mathewhe/aqua_rat huggingface dataset:
Question: If r is a positive integer and 10^r – 74 in decimal notation has digits whose sum is 440, what is the value of r?
(A) 40
(B) 44
(C) 45
(D) 46
(E) 50
Rationale: Answer E = 50
We have (10^r)-74, where the sum of the digits is 440.
100-74 = 26, so we already have 2+6 = 8 from the 440.
Because we have a power of 10, we will have numbers like 100, 1000, 10000 and so on. This minus 74 rests 26 and a lot of 9s. E.g: 1000-74 = 9926.
So dividing the 432/9 = 48, that`s the number of 9s. and we have 2 other numbers (2 and 6) wich were 00 before the subtraction.
So we have 48 + 2 as an r = 50
Answer: (E) 50
Question: Find the odd man out
2, 4, 8, 16, 48, 64
(A) 48
(B) 8
(C) 16
(D) 4
(E) 2
Rationale: 2*2 = 4
4*2 =8
8*2=16
16*2=32
32*2=64
ANSWER:A
Answer: (A) 48
Question: Pipes A and B can fill a tank in 4 and 8 hours respectively. Pipe C can empty it in 16 hours. If all the three pipes are opened together, then the tank will be filled in?
(A) 3 9/97 hrs
(B) 3 1/5 hrs
(C) 3 9/17 hrs
(D) 3 9/27 hrs
(E) 3 9/19 hrs
Rationale: Net part filled in 1 hour = 1/4 + 1/8 - 1/16
= 5/16
The tank will be full in 16/5 hrs, i.e., 3 1/5 hrs.
Answer:B
Answer: (B) 3 1/5 hrs
Question: The fourth proportional to 8, 13, 56 is:
(A) 91
(B) 92
(C) 93
(D) 94
(E) 95
Rationale: Let the fourth proportional to 8, 13, 56 be x.
Then, 8 : 13 : 56 : x
8x = (13 x 56)
x =	(13 x 56)/8
x=728/8 =91
Answer: Option A
Answer: (A) 91
Question: Each of the three people individually can complete a certain job in 4, 5, and 8 hours, respectively. What is the lowest fraction of the job that can be done in 1 hour by 2 of the people working together at their respective rates?
(A) 9/20
(B) 11/20
(C) 11/32
(D) 13/40
(E) 17/40
Rationale: The two slowest people work at rates of 1/5 and 1/8 of the job per hour.
The sum of these rates is 1/5 + 1/8 = 13/40 of the job per hour.
The answer is D.
Answer: (D) 13/40
Question: A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
(A) 40 sec
(B) 70 sec
(C) 49 sec
(D) 47 sec
(E) 42 sec
Rationale: Speed = 45 * 5/18
= 25/2 m/sec
Total distance covered
= 360 + 140
= 500 m
Required time
= 500 * 2/25
= 40 sec
Answer: A
Answer: (A) 40 sec
Question: Paul sells encyclopedias door-to-door. He earns $140 on every paycheck, regardless of how many sets he sells. In addition, he earns commission as follows:
Commission Sales
10% $0.00 - $10,000.00
5% $10,000.01 --->
He does not earn double commission.That is, if his sales are $12,000, he earns 10% on the first $10,000 and 5% on the remaining $2,000.
His largest paycheck of the year was $1,320. What were his sales for that pay period?
(A) 13,600
(B) 14,800
(C) 16,400
(D) 15,800
(E) 19,600
Rationale: His pay check was $1320.
Out of this, $140 was his fixed salary so the total commission he earned was $1320 - $140 = $1180
He earns 10% on the sales of first $10,000 which gives a commission of $1000.
He earns 5% on every subsequent dollar. Since he earns another $180, he must have had sales of another 180*(100/5) = 3600
So his total sales must have been $10,000 + $3600 = $13,600
A
Answer: (A) 13,600
Question: 150 men consume 1050 kg of rice in 30 days. In how many days will 70 men consume 980 kg of rice?
(A) 968
(B) 960
(C) 911
(D) 989
(E) 922
Rationale: Rate of consumption of each man = 1050/(150 * 30) = 7/30 kg/day
Let us say 70 men take x days to consume 150 kg.
