mathewhe/aqua_rat huggingface dataset:
Question: In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?
(A) 209
(B) 210
(C) 211
(D) 213
(E) 215
Rationale: In a group of 6 boys and 4 girls, four children are to be selected such that at least one boy should be there.
Hence we have 4 options as given below
We can select 4 boys ...(option 1)
Number of ways to this = 6C4
We can select 3 boys and 1 girl ...(option 2)
Number of ways to this = 6C3 × 4C1
We can select 2 boys and 2 girls ...(option 3)
Number of ways to this = 6C2 × 4C2
We can select 1 boy and 3 girls ...(option 4)
Number of ways to this = 6C1 × 4C3
Total number of ways
= 6C4 + 6C3 × 4C1 + 6C2 × 4C2 + 6C1 × 4C3
= 6C2 + 6C3 × 4C1 + 6C2 × 4C2 + 6C1 × 4C1[∵ nCr = nC(n-r)]
=
6
×
5
2
×
1
+
6
×
5
×
4
3
×
2
×
1
×
4
=6×52×1+6×5×43×2×1×4
+
6
×
5
2
×
1
×
4
×
3
2
×
1
+
6
×
4
+6×52×1×4×32×1+6×4
=
15
+
80
+
90
+
24
=
209
Answer is A
Answer: (A) 209
Question: Set S contains points whose abscissa and ordinate are both natural numbers. Point P, an element in set S has the property that the sum of the distances from point P to the point (8, 0) and the point (0, 12) is the lowest among all elements in set S. How many such points P exist in set S?
(A) 1
(B) 5
(C) 11
(D) 8
(E) 3
Rationale: Explanatory Answer
The sum of the distances from point P to the other two points will be at its lowest only when point P lies on the line segment joining the points (8, 0) and (0, 12).
The equation of the line segment joining the points (8, 0) and (0, 12) is x/8 + y/12 = 1
Or the equation is 12x + 8y = 96 or 3x + 2y = 24.
The question states that the elements of set S contain points whose abscissa and ordinate are both natural numbers.
The equation of the line is 3x + 2y = 24 and hence, x will take even values while y will take values that are multiples of 3.
The values are x = 2, y = 9; x = 4, y = 6; x = 6, y = 3.
Hence, there are 3 such points that exist in set S.
The correct choice is (E)
Answer: (E) 3
Question: When n is divided by 15, the remainder is 8. What is the remainder when 5n is divided by 6?
(A) 2
(B) 6
(C) 3
(D) 4
(E) 1
Rationale: Let n=8 (leaves a remainder of 8 when divided by 48)
5n = 5(8) =40, which leaves a remainder of 4 when divided by 6.
Answer D
Answer: (D) 4
Question: In an express train, the passengers travelling in A.C. sleeper class, First class and Sleeper class are in the ratio 1 : 2 : 7, and rate for each class is in the ratio 5 : 4 : 2. If the total income from this train is 54,000 , find the income of Indian Railways from A.C. sleeper class.
(A) 12,000
(B) 20,000
(C) 22,000
(D) 10,000
(E) None of these
Rationale: Let number of passengers = x, 2x, 7x
and Rate = 5y, 4y, 2y
Now, since income = Rate × Number of passengers
∴ Income = 5xy, 8xy, 14xy
∴ Income in ratio = 5 : 8 : 14
∴ Income from A.C. sleeper class = 5/5+8+14×54,000
= 10,000
Answer D
Answer: (D) 10,000
Question: A garrison of 2000 men has provisions for 54 days. At the end of 15 days, a reinforcement arrives, and it is now found that the provisions will last only for 20 days more. What is the reinforcement?
(A) 1900
(B) 2776
(C) 8888
(D) 1666
(E) 1878
Rationale: 2000 ---- 54
2000 ---- 39
x ----- 20
x*20 = 2000*39
x = 3900
2000
-------
1900
Answer: A
Answer: (A) 1900
Question: 1000 men have provisions for 20 days. If 650 more men join them, for how many days will the provisions last now?
