mathewhe/aqua_rat huggingface dataset:
Question: Average of five numbers is 30 . If one number is excluded the average becomes 26. The excluded number is
(A) 35
(B) 45
(C) 55
(D) 46
(E) 67
Rationale: Explanation:
Number is (5*30) - (4*26) = 150-104 = 46
Answer: Option D
Answer: (D) 46
Question: Insert the missing number. 2, 7, 8, 17, 16, 27, 22
(A) 42
(B) 52
(C) 46
(D) 62
(E) 37
Rationale: Explanation :
There are two series here
2, 8, 16, 22 ... (Increase by 6)
7, 17, 27, 37 ... (Increase by 10)
Hence, next term is 27+10 = 37
Answer : Option E
Answer: (E) 37
Question: Ron scored 344 marks out of 400 marks and his elder brother Ben scored 582 marks out of 600 marks. Who scored percentage is better?
(A) 2333
(B) 2778
(C) 1000
(D) 2776
(E) 2881
Rationale: An alloy contains 26 % of copper. What quantity of alloy is required to get 260 g of copper?
Solution:
Let the quantity of alloy required = m g
Then 26 % of m =260 g
⇒ 26/100 × m = 260 g
⇒ m = (260 × 100)/26 g
⇒ m = 26000/26 g
⇒ m = 1000 g
Answer:C
Answer: (C) 1000
Question: The seats in an Engineering college for Computer science, electronics and civil are in the ratio of 5 : 7 :
8. There is a proportion to increase these seats by 40%, 50% and 75% respectively. What will be the
ratio of increased seats ?
(A) 2 : 3 : 4
(B) 6 : 7 : 8
(C) 6 : 8 : 9
(D) none of these
(E) Insufficient data
Rationale: Expl : Originally, let the number of seats for Computer science, electronics and civil
are 5x : 7x : 8x respectively.
Number of increased seats are (140% of 5x), (150% of 7x) and (175% of 8x)
7x : 21x/2 : 14x = 14x : 21x : 28x = 2 : 3 : 4.
Answer: A
Answer: (A) 2 : 3 : 4
Question: What is the perimeter of a rectangular field whose diagonal is 10m and length is 3m ?
(A) 12 m
(B) 5 m
(C) 10 m
(D) 8 m
(E) 6 m
Rationale: Sol:
Breadth of the rectangular plot is=10^2-3^2=1m
Therefore,
Perimeter of the rectangular plot= 2(3+1)=8m
D) 8m
Answer: (D) 8 m
Question: The average of a set of five distinct integers is 400. If each number is less than 2,000, and the median of the set is the greatest possible value, what is the sum of the two smallest numbers?
(A) -4,494
(B) -3,994
(C) -3,494
(D) -3,194
(E) The answer cannot be determined from the information given
Rationale: Sum of the set = 400*5=2000 Each number is less than 2000 and median of the set is the greatest possible value.
Therefore last 3 numbers can be 1999,1998 and 1997. Their sum=5994.
Therefore sum of two smallest numbers= 2000-5994= -3994
Answer=B
Answer: (B) -3,994
Question: A can complete a journey in 1 hours. He travels first half of the journey at the rate of 21km/hr and second half at the rate of 24km/hr. Find the total journey in km?
(A) 120km
(B) 150km
(C) 200km
(D) 224km
(E) 287km
Rationale: Let the total distance be xkm
x/2/21 + x/2/24 = 10
x/21 + x/24 = 20
15x = 168*20
x = 224km
Answer is D
Answer: (D) 224km
Question: The average age of an adult class is 40years. 15new students with an avg age of 32years join the class. Therefore decreasing the average by 4year. Find what was theoriginal strength of class?