Quantity consumed by each item in x days = (7x/30) kg
Quantity consumed by 70 men in x days = (7/30 x)(70) kg
= (7/30 x) * (70) = 960
x = 60 days.
Answer:B
Answer: (B) 960
Question: How many 4-letter words with or without meaning, can be formed out of the letters of the word, ‘LOGARITHMS’, if repetition of letters is not allowed?
(A) 40
(B) 400
(C) 5040
(D) 2520
(E) None
Rationale: Solution
'LOGARITHM' contain 10 different letters.
Required number of words = Number of Arrangement of 10 letters, taking 4 at a time
= 10 P 4 = (10 × 9 × 7) = 5040 .
Answer C
Answer: (C) 5040
Question: In 15 year’s time the combined age of my four brothers will be 107. What will it be in six year’s time?
(A) 56
(B) 64
(C) 71
(D) 46
(E) 77
Rationale: C
Combined age in 15 years = 107.
4 × 15 = 60, therefore combined age now is 107 – 60 = 47.
In 6 years time, therefore, combined age will be
47 + 24 (4 × 6) = 71.
Answer: (C) 71
Question: Naomi made a scarf for her brother using the yarn that cost $2.50 per skein. He offered to pay
Naomi for the yarn she used. If she used 1.5 skeins of yarn to make the scarf, what was the total
cost of the yarn?
(A) $2.25
(B) $3.25
(C) $4.25
(D) $5.25
(E) $6.25
Rationale: $2.50 x 1.13 = 2.83 for one skein (rounded)
$2.83 x 1.5 = $4.25 (rounded)
You could have found the basic cost of 1.5 skeins first, and then figured tax and
shipping. Your answer may be slightly different because of rounding.
correct answer C
Answer: (C) $4.25
Question: Carol is Four times Alice’s age but only twice as old as Betty. Alice is eighteen years younger than Carol. How old is Betty?
(A) 6
(B) 9
(C) 12
(D) 18
(E) 24
Rationale: ans B..9..
given that C=4A=2B..AND A=C-18=4A-18
substituting the values A=6,C=18 AND B=9..
Answer: (B) 9
Question: George baked a total of 100 pizzas for 7 straight days, beginning on Saturday. He baked 3/5 of the pizzas the first day, and 3/5 of the remaining pizzas the second day. If each successive day he baked fewer pizzas than the previous day, what is the maximum number of pizzas he could have baked on Wednesday?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: 3/5 of the 100 pizzas cooked on Saturday = 60 pizzas
3/5 of the remaining pizzas on Sunday = 24 pizzas
We're left with (100-60-24) =16 pizzas for the remaining 5 days. The prompt tells us that each day has FEWER pizzas than the day before it, so we can't have duplicate numbers.
M T W TH F
6 4 3 2 1 =16
W =3
A
Answer: (A) 3
Question: In what time will a train 200 m long cross an electric pole, it its speed be 144 km/hr?
(A) 2.0 sec
(B) 2.7 sec
(C) 3.5 sec
(D) 5.0 sec
(E) 9.5 sec
Rationale: Speed = 144 * 5/18 = 40 m/sec
Time taken = 200/40
= 5.0 sec.
Answer: D
Answer: (D) 5.0 sec
Question: A man can reach certain place in 50hours. If he reduces his speed by 1/10th, he goes 300km less in time. Find his speed?
(A) 20km/hr
(B) 30km/hr
(C) 60km/hr
(D) 50km/hr
(E) 60km/hr
Rationale: Let the speed be x km/hr
50x-50* 9/10 *x = 300
50x - 45x = 300
5x = 300
x = 60km/hr
Answer is C
Answer: (C) 60km/hr
Question: How many integers between 324,700 and 375,600 have tens digit 1 and units digit 3?
(A) 509
(B) 624
(C) 756
(D) 832
(E) 947
Rationale: The integers are:
324,713
324,813
etc...
375,513
The number of integers is 3756 - 3247 = 509
The answer is A.
Answer: (A) 509
Question: There were totally 100 men.82 are married.75 have T.V, 85 have radio,70 have A.C. How many men have T.V, radio, A.C and also married?