(A) 12.9
(B) 12.5
(C) 12.6
(D) 12.2
(E) 12.1
Rationale: 1000*20 = 1650*x
x = 12.1
Answer: E
Answer: (E) 12.1
Question: Danny spends $360 buying his favorite dolls. If he buys only small LemonHead dolls, which are $1 cheaper than the large LemonHead dolls, he could buy 5 more dolls than if he were to buy only large LemonHead dolls. How much does a large LemonHead doll cost?
(A) $5
(B) $6
(C) $7.2
(D) $8
(E) $9
Rationale: X: Price of small dolls; Y: Price of big dolls.
Y = X +1
360(1/x - 1/y) = 5
<=>x.y = 72
We can make trial: 9x8 = 72.
Choose (E) y = 9.
Answer: (E) $9
Question: For what range of values of 'x ' will the inequality 15x - 2/x > 1?
(A) x > 0.4
(B) x < 1/3
(C) -1/3 < x
(D) -1/3 < x and x< 0, x > 2/5
(E) x < -1/3 and x > 2/5
Rationale: In Case 1 where x > 0, I agree. I calculated x > (-1/3) and x > 2/5, and because x > 0, it must be x > 2/5.
In Case 2 where x < 0, I don't understand why you say that the range must be x > -1/3 and x < 0, since the values that satisfy the inequality 15x^2 - x - 2 < 0show that x < -1/3 and x < 2/5.
I have the same doubt. Shouldn't the answer be D?
____________
The answer IS D.
Answer: (D) -1/3 < x and x< 0, x > 2/5
Question: The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 320 resolutions?
(A) 724 m
(B) 704 m
(C) 287 m
(D) 450.6 m
(E) 927 m
Rationale: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 320 resolutions.
= 320 * 2 * 22/7 * 22.4 = 45056 cm
= 450.6 m
Answer:D
Answer: (D) 450.6 m
Question: The distance between Delhi and Mathura is 110 kms. A starts from Delhi with a speed of 20 kmph at 7 a.m. for Mathura and B starts from Mathura with a speed of 25 kmph at 8 p.m. from Delhi. When will they meet?
(A) 12a.m
(B) 10a.m
(C) 19a.m
(D) 76a.m
(E) 37a.m
Rationale: D = 110 – 20 = 90
RS = 20 + 25 = 45
T = 90/45 = 2 hours
8 a.m. + 2 = 10 a.m.
Answer: B
Answer: (B) 10a.m
Question: In a partnership between A, B and C. A's capital is Rs.2000. If his share of a profit of Rs.600 is Rs.200 and C's share is Rs.130, what is B's capital?
(A) Rs.5500
(B) Rs.5600
(C) Rs.5700
(D) Rs.5300
(E) Rs.5400
Rationale: 200 + 130 = 330
600 - 330 = 270
200 ---- 2000
270 ---- ? => Rs.5400
ANSWER:E
Answer: (E) Rs.5400
Question: A certain auto manufacturer sold 5% fewer vehicles in 2007 than in 2006. If the manufacturer sold 3.0 million vehicles in 2006, how many vehicles, to the nearest 10,000, did the manufacturer sell in 2007?
(A) 24,00,000
(B) 25,00,000
(C) 28,50,000
(D) 29,50,000
(E) 29,70,000
Rationale: Let's assume in 2006 the manufacturer sold X.
In 2007 he sold X-5/100(X)
If sales in 2006,X= 3.0 million find X-5/100(X)
(3.0 x 10^6)-5/100(3.0 x 10^6)
3000000-1,50,000=28,50,000-----> 28,50,000(approx)
Answer-C
Answer: (C) 28,50,000
Question: What is the probability of flipping a fair coin five times and the coin landing on heads on at least two flips?
(A) 5/8
(B) 7/8
(C) 11/16
(D) 13/16
(E) 27/32
Rationale: The number of possible outcomes is 2^5=32.
0 heads: There is 1 way to have all tails.
1 head: There are 5 ways to have one head.
P(0 or 1 head)=6/32=3/16
P(at least 2 heads)=1 - 3/16 = 13/16
The answer is D.
Answer: (D) 13/16
Question: The greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively, is:
(A) 234
(B) 127
(C) 274
(D) 918
(E) 121
Rationale: Required number = H.C.F. of (1657 - 6) and (2037 - 5)
= H.C.F. of 1651 and 2032 = 127.