(A) 8
(B) 12
(C) 15
(D) 17
(E) 18
Rationale: Let original strength = y
Then , 40y + 15 x 32 = ( y + 15) x 36
â‡’ 40y + 480 = 36y + 540
â‡’ 4y = 60
âˆ´ y = 15
C
Answer: (C) 15
Question: the cyclist going at a constant rate of 18 miles per hour is passed by a motor-cyclist traveling in the same direction along the same path at 48 miles per hour. the motor-cyclist stops to wait for the cyclist 15 minutes after passing cyclist, while the cyclist continues to travel at constant rate, how many minutes must the motor-cyclist wait until the cyclist catches up?
(A) 25
(B) 30
(C) 35
(D) 40
(E) 45
Rationale: For the 15 minutes the motor-cyclist continues to overtake the cyclist, she is going at 30 miles per hour faster than the cyclist.
Once the motor-cyclist stops, the cyclist is going at 18 miles per hour while the motor-cyclist is at rest
So the amount of time the cyclist will take to cover the distance between them is going to be in the ratio of the relative speeds. 30/18 * 15 or 25 minutes
Answer is (A)
Answer: (A) 25
Question: A man can row with a speed of 15 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is?
(A) 10 kmph
(B) 5 kmph
(C) 20 kmph
(D) 22 kmph
(E) 25 kmph
Rationale: M = 15
S = 5
DS = 15 + 5 = 20
ANSWER:C
Answer: (C) 20 kmph
Question: A and B can do a piece of work in 12 days. With the help of C they finish the work in 6 days. C alone can do that piece of work in?
(A) 33
(B) 878
(C) 30
(D) 88
(E) 12
Rationale: C = 1/6 â€“ 1/12 = 1/12 => 12 days
Answer: E
Answer: (E) 12
Question: If a – 8 = b, then determine the value of | a - b| - | b - a|.
(A) 16
(B) 0
(C) 4
(D) 2
(E) 1
Rationale: Sol.(b) | a - b| = |8| = 8
=> | b - a| = |-8| = 8
=> | a - b| - | b - a| = 8 - 8 = 0.
Answer B
Answer: (B) 0
Question: Peter can cover a certain distance in 1 hr. 24 min. by covering two-third of the distance at 4 kmph and the rest at 5 kmph. Find the total distance.
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: Let the total distance be x km . Then,
=(2 x/3)/4 + (1x/3)/5
= 7/5 = x/6 + x/15 = 7/5
= 7x = 42
= x = 6
Answer is E.
Answer: (E) 6
Question: A motorcycle importer is planning on increasing the price of a certain model by $1000. At this new price 7 fewer motorcycles will be sold per month, but the total revenues will increase by $26,000 to $594,000. What is the number of motorcycles the manufacturer will sell at this new price?
(A) 62
(B) 63
(C) 64
(D) 65
(E) 72
Rationale: I will make an equation in x and then make educated guesses. Here's how:
Assuming x motorcycles were sold every month initially.
(568000/x + 1000)(x-7) = 594000
(568/x + 1)(x-7) = 594
Now 568 = 8*71
Assuming x = 71 (We have all integers so it is obvious that 568/x should be an integer.
We get 9*66 = 594 (matches)
So he will sell 71 - 7 = 64 bikes this month
Answer (C)
Answer: (C) 64
Question: What no. should be subtracted from x^3+4x^2−7x+12x^3+4x^2−7x+12, if it is to be perfectly divisible by x+3x+3?
(A) 30
(B) 42
(C) 45
(D) 49
(E) 51
Rationale: According to remainder theorem when dfracf(x)x+adfracf(x)x+a, then the remainder is f(−a)f(−a).
In this case, as x+3x+3 divides x3+4x2−7x+12–kx3+4x2−7x+12–k perfectly (kk being the number to be subtracted), the remainder is 0 when the value of xx is substituted by -3.
i.e., (−3)3+4(−3)2−7(−3)+12−k=0(−3)3+4(−3)2−7(−3)+12−k=0
or −27+36+21+12=k−27+36+21+12=k
or k=k= 42
B
Answer: (B) 42
Question: Two pipes can fill a tank in 8 minutes and 5 minutes. An outlet pipe can empty the tank in 12 minutes. If all the pipes are opened when the tank is empty, then how many minutes will it take to fill the tank?