(A) 11
(B) 12
(C) 13
(D) 14
(E) 15
Rationale: 100-(100-82)-(100-75)-(100-85)-(100-70)= 100-18-25-15-30=100-88=12
ANSWER:B
Answer: (B) 12
Question: In Net's hair salon 38% of the customers dye their hair blond, 36% dye their eyebrows blond and 35% straighten their hair. 20% of the customers have none of these three procedures, while 12% take all of these three procedures. What percent of the customers come for exactly 2 of these 3 procedures?
(A) 5%
(B) 9%
(C) 12%
(D) 15%
(E) 21%
Rationale: Let a total of 100 people visit the salon.
Total = 100
Dye hair blonde (A) = 38 % = 38
Dye Eyebrows blonde (B) = 36% = 36
Straighten Hair (C) = 35% = 35
Neither = 20% = 20
All Three = 12% =12
Total = A+B+C - (Sum of Exactly Two group overlaps) - 2*(All three) + Neither
100 = 38+36+35 - (Sum of Exactly Two group overlaps) - 2*12 + 20
(Sum of Exactly Two group overlaps) = 9
%of customers coming for exactly 2 of the 3 procedures = 5%
A
Answer: (A) 5%
Question: What is the area of a square field whose diagonal of length 26 m?
(A) 287
(B) 269
(C) 338
(D) 200
(E) 230
Rationale: d2/2 = (26 * 26)/2
= 338
Answer:C
Answer: (C) 338
Question: A girl was asked to multiply a certain number by 43. She multiplied it by 34 and got his answer less than the correct one by 1233. Find the number to be multiplied.
(A) 130
(B) 132
(C) 134
(D) 137
(E) 138
Rationale: Let the required number be x. Then,
43x – 34x = 1233 or 9x = 1233 or x = 137.
Required number = 137.
ANSWER:D
Answer: (D) 137
Question: Excluding stoppages, the speed of a train is 60 kmph and including stoppages it is 36 kmph. Of how many minutes does the train stop per hour?
(A) A)12
(B) B)18
(C) C)24
(D) D)30
(E) E)36
Rationale: Explanation:
T = 24/60 * 60 = 24
Answer: Option C
Answer: (C) C)24
Question: Two vessels P and Q contain 62.5% and 87.5% of alcohol respectively. If 6 litres from vessel P is mixed with 4 litres from vessel Q, the ratio of alcohol and water in the resulting mixture is?
(A) 19:2
(B) 18:3
(C) 29:11
(D) 29:5
(E) 29:4
Rationale: Quantity of alcohol in vessel P = 62.5/100 * 6 = 15/4 litres
Quantity of alcohol in vessel Q = 87.5/100 * 4 = 7/2 litres
Quantity of alcohol in the mixture formed = 15/4 + 7/2 = 29/4 = 7.25 litres
As 10 litres of mixture is formed, ratio of alcohol and water in the mixture formed = 7.25 : 2.75 = 29 : 11.
Answer:C
Answer: (C) 29:11
Question: A computer program generates a sequence of numbers a1, a2, a3,... such that a1=1, a2=2, and ak = a(k-1) + 3ak-2 for 2 < k < n for n=20. Find a5.
(A) 10
(B) 24
(C) 28
(D) 32
(E) 38
Rationale: a1=1
a2=2
a3=3*2-2=4
a4=3*4-2=10
a5=3*10-2=28
28
Answer: (C) 28
Question: It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. It takes 20 minutes more, if 200 km is done by train and the rest by car. The ratio fo the speed of the train to that of the car is :
(A) 3:3 km
(B) 3:5 km
(C) 3:4 km
(D) 2:3 km
(E) None
Rationale: Sol.
Let the speed of the train b x km/hr and that of the car be y km/hr.
Then, 120/x + 480/y = 8 or 1/x + 4/y = 1/5
And, 200/x + 400/y = 25/3 or 1/x + 2/y = 1/24
Soving (i) and (ii), we get x = 60 and y = 80. ∴ Ratio of speeds = 60 : 80 = 3:4.