Answer:B
Answer: (B) 127
Question: A runner runs the 40 miles from Marathon to Athens at a constant speed. Halfway through the run she injures her foot, and continues to run at half her previous speed. If the second half takes her 8 hours longer than the first half, how many hours did it take the runner to run the second half?
(A) 10
(B) 12
(C) 16
(D) 20
(E) 24
Rationale: The runner runs the first 20 miles at speed v and the second 20 miles at speed v/2.
The time T2 to run the second half must be twice the time T1 to run the first half.
T2 = 2*T1 = T1+8
T1 = 8 and so T2 = 16.
The answer is C.
Answer: (C) 16
Question: How many multiples of 5 are there between 5 to 105?
(A) 9
(B) 18
(C) 17
(D) none of these
(E) 19
Rationale: Explanation :
As you know, multiples of 5 are integers having 0 or 5 in the digit to the extreme right (i.e. the units place).
So the numbers are 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100.
Answer : E
Answer: (E) 19
Question: A and B can together finish a work in 40days. They worked together for 10days and then B left. After another 12days, A finished the remaining work. In how many days A alone can finish the job?
(A) 10
(B) 25
(C) 60
(D) 16
(E) 20
Rationale: A+B 10days work = 10*1/40 = 1/4
Remaining work = 1-1/4 = 3/4
3/4 work is done by A in 12 days
whole work will be done by A in 12*4/3 = 16days
Answer is D
Answer: (D) 16
Question: If 60% of 3/5 of a number is 36, then the number is?
(A) 80
(B) 100
(C) 75
(D) 90
(E) None of these
Rationale: Let the number be x. Then 60% of 3/5 of x=36
60/100*3/5*x=36
x=(36*25/9)=100
Required number=100.
Correct Option: B
Answer: (B) 100
Question: A man can do a piece of work in 15 days, but with the help of his son, he can do it in 6 days. In what time can the son do it alone?
(A) 13
(B) 9
(C) 15
(D) 8
(E) 10
Rationale: Son's 1day's work = (1/6)-(1/15) = 3/30= 1/10
The son alone can do the work in 10 days
Answer is E
Answer: (E) 10
Question: What is the probability Q of randomly selecting an arrangement of the letters of the wordMEDITERRANEANin which the first letter is E and the last letter is R?
(A) 1/13
(B) 1/20
(C) 1/26
(D) 1/50
(E) 1/100
Rationale: Why do you calculate the total combinations and everything, it is much easier to calculate as follows:
3/13 * 1 * 1 * 1 * 1 ..... * 2/12 = 6/156 = 1/26
This is because 3/13 = Probability that first letter will be E and 2/12 = probability that thefirstletter will be R. Between everything else cuts down to 1*1*1... e.g. probability Q of the second letter is 11/11 = 1, > we do not care what's in between.C
Answer: (C) 1/26
Question: There r 4 prime numbers in ascending order. The multiplication of first 3 is 385 and that of last 3is 1001. what is the last number is
(A) 8
(B) 10
(C) 11
(D) 13
(E) 14
Rationale: Explanation:
abcbcd=3851001=>ad=513
abcbcd=3851001=>ad=513
So d = 13
D
Answer: (D) 13
Question: Charles’s and Sarah’s current ages are C years and S years, respectively. If 6 years from now, Charles will be at least as old as Sarah was 2 years ago, which of the following must be true?
(A) C + 6 < S − 2
(B) C + 6 ≤ S + 2
(C) . C + 6 = S − 2
(D) C + 6 > S − 2
(E) C + 6 ≥ S − 2
Rationale: Now: Charles = C, Sarah = S
in 6Y: C+6≥S−2,
Answer E
Answer: (E) C + 6 ≥ S − 2
Question: Real-estate salesman Z is selling a house at a 30 percent discount from its retail price. Real-estate salesman X vows to match this price, and then offers an additional 15 percent discount. Real-estate salesman Y decides to average the prices of salesmen Z and X, then offer an additional 40 percent discount. Salesman Y's final price is what fraction of salesman X's final price?