(A) 30 minutes
(B) 17 minutes
(C) 15 minutes
(D) 10 minutes
(E) 14 minutes
Rationale: Part of the filled by all the three pipes in one minute
= 1/8 + 1/5 - 1/12 = (15 + 24 - 10)/120 = 29/120
So, the tank becomes full in 14 minutes.
Answer: E
Answer: (E) 14 minutes
Question: What is the positive difference between the sum of the squares of the first 3 positive integers and the sum of the prime numbers between the first square and fourth square?
(A) 11
(B) 12
(C) 13
(D) 24
(E) 27
Rationale: Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.
the sum of the squares of the first 4 positive integers = 1^2 + 2^2 + 3^2 = 14
the sum of the prime numbers between the first square(=1) and fourth square(=16) = 2+3+5+7+11+13=41.
So the difference between 41 and 14 is 27.
So the answer is (E).
Answer: (E) 27
Question: Three rugs have a combined area of 200 square meters. By overlapping the rugs to cover floor area of 138 square meters, the area that is covered by exactly two layers of rug is 24 square meters. What is the area that is covered with three layers of rug ?
(A) 18 square meters
(B) 19 square meters
(C) 24 square meters
(D) 28 square meters
(E) 30 square meters
Rationale: Total = Rug1 + Rug2 + Rug3 - {overlap of exactly 2 rugs} - 2*{overlap of exactly 3 rugs}
138 = 200 - 24 - 2*{overlap of exactly 2 rugs} --> {overlap of exactly 3 rugs} = 19.
Answer: B.
Answer: (B) 19 square meters
Question: Two employees X and Y are paid a total of Rs. 590 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?
(A) s.268
(B) s.288
(C) s.298
(D) s.300
(E) s.388
Rationale: Let the amount paid to X per week = x
and the amount paid to Y per week = y
Then x + y = 590
But x = 120% of y = 120y/100 = 12y/10
∴12y/10 + y = 590
⇒ y[12/10 + 1] = 590
⇒ 22y/10 = 590
⇒ 22y = 5900
⇒ y = 5900/22 = 500/2 = Rs.268
A)
Answer: (A) s.268
Question: The sequence a1, a2, a3, a4. a5 is such that an = a n-1 +5 for 2≤ n ≤ 5. If a5 = 39 what is the value of a1 ?
(A) 1
(B) 6
(C) 19
(D) 16
(E) 21
Rationale: Here, each value of an is the previous value plus 5
Since the numbers are less, the fastest way to solve this problem is to successively subtract 5 from a5 till you reach a1
a5 = 39
a4 = 34
a3 = 29
a2 = 24
a1 = 19 <<<< Ans C
Answer: (C) 19
Question: What is the probability that Company Q's advertisement will be one of the first two be shown during the first commercial break?
(A)  1/ 225
(B)  1 / 30
(C)  1 /15
(D)  2 / 15
(E)  4 /15
Rationale: Q 1/15 + (14/15) * 1/14 = 2/15 D
Answer: (D)  2 / 15
Question: In a jar there are balls in different colors: blue, red, green and yellow.
The probability of drawing a blue ball is 1/8.
The probability of drawing a red ball is 2/5.
The probability of drawing a green ball is 7/10.
If a jar cannot contain more than 50 balls, how many yellow balls are in the Jar?
(A) 12
(B) 15
(C) 23
(D) 7
(E) 5
Rationale: answer of 1st
just add the given probabilities p(blue)+p(red)+p(green) i.e
1/8+2/5+ 3/10=5+16+12/40
now we know p(blue)+p(red)+p(green)+p(yellow)=1
33/40+p(yellow)=1
p(yellow)=33/40
i.e why yellow balls are 7.