Answer C
Answer: (C) 3:4 km
Question: A rectangular courtyard, the sides of which are in the ratio of 4:3, cost Rs.600 for paving at 50 p per m2; find the length of the diagonal of the courtyard?
(A) 25 m
(B) 11 m
(C) 77 m
(D) 86 m
(E) 46 m
Rationale: 1 m2 ---- 1/2
? ----- 600 => 1200 m2
4x * 3x = 1200 => x = 10
Answer:A
Answer: (A) 25 m
Question: 21 ball numbered 1 to 21. A ballis drawn and then another ball is drawn without replacement.
(A) 2/17
(B) 3/37
(C) P(E) 9 by 42
(D) 8/97
(E) 12/31
Rationale: The probability that first toy shows the even number,
=1021= 1021
Since, the toy is not replaced there are now 9 even numbered toys and total 20 toys left.
Hence, probability that second toy shows the even number,
=920=920
Required probability,
=(1021)×(920)= (1021)×(920)
=9/42
C
Answer: (C) P(E) 9 by 42
Question: What will be the compound interest on a sum of Rs. 25,000 after 3 years at the rate of 12% p.a.?
(A) Rs.10123.22
(B) Rs.10823.20
(C) Rs.10123.20
(D) Rs.10123.29
(E) Rs.10123.28
Rationale: Explanation:
Amount = [25000 * (1 + 12/100)3]
= 25000 * 28/25 * 28/25 * 28/25 = Rs. 35123.20
C.I. = (35123.20 - 25000) = Rs.10123.20
Answer:C
Answer: (C) Rs.10123.20
Question: When x is divided by y, the quotient is v with remainder r. What is x in terms of r, y, and v?
(A) y + r +v
(B) yv + r
(C) x/y+r
(D) y/v+r
(E) rv + y
Rationale: (x/y) = v + r
solve for x
x=(v*y)+r
Ans B.
Answer: (B) yv + r
Question: In a certain sequence of numbers, a1, a2, a3, ..., an, the average (arithmetic mean) of the first m consecutive terms starting with a1 is m, for any positive integer m. If a1=1, what is a11?
(A) 100
(B) 55
(C) 21
(D) 19
(E) 1
Rationale: .
As stated above, (a1+a2+a3......+a10+a11)/11=11
therefore a1+a2+a3.......a11=121 (1)
using the same logic, we got a1+a2+a3..........+a9+a10=100 (2)
(2)-(1) we got a11=21
C
Answer: (C) 21
Question: A man buys a cycle for Rs. 1400 and sells it at a loss of 15%. What is the selling price of the cycle?
(A) Rs. 1090
(B) Rs. 1160
(C) Rs. 1190
(D) Rs. 1202
(E) Rs. 1092
Rationale: S.P. = 85% of Rs. 1400 = Rs.	85	x 1400/100 = Rs. 1190
Answer: Option C
Answer: (C) Rs. 1190
Question: The number of sailors on a ship is 85% more than the number of officers. The ratio of sailors to officers would be
(A) 37:20
(B) 47:20
(C) 47:25
(D) 22:25
(E) 97:50
Rationale: Sailor = 1.85 * Officer
Sailor/Officer = 1.85/1 = 185/100 = 37/20
Answer will be A
Answer: (A) 37:20
Question: which of the following options is the correct value of b, given the equation b^(-2) +b^3 = 64.1?
(A) 2
(B) 1
(C) 3
(D) 7
(E) 4
Rationale: Plugging in the various option into the equation to find out which is correct:
b^(-2)+b^3 = 64.1
4^(-2)+4^3 Ans. E
Answer: (E) 4
Question: A circular wheel 28 inches in diameter rotates the same number of inches per second as a circular wheel 35 inches in diameter. If the smaller wheel makes x revolutions per second, how many revolutions per minute does the larger wheelmakes in terms of x ?
(A) 48pi/x
(B) 75x
(C) 46x
(D) 24x
(E) 48x
Rationale: C = (pi)d
C(small): (pi)*28
C(large): (pi)*35
Lets say the time horizon is 60 seconds, so during that time the smaller wheel covers a distance of (pi)*28*60 = (pi)*(1680) inches
(pi)*(1680) = (pi)*(35)(x)
pi*(48) = pi*(x)
48=x
Answer: E. 48x
Answer: (E) 48x
Question: Can you please walk me through how to best approach this problem? Thanks
If #p# = ap^3+ bp – 1 where a and b are constants, and #-5# = 10, what is the value of #5#?