(A) 39/6
(B) 62/11
(C) 11/61
(D) 21/61
(E) 20/61
Rationale: Let the retail price be = x
Selling price of Z = 0.7x
Selling price of X = 0.85*0.7x = 0.60x
Selling price of Y = ((0.7x + 0.6x)/2)*0.60 = 0.65x * 0.60 = 0.39x
0.39x = k * 0.60x
k = 0.39/0.6 = 39/6
Answer: A
Answer: (A) 39/6
Question: A jar is filled with red, white, and blue tokens that are equivalent except for their color. The chance of randomly selecting a red token, replacing it, then randomly selecting a white token is the same as the chance of randomly selecting a blue token. If the number of tokens of every color is a multiple of 8, what is the smallest possible total number of tokens in the jar?
(A)  9
(B)  12
(C)  15
(D)  18
(E)  21
Rationale: (Red / Total Coins)*(White / Total Coins) = (Blue / Total Coins)
í.ẹ. Red*White = Blue*Total Coins
Let, Red = 3a
White = 3b
Blue = 3c
Total Coins = 3(a+b+c)
í.ẹ. 3a * 3b = 3c*3(a+b+c)
í.ẹ. a*b = c*(a+b+c)
For smallest values of a, b and c
2*3 = 1*(1+2+3)
í.ẹ. Minimum Total Coins = 3*(1+2+3) = 15
Answer: Option C
Answer: (C)  15
Question: A conical vessel, whose internal radius is 12 cm and height 50 cm, is full of liquid. The contents are emptied into a cylindrical vessel with internal radius 10 cm. Find the height to which the liquid rises in the cylindrical vessel.
(A) 24 cm
(B) 14 cm
(C) 20 cm
(D) 37 cm
(E) 17 cm
Rationale: Volume of the liquid in the cylindrical vessel
= Volume of the conical vessel
= ((1/3)* (22/7)* 12 * 12 * 50) )cm3 = (22 *4 *12 * 50)/7 cm3.
Let the height of the liquid in the vessel be h.
Then (22/7)*10*10*h =(22*4*12*50)/7 or h = (4*12*50)/100 = 24 cm
ANSWER A 24 cm
Answer: (A) 24 cm
Question: When processing flower-nectar into honey bees' extract, a considerable amount of water gets reduced. How much flower-nectar must be processed to yield 1kg of honey, if nectar contains 50% water, and the honey obtained from this nectar contains 40% water?
(A) 1.2 kg
(B) 1.5 kg
(C) 1.7 kg
(D) 1.9 kg
(E) None of these
Rationale: Explanation :
Flower-nectar contains 50% of non-water part.
In honey this non-water part constitutes 60% (100-40).
Therefore 0.5 X Amount of flower-nectar = 0.60 X Amount of honey = 0.60 X 1 kg
Therefore amount of flower-nectar needed =
(0.60/0.51)kg=1.2 kgs
Answer : A
Answer: (A) 1.2 kg
Question: A hollow iron pipe is 21 cm long and its external diameter is 8 cm. If the thickness of the pipe is 1 cm and iron weighs 8 g/cm3, then the weight of the pipe is:
(A) 3.6 kg
(B) 3.696 kg
(C) 36 kg
(D) 36.9 kg
(E) None
Rationale: Solution
External radius = 4 cm,
Internal radius = 3 cm.
Volume of iron	=(22/7×(42)-(32)×21)cm3
= (22/7×7 ×1×21)cm3
= 462 cm3.
Weight of iron = (462 x 8) gm = 3696 gm = 3.696 kg.
