Answer: (A) 14
Question: Of all the homes on Gotham Street, 1/3 are termite-ridden, and 7/10 of these are collapsing. What fraction of the homes are termite-ridden, but NOT collapsing?
(A) 1/4
(B) 1/6
(C) 1/8
(D) 1/9
(E) 1/10
Rationale: The fraction of homes which are termite-infested but not collapsing is 3/10*1/3 = 1/10
The answer is E.
Answer: (E) 1/10
Question: According to the direction on a can of frozen orange juice concentrate is to be mixed with 3 cans of water to make orange juice . How many 5 - ounce cans of the concentrate are required to prepare 200 6-ounce servings of orange juice?
(A) 25
(B) 34
(C) 50
(D) 60
(E) 100
Rationale: Orange juice concentrate: water::1:3
total quantity of orange juice = 200*6 = 1200 oz
so Orange juice concentrate: water :: 300 oz:900 oz
no. of 5 oz can = 300 oz/5 oz = 60
Answer D, 60 cans
Answer: (D) 60
Question: A and B are two circles. The radius of A is four times as large as the diameter of B. What is the ratio between the areas of the circles?
(A) 1:8.
(B) 1:2.
(C) 1:24.
(D) 1:64.
(E) 1:6.
Rationale: Given : The radius of A is 4 times as large as the diameter of B. => R(a) = 4*D(b) = 4*2*R(b) = 8R(b). The radius are in ratio of 1:8 thus the area will be in the ratio of square of radius. 1:64. Hence D.
Answer: (D) 1:64.
Question: In State X, all vehicle license plates have 3 letters from the 26 letters of the alphabet followed by 2 one digit numbers. How many different license plates can State X have if repetition of letters and numbers is allowed?
(A) 23,400
(B) 60,840
(C) 67,600
(D) 608,400
(E) 1,757,600
Rationale: The choices give us the answer without any calculations--
2 one digits places can take 10*10 ways..
3 letter places can be filled up in 26 * 26 *26 ways
ans= 26*26*26*10*10=1757600
ans E
Answer: (E) 1,757,600
Question: A computer is programmed to multiply consecutive even integers 2*4*6*8*…*n until the product is divisible by 1947, What is the value of n?
(A) 22
(B) 38
(C) 62
(D) 122
(E) 118
Rationale: Factorise 1947.. 3*11*59..
So n has to be a multiple of largest prime number,61..
So n=2*59=118..
Ans :E
Answer: (E) 118
Question: In a certain game, you pick a card from a standard deck of 52 cards. If the card is a clever, you win. If the card is not a clever, the person replaces the card to the deck, reshuffles, and draws again. The person keeps repeating that process until he picks a clever, and the point is to measure how many draws did it take before the person picked a clever and won. What is the probability that there will be at least three draws involved in a win, i.e. someone picking her clever on the third draw or later?
(A)  11/16
(B)  9/16
(C)  14/16
(D)  13/16
(E)  15/16
Rationale: Probability of picking a heart on any draw = 1/4
Probability of NOT picking a heart on the first draw AND on the second draw = [1-(1/4)] X [1-(1/4)] = 3/4 X 3/4 = 9/16
Answer : A
Answer: (A)  11/16
Question: A can complete a work in 10days and B can do the same work in 5days. If A after doing 2days, leaves the work, find in how many days B will do the remaining work?
(A) 2days
(B) 4days
(C) 6days
(D) 7days
(E) 10days
Rationale: The required answer = (10-2)*5 / 10 = 40/10 = 4days
Answer is B
Answer: (B) 4days
Question: The length of a room is 5.5 m and width is 3.75 m. What is the cost of paying the floor by slabs at the rate of Rs.800 per sq. metre.
(A) 16200
(B) 16350
(C) 16500
(D) 16750
(E) 16250
Rationale: Area =5.5×3.75 sq. metre.
Cost for 1 sq. metre. = Rs.800
Hence, total cost
=5.5×3.75×800=5.5×3000= Rs.16500
Answer is C.
Answer: (C) 16500
Question: A bag contains nine white and four red balls. Two balls are picked at random from the bag. What is the probability that they both are different color?
(A) 5/8
(B) 6/13
(C) 5/16
(D) 5/13
(E) 5/11
Rationale: Two balls can be picked from thirteen balls in 13Câ‚‚ ways.
We select one white ball and one red ball from five white balls and four red balls. This can be done âµ ways.
The required probability = (9 * 4) = 36/78 = 6/13
Answer: B
Answer: (B) 6/13
Question: when W is divided by 13, the reminder is 0. if W is one lesser than it value and when divided by 5 its remainder is 0. what is the value of W ?
(A) 13
(B) 25
(C) 26
(D) 52
(E) 65
Rationale: W is divided by 13 so that is multiple of 14 as 13,26,39...
W-1 is divided by 5 the remainder is 0 so it is divisible by 5. Consider from option let us take the number is 13 it is divisible by 13 but 13-1 is not divisible by 5 so it is not answers so let us take 2nd option 25 which is not divisible by 13 in 3rd option 26 is divisible by 13 and 26-1 is divisible by 5 so ans is C
Answer: (C) 26