(A) 5
(B) -12
(C) -2
(D) -3
(E) -5
Rationale: #p# = ap^3 + bp - 1
#-5# = 10
putting p = -5 in above equation
-125a -(5b +1) = 10 or
#-5# = (125a+5b+1) = -10
therefore 125a+5b = -11 .....(1
now putting p = 5
#5# = 125 a+5b - 1
using equation 1(125a+5b = -11)
#5# = -11-1 = -12
hence B
Answer: (B) -12
Question: Jim is now twice as old as Fred, who is two years older than Sam. Seven years ago, Jim was three times as old as Sam. How old is Jim now?
(A) 18
(B) 20
(C) 24
(D) 32
(E) 40
Rationale: J = 2F = 2(S+2) = 2S+4
J-7 = 3*(S-7)
(2S+4)-7 = 3S-21
S = 18 and so J = 40
The answer is E.
Answer: (E) 40
Question: A child has 12 crayons, then she finds 4 more crayons. Now how many crayons does she have.
(A) A) 8
(B) B) 14
(C) C) 22
(D) D) 18
(E) E) 16
Rationale: 12 + 4 = 16. Answer is E).
Answer: (E) E) 16
Question: If 63 percent of a class answered the first question on a certain test correctly, 49 percent answered the second question on the test correctly, and 20 percent answered neither of the questions correctly, what percent answered both correctly?
(A) 22%
(B) 24%
(C) 26%
(D) 28%
(E) 32%
Rationale: 63% answered the first question correctly and 20% answered neither correctly.
Then 17% missed the first question but answered the second question correctly.
Then the percent who answered both correctly is 49% - 17% = 32%.
The answer is E.
Answer: (E) 32%
Question: If m is the average (arithmetic mean) of the first 10 positive multiples of 4 and if M is the median of the first 10 positive multiples of 4, what is the value of M – m ?
(A)  0
(B)  -5
(C)  5
(D)  25
(E)  27.5
Rationale: The first 10 positive multiples of 4 is an evenly spaced set. One of the most important properties of evenly spaced set (aka arithmetic progression) is:in any evenly spaced set the arithmetic mean (average) is equal to the median.
Hence M=m --> M-m=0.
Answer: A.
Answer: (A)  0
Question: The average height of 35 boys in a class was calculated as 182cm. 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) 180.27 cm
(B) 180.29 cm
(C) 978.29 cm
(D) 178.89 cm
(E) 176.29 cm
Rationale: Calculated average height of 35 boys = 182 cm.
Wrong total height of 35 boys = 182 * 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 = 182cm - (166 cm - 106 cm)/35
= 182 cm - 60 /35 cm
= 182 cm - 1.71 cm = 180.29 cm.
Answer: B
Answer: (B) 180.29 cm
Question: A, B and C invest in a partnership in the ratio: 7/2, 4/3, 6/5. After 4 months, A increases his share 50%. If the total profit at the end of one year be Rs. 21,600, then what is B's share in the profit?
(A) Rs. 2000
(B) Rs. 3000
(C) Rs. 4000
(D) Rs. 5000
(E) None of these
Rationale: Explanation :
Ratio of the initial investment = 7/2 : 4/3 : 6/5
= 105 : 40 : 36
From this ratio, we can assume that actual initial investments of A, B and C
are 105x, 40x and 36x respectively
A increases his share 50% after 4 months. Hence the ratio of their investments =
(105x * 4) + (105x * 150/100 * 8) : 40x * 12 : 36x : 12
= 105 + (105 * 3/2 * 2) : 40*3 : 36 * 3
= 105 * 4 : 40 *3 : 36 * 3
= 35 * 4 : 40 : 36
= 35 : 10 : 9
B's share = total profit * (10/54) = 21,600 * 10/54 = 4000. Answer : Option C
Answer: (C) Rs. 4000
Question: Find the compound ratio of (1:2), (2:3) and (3:4) is
(A) 1:2
(B) 3:5
(C) 5:7
(D) 1:4
(E) 2:1
Rationale: Required ratio = 1/2 * 2/3 * 3/4 = 1/4 = 1:4
Answer is D
Answer: (D) 1:4
Question: In the xy-plane, the line y = k is the perpendicular bisector of the line segment PQ and the line x = e is the perpendicular bisector of the line segment RQ. If the coordinates of the point R are (-e, -k), then what are the coordinates of the point P?