Answer B
Answer: (B) 3.696 kg
Question: A bread merchant declares a 20% discount after 8 P.M. Each bread costs Rs.40 when it is not on sale. Sam goes before 8 P.M. to buy 4 pieces of bread. Max goes after 8 P.M. with the same amount of money that Sam had to buy bread. How many pieces did Max get over Sam?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Explanation:
Sam: 4 pieces * 40 = 160
Max: Max had 160. 160 / (40*(1-20%)) = 160 / (40*0.80) = 160 / 32 = 5 pieces
Max - Sam = 5 - 4 = 1
Correct Option: A
Answer: (A) 1
Question: A courtyard is 18 meter long and 12 meter board is to be paved with bricks of dimensions 12 cm by 6 cm. The total number of bricks required is :
(A) 16000
(B) 18000
(C) 20000
(D) 30000
(E) None of these
Rationale: Explanation:
Number of bricks =Courtyard area /1 brick area
=(1800Ã—1200 /12Ã—6)=30000
Option D
Answer: (D) 30000
Question: The cube root of .000216 is:
(A) .6
(B) .06
(C) 77
(D) 87
(E) 89
Rationale: Explanation:
(.000216)1/3	= [216/(10)6	]	1/3 = 6/100 =0.06
ANSWER IS B
Answer: (B) .06
Question: Find k if 64 / k = 4.
(A) 16
(B) 17
(C) 18
(D) 14
(E) 13
Rationale: Since 64 /k = 4 and 64/ 16 = 4, then
k = 16 correct answer A
Answer: (A) 16
Question: A train 120 meter long passes an electric pole in 12 seconds and another train of same length traveling in opposite direction in 8 seconds. The speed of the second train is
(A) 10m/s
(B) 20m/s
(C) 30m/s
(D) 40m/s
(E) 50m/s
Rationale: speed of 1st train=120/12=10m/s
let the speed of 2nd is v
then
240/(v+10)=8
8v=160
v=20m/s
ANSWER:B
Answer: (B) 20m/s
Question: A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
(A) 378
(B) 240
(C) 772
(D) 281
(E) 213
Rationale: Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train
= (15 x 20)m
= 300 m. Let the length of the platform be x meters. Then, (x + 300)/36
= 15 ==> x + 300 = 540
==> x
= 240 m.
Answer: B
Answer: (B) 240
Question: How many words with or without meaning, can be formed by using all the letters of the word, ‘ORANGE’, using each letter exactly once?
(A) 700
(B) 720
(C) 750
(D) 800
(E) 820
Rationale: The word ‘ORANGE’ contains 6 different letters.
Therefore, Required number of words= Number of arrangement of 6 letters, taken all at a time
=6P6
= 6!
= 6*5*4*3*2*1
= 720
ANSWER:B
Answer: (B) 720
Question: The average age of three boys is 12 years and their ages are in the proportion 2 : 6 : 8. The age of the youngest boy is:
(A) 21 years
(B) 8.75 years
(C) 6.75 years
(D) 9 years
(E) None of these
Rationale: Total age of 3 boys = (12 Ã— 3) years = 36 years. Ratio of their ages = 2 : 6 : 8.
Age of the youngest = (36 Ã— 3â„16) years = 6.75 years.
Answer C
Answer: (C) 6.75 years
Question: Square RSTU shown above is rotated in a plane about its center in a clockwise direction the minimum number of degrees necessary for R to be in the position where T is now shown. The number of degrees through which RSTU is rotated is
(A)  135 degree
(B)  180 degree
(C)  225 degree
(D)  270 degree
(E)  315 degree
Rationale: From the options, I am assuming the positioning of T and R relative to each other to be as shown. To replace T by R, focus on OR. Say, you rotate OR clockwise (and with it the entire square) and bring it in place of OT. How many degrees did you go? You covered 2 right angles i.e. 180 degrees.
Answer : B
Answer: (B)  180 degree
Question: Set M contains number that satisfy the condition that, if integer x is in the set then x + 6 will also be in the set M. If -4 is one value in the set, which of the following values must also be present in the set M? I) -10 II) 2 III) 8
(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) I, II and III
Rationale: Since -4 is in the set, then the set must also include 2, 8, 14, 20, etc...
Depending on whether -4 is the starting element in the set or not, we can have -10...or not.
The answer is D.
Answer: (D) II and III only
Question: Two taps can separately fill a cistern 10 minutes and 15 minutes respectively and when the waste pipe is open, they can together fill it in 18 minutes. The waste pipe can empty the full cistern in?