D
Answer: (D) 7
Question: In a box, there are 10 blue, 12 white and 10 yellow bulbs. One bulb is picked up randomly. What is the probability that it is neither white nor blue?
(A) 3/16
(B) 5/16
(C) 8/32
(D) 2/32
(E) 9/32
Rationale: Total number of bulbs = (10 + 12 + 10) = 32.
Let E = event that the bulb drawn is neither white nor blue = event that the bulb drawn is yellow.
Therefore, P(E)=10/32= 5/32
ANSWER:B
Answer: (B) 5/16
Question: A car takes 6 hours to cover a distance of 540 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?
(A) 35 Kmph
(B) 48 Kmph
(C) 52 Kmph
(D) 54 Kmph
(E) 60 Kmph
Rationale: Time = 6
Distance = 540
3/2 of 6 hours = 6 * 3/2 = 9 Hours
Required speed = 540/9 = 60 Kmph
E)
Answer: (E) 60 Kmph
Question: Edward traveled the entire 60 miles trip. If he did the first 3 miles of at a constant rate 24 miles per hour and the remaining trip of at a constant rate 48 miles per hour, what is the his average speed, in miles per hour?
(A) 20mph
(B) 24mph
(C) 30mph
(D) 32mph
(E) 53mph
Rationale: Average speed=sum of distance/sum of time. If he travelled the first 3 miles at 24 miles/hr, it would take 0.125 hr. For the remaining trip, if he went at 48 miles/1hr, it would take 1 hour. Then, the average speed is 60miles/(0.125+1)hrs=53miles/1hr.
Therefore, the answer is E.
Answer: (E) 53mph
Question: How many different 6-letter sequences are there that consist of 2A, 7B's and 3C's ?
(A) 6
(B) 60
(C) 120
(D) 360
(E) 720
Rationale: How many different 6-letter sequences are there that consist of 2 A, 7B's, and 3 C's?
(A) 6
(B) 60
(C) 120
(D) 360
(E) 720 (ANS C)
Answer: (C) 120
Question: 100 liters of a mixture contains milk and water in the ratio 7:3. If 10 liters of this mixture be replaced by 10 liters of milk, the ratio of milk to water in the new mixture would be?
(A) 7:8
(B) 8:3
(C) 3:8
(D) 8:7
(E) 7:1
Rationale: Quantity of milk in 100 liters if mix = 100*7/10 =70 liters
Quantity of milk in 110 liters of new mix = 80+10 = 80liters
Quantity of water in it = 110-80 = 30 liters
Ratio of milk and water in new mix = 80:30 = 8:3
Answer is B
Answer: (B) 8:3
Question: What is the sum of all digits for the number 10^29 - 41?
(A) 257
(B) 242
(C) 231
(D) 202
(E) 187
Rationale: 10^29 is a 30-digit number: 1 followed by 29 zeros.
10^29 - 41 is a 29-digit number: 27 9's and 59 at the end.
The sum of the digits is 27*9+5+9=257.
The answer is A.
Answer: (A) 257
Question: The ratio of Red Balls to Blue Balls is 3:7. 70% of the Red balls and 30% of the Blue balls are tennis balls. How many of the balls are tennis balls?
(A) 44%
(B) 40%
(C) 45%
(D) 42%
(E) 48%
Rationale: let total no of Balls 100, Red Ball 30 and Blue Ball 70, so tennis ball for Red and Blue Ball respectively 30* 70/100=21 and 70* 30/100=21
so total 42 tennis balls out of 100 balls..so required % is 42%
ANSWER:D
Answer: (D) 42%
Question: 20% loss on the selling price is what percent loss on the cost price?