(A) (-5e, -5k)
(B) (-3e, -3k)
(C) (2e, 2k)
(D) (3e, 3k)
(E) (5e, 5k)
Rationale: firstly the Question tells us that RQ and PQ are perpendicular at Q..
Now the coordinates of the point R are (-e, -k), so R is at a distance of 2e from line x and at dist of 2k from line Y..
as line X bisect RQ .... length of RQ =4e and coord (3e,-k)..
as line Y bisect PQ .... length of PQ =4k and coord (3e,3k).ans D
Answer: (D) (3e, 3k)
Question: In Town X, 64 percent of the population are employed, and 42 percent of the population are employed males. What percent of the employed people in Town X are females?
(A) 16%
(B) 25%
(C) 32%
(D) 40%
(E) 34%
Rationale: We are asked to find the percentage of females in employed people.
Total employed people 64%, out of which 42 are employed males, hence 22% are employed females.
(employed females)/(total employed people)=22/64=1/4=34%
Answer: E.
Answer: (E) 34%
Question: A man can row a boat at 20 kmph in still water. If the speed of the stream is 6 kmph, what is the time taken to row a distance of 72 km downstream?
(A) 30/16 hours
(B) 36/13 hours
(C) 30/73 hours
(D) 30/13 hours
(E) 50/13 hours
Rationale: Speed downstream = 20 + 6 = 26 kmph.
Time required to cover 60 km downstream
= d/s = 72/26
= 36/13 hours.
Answer:B
Answer: (B) 36/13 hours
Question: The average (arithmetic mean) of a normal distribution of a school's test scores is 65, and standard deviation of the distribution is 6.5. A student scoring a 70 on the exam is in what percentile of the school?
Choices
(A) 63rd percentile
(B) 68th percentile
(C) 84th percentile
(D) 96th percentile
(E) 98th percentile
Rationale: (78-65)/6.5 = 2 sigmas or 95.5th percentile for +-2 sigma but in our case we need only upper tail, so it's 100 - (100 - 95.5)/2 = 63th percentile
A
Answer: (A) 63rd percentile
Question: David, a painter, has 9 jars of paint: 4 are black, 2 are yellow, and the rest are brown. David will combine 3 jars of paint into a new container to make a new colour, which he will name according to the following conditions: 1) C1, if the paint contains 2 jars of brown paint and no black paint 2) C2, if the paint contains 3 jars of brown paint. 3) J1, if the paint contains at least 2 jars of black paint 4) J2, if the paint contains exactly 1 jar of black paint What is the probability that the new colour will be a shade of J (J1 or J2)?
(A) 42/37
(B) 21/37
(C) 37/42
(D) 18/37
(E) 8/37
Rationale: the probability that it would be J1 or J2 is same as 1-()probability that it is C1 or C2
For C1-3C2(Brown)*2C1(Yellow)=3*2=6
For C2-3C3(all brown)=1
Total=9C3=84
1-7/84=77/84= 37/42
Answer : C
Answer: (C) 37/42
Question: An error 2% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is
(A) 4.04%
(B) 4.34%
(C) 4.45%
(D) 4.64%
(E) 4.70%
Rationale: 100 cm is read as 102 cm.
A1 = (100 x 100) cm2 and A2 (102 x 102) cm2.
(A2 - A1) = [(102)2 - (100)2]
= (102 + 100) x (102 - 100)
= 404 cm2.
Percentage error = 404 x 100 % = 4.04%
100 x 100
A)
Answer: (A) 4.04%
Question: If the quantity 4^2+ 4^4 + 4^8 is written as (a + b)(a – b), in which both a and b are integers, which of the following could be the value of b?