(A) 6
(B) 5
(C) 7
(D) 9
(E) 2
Rationale: 1/10 + 1/15 - 1/x
= 1/18
x = 9
Answer:D
Answer: (D) 9
Question: Cereal A is 10% sugar by weight, whereas healthier but less delicious Cereal B is 2% sugar by weight. To make a delicious and healthy mixture that is 6% sugar, what should be the ratio of Cereal A to Cereal B, by weight?
(A) 2:9
(B) 2:7
(C) 1:6
(D) 1:4
(E) 1:1
Rationale: Ratio of A / Ratio of B = (Average Wt of Mixture - Wt of B)/(Wt of A - Average Wt of Mixture)
=> Ratio of A / Ratio of B = (6 - 2)/(10 - 6) =4/4
So they should be mixed in the ratio 1:1
Answer - E
Answer: (E) 1:1
Question: Every day a cyclist meets a car at the station.The road is straight and both are travelling in the same direction. The cyclist travels with a speed of 12 mph.One day the cyclist comes late by 20 min. and meets the car 5miles before the Station. What is the speed of the car?
(A) 40 Kmph.
(B) 50 Kmph.
(C) 60 Kmph.
(D) 70 Kmph.
(E) 80 Kmph.
Rationale: If they normally meet at 8AM, then
cyclist will reach at station on that day at 8:20 AM. But train will reach station at 8AM only.
and he will be at at point 5 miles before station at 7.55 AM ( i.e 25 min before 8:20 AM)
so train will take 5 mins to travel( to reach stn at 8AM) 5 miles.
so speed of train = 60 Kmph.
ANSWER:C
Answer: (C) 60 Kmph.
Question: What is the sum of all remainders obtained when the first 130 natural numbers are divided by 9?
(A) 397
(B) 401
(C) 403
(D) 412
(E) 399
Rationale: A positive integer can give only the following 9 remainders when divided by 9: 1, 2, 3, 4, 5, 6, 7, 8, and 0.
1 divided by 9 gives the remainder of 1;
2 divided by 9 gives the remainder of 2;
...
8 divided by 9 gives the remainder of 8;
9 divided by 9 gives the remainder of 0.
We'll have 11 such blocks, since 99/9=11. The last will be:
91 divided by 9 gives the remainder of 1;
92 divided by 9 gives the remainder of 2;
...
98 divided by 9 gives the remainder of 8;
99 divided by 9 gives the remainder of 0.
The last number, 100, gives the remainder of 1 when divided by 9, thus the sum of all remainders will be:
11(1+2+3+4+5+6+7+8+0)+1=412.
Answer: D.
Answer: (D) 412
Question: A merchant marks his wares 40% more than the real price and allows 20% discount. His profit is:
(A) 20%
(B) 18%
(C) 16%
(D) 12%
(E) None of these
Rationale: Let the CP = 100 Rs.
Mark Price = 140
Discount = 20%
Selling price 80/100 × 140
Hence profit = 12%
Answer: D.
Answer: (D) 12%
Question: (161)^2 - (162)^2 =
(A) 1
(B) 100
(C) 229
(D) 325
(E) 349
Rationale: Using the formula:
(a+1)^2 - a^2 = 2a+1
So, Answer = 162*2 + 1
= 324+1 = 325 = Answer = D
Answer: (D) 325
Question: The smallest fraction, which each of 6/7, 5/14, 10/21 will divide exactly is?
(A) 30/7
(B) 30/9
(C) 30/2
(D) 30/3
(E) 30/6
Rationale: Required fraction = L.C.M of 6/7, 5/14, 10/21
= (L.C.M of 6, 5, 10) / (H.C.F of 7, 14, 21) = 30/7
Answer:A
Answer: (A) 30/7
Question: Rhoda tosses a coin 5 times. Find the probability of getting exactly 4 heads.
(A) 5/32
(B) 6/32
(C) 5/16
(D) 4/32
(E) 8/32
Rationale: Exactly 4 heads out of 5 would be: HHHHT, HHTHH, or many other combinations.
therefore, no. of possible combinations are 5!/4!*1! = 5
Probability = 5/2^5 = 5/32
ANSWER:A
Answer: (A) 5/32
Question: A trader sold two items for Rs.2500 each, if he made a profit of 28% from the first item and a loss of 20% from the second item, calculate his total gain or loss.