(A) 16
(B) 14
(C) 15
(D) 21
(E) 22
Rationale: (a+b)(a-b) = a^2 - b^2
4^2+ 4^4 + 4^6 = 4^2 (1+4^2+4^6)
if the above expression is solved even then every term of the expression will remain a multiple of 4^2 which is out of parenthesis
hence, b must be a multiple of 4^2 i.e. 16
Answer: option A
Answer: (A) 16
Question: lexus car agency has 135 cars.he sold some cars at 9% profit and rest at 36% profit thus he gains 17% on the sale of all his cars.the no. of cars sold at 36% profit is?
(A) 36
(B) 37
(C) 38
(D) 39
(E) 40
Rationale: ratio of 36% profit cars to 9% profit cars = 8:19
so no. of cars sold at 36% profit = 135*8/27= 40 cars
ANSWER:E
Answer: (E) 40
Question: What is the greatest integer that will always evenly divide the sum of five consecutive integers?
(A) 2
(B) 3
(C) 4
(D) 6
(E) 5
Rationale: Let the three consecutive even integers be x , x + 5 , x+10 , x+15, x+20
Sum = x + x + 5 + x + 10 + x + 15 + x + 20
= 5x+50 = 5(x+10)
Therefore , 5 will always be a factor .
Answer E
Answer: (E) 5
Question: If a solid sphere of radius 10 cms is moulded into 8 spherical solid balls of equal radius, then surface area of each ball (in sq.cm) is ?
(A) 100 π
(B) 101/π
(C) 99 π/12
(D) 54/13π
(E) 22/10π
Rationale: Explanation:
4/3 π x 10 x 10 x 10 = 8 x 4/3 π rxrxr
r = 5
4π x 5 x 5 = 100π
ANSWER IS A
Answer: (A) 100 π
Question: Robin is traveling from one end of a forest to the other. In order to find her way back, she is leaving morsels of bread in the following pattern: 2 morsels of RICE , 3 morsels of white, and 1 morsel of rye. The pattern repeats after she leaves the morsel of rye. If Robin drops 2,000 morsels of bread, what are the last 3 morsels of bread that she drops?
(A) rye − wheat − wheat
(B) RY-R-R
(C) white − rye − wheat
(D) white − white − white
(E) white − white − rye
Rationale: Q is nothing BUT asking about remainder..
total morsels thrown before the pattern is repeated = 2+3+1 = 6..
so REMAINDER when 2000 is div by 6..
1998 is EVEN and also div by 3, so remainder is 2..
Last 3 of morsels are 1998-1999-2000
so he uses the last of morsel of pattern in 1998 two of the first morsels of the pattern in 1999 and 2000, and the pattern is R, R, W, W, W, RY..
ans RY-R-R
B
Answer: (B) RY-R-R
Question: A train 125 m long passes a man, running at 6 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is?
(A) 51
(B) 50
(C) 88
(D) 65
(E) 22
Rationale: Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr
= 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 6) km/hr. x - 6 = 45 ==> x
= 51 km/hr.
Answer:A
Answer: (A) 51
Question: Pipe A can fill a tank in 6 hours. Due to a leak at the bottom, it takes 12 hours for the pipe A to fill the tank. In what time can the leak alone empty the full tank?
(A) 67
(B) 88
(C) 18
(D) 26
(E) 12
Rationale: Let the leak can empty the full tank in x hours 1/6 - 1/x = 1/12
=> 1/x = 1/6 - 1/12 = (3 - 2)/12 = 1/12
=> x = 12. Answer:E
Answer: (E) 12
Question: On Monday morning, Chris receives tickets to a baseball game that will be played at 7pm on the next evening that it does not rain. However, Chris is only in town until Wednesday morning, at which point he must fly to another city. If there is a 45% chance of rain each of the next two evenings, what is the probability that Chris will be able to attend the game?
(A)  36%
(B)  79.75%
(C)  80%
(D)  82%
(E)  84%
Rationale: Chris won't be able to attend the game if it be raining on Monday eveningandTuesday evening. The probability of that is 0.45*0.45 = 0.2025. So, the probability that he will be able to attend is 1 - 0.2025 = 0.7975.
Answer: B.
Answer: (B)  79.75%