(A) 2.6
(B) 12.6
(C) 3.6
(D) 7.6
(E) 5.6
Rationale: (28*20)/100 = 5.6%
Answer: E
Answer: (E) 5.6
Question: While working alone at their constant rates, computer X can process 240 files in 4 hours, and computer Y can process 240 files in 6 hours. If all files processed by these computers are the same size, how many hours would it take the two computers, working at the same time at their respective constant rates, to process a total of 240 files?
(A) 2
(B) 2.2
(C) 2.4
(D) 2.6
(E) 2.8
Rationale: Both computers together process files at a rate of 240/4 + 240/6 = 60+40 = 100 files per hour.
The time required to process 240 files is 240/100 = 2.4 hours
The answer is C.
Answer: (C) 2.4
Question: A sum of Rs. 1530 has been divided among A, B and C such that A gets of what B gets and B gets of what C gets. B’s share is:
(A) Rs. 120
(B) Rs. 160
(C) Rs. 270
(D) Rs. 300
(E) None
Rationale: EXPLANATION
Let C’s share = Rs. x
Then, B’s share = Rs. x/4 , A’s share = Rs. (2/3 x x/4 ) = Rs. x/6
=x/6 + x/4 + x = 1530
=> 17x/12 = 1530
=> 1530 x 12/ 17 = Rs.1080
Hence, B’s share = Rs. (1080/4) = Rs. 270.
Answer C
Answer: (C) Rs. 270
Question: The average amount with a group of seven numbers is Rs. 30. If the newly joined member has Rs. 55 with him, what was the average amount with the group before his joining the group?
(A) s. 25.6
(B) s. 155/6
(C) s. 16.6
(D) s. 260/6
(E) s. 25
Rationale: Total members in the group = 7
Average amount = Rs. 30
Total amount with them = 7 * 30 = Rs. 210
One number has Rs. 55. So, the amount with remaining 6 people = 210 - 55= Rs. 155
The average amount with them = 155/6
ANSWER:B
Answer: (B) s. 155/6
Question: Three of the sides of a rectangular prism have areas of 91, 39, and 21. What is the volume of the rectangular prism?
(A) 252
(B) 269
(C) 273
(D) 920
(E) 1911
Rationale: One easy way to get the answer for this question is just multiply the unit's digits of these three numbers, i.e (1*9*1 = 9) (Why the multiplication is needed?, you can see the solution suggested by Bunuel in the above post)
Now look out for the answer whose square gives us a 9 in the unit place.
So, it is easy to pic (C) 273 whose square will give us a 9 in the unit place( 3*3), and hence this is the answer.
Answer: (C) 273
Question: If a randomly selected positive single digit multiple of 3 is multiplied by a randomly selected prime number less than 20, what is the probability E that this product will be a multiple of 45?
(A) 1/32
(B) 1/28
(C) 1/24
(D) 1/16
(E) 1/14
Rationale: There are 3 single digit multiple of 3, that is, 3,6,9.
There are 8 prime nos less than 20 - 2,3,5,7,11,13,17,19
Total outcome - 8*3 = 24
Favourable outcome = 1 (9*5)
Hence required probability E= 1/24. Answer C.
Answer: (C) 1/24
Question: At a conference, the only events scheduled for the day are seminars and breaks. All seminars are the same length and are 10 times as long as each break. A break must be between two consecutive seminars. If the first seminar begins at 9:00 a.m. and the third one ends at 11:00 a.m., how long will the conference last if there are a total of 6 seminars that day?
(A) hours and 15 minutes
(B) hours and 20 minutes
(C) hours and 25 minutes
(D) hours and 30 minutes
(E) hours and 35 minutes
Rationale: Well its like this S B S B S B S B S B S
the interval between 9 am to 11:40 am is 160 min having 3 seminars and 2 breaks .If 1 break is of 5 min than time for 3 seminars = 160 - 2*5=150
Time of 1 seminar =150 /3=50 min .
So calculating for 6 seminars and 5 breaks ,total time comes out to be 5 hrs and 35 min .
Answer is E.
Answer: (E) hours and 35 minutes