(A) 27/7%
(B) 47/11%
(C) 50/3%
(D) 63/8%
(E) 101/110%
Rationale: Let S.P. = $100
Then, loss = $20
C.P. = 100+20 = $120
Loss% = 20/120 * 100 = 50/3%
Answer is C
Answer: (C) 50/3%
Question: When the number 9y30012 is exactly divisible by 11, what is the smallest whole number that can replace y?
(A) 1
(B) 2
(C) 5
(D) 6
(E) 8
Rationale: The given number =9y30012
Sum of the odd places =2+0+3+9=14
Sum of the even places = 1+0+y
(Sum of the odd places)- (Sum of even places) = Number (exactly divisible by 11)
14-(1+y) = divisible by 11
13 � y = divisible by 11.
Y must be 2, to make given number divisible by 11.
B
Answer: (B) 2
Question: If 6 persons can do 6 times of a particular work in 6 days, then, 7 persons can do 7 times of that work in
?
(A) 3 days
(B) 7 days
(C) 6 days
(D) 11 days
(E) 15 days
Rationale: That is, 1 person can do one time of the work in 6 days.
Therefore, 7 persons can do 7 times work in the same 6 days itself.
Option 'C'
Answer: (C) 6 days
Question: A boat goes 100 km downstream in 10 hours, and 75 m upstream in 15 hours. The speed of the stream is?
(A) 22 1/2
(B) 22 18/2
(C) 28 1/2
(D) 22 1/5
(E) 22 1/4
Rationale: 100 --- 10 DS = 10
? ---- 1
75 ---- 15 US = 5
? ----- 1 S = (10 - 5)/2
= 22 1/2 kmph.Answer: A
Answer: (A) 22 1/2
Question: Of the three- digit integers greater than 700, how many have two digits W that are equal to each other and the remaining digit different from the other two?
(A) 90
(B) 82
(C) 80
(D) 45
(E) 36
Rationale: three-digit integers greater than 700: 701 to 999, inclusive.
possible values for hundreds-digit--> 7,8,9
possible values for tens-digit and ones-digit --> 0, 1,2,3,4,5,6,7,8,9
when hundreds-digit and tens-digit are the same: (3x1x10)-3=27 ---> we minus three to exclude 777, 888 and 999
when hundreds-digit and ones-digit are the same: (3x10x1)-3=27 ---> we minus three to exclude 777, 888 and 999
when tens-digit and hundreds-digit are the same:[(3x10x1)-3]-1=26 ---> we minus three to exclude 777, 888 and 999; we minus one to exclude 700
W=27+27+26 = 80
Answer: C
Answer: (C) 80
Question: A cheese factory sells its cheese in rectangular blocks. A normal block has a volume of three cubic feet. If a large block has twice the width, twice the depth, and three times the length of a normal block, what is the volume of cheese in a large block in cubic feet?
(A) 18
(B) 6
(C) 27
(D) 48
(E) 36
Rationale: Volume of cube=lbh=3
New cube l ,b, h are increases of 3l,2b,2h
New volume of cube =3l*2b*2h=12lbh
=12*3
=36
Answer: E
Answer: (E) 36
Question: A can do a piece of work in 12 days. When he had worked for 2 days B joins him. If the complete work was finished in 8 days. In how many days B alone can finish the work?
(A) 2 days
(B) 25days
(C) 9 days
(D) 18 days
(E) 3 days
Rationale: Explanation:
8/12 + 6/x = 1
X = 18 days
Answer: D
Answer: (D) 18 days
Question: The length of the longest tape in cm which can be used to measure exactly, the length 10m; 3m 85cm; and 11m 50cm is:
(A) 5
(B) 35
(C) 34
(D) 36
(E) 38
Rationale: The three lengths in cm are 1000, 385 & 1150.
HCF of 700, 385 & 1295 is 5.
Hence, the answer is 5 cm.
ANSWER:A
Answer: (A) 5
Question: If y exceeds x by 35%, then x is less than y by?
(A) 16 2/9%
(B) 25 5/27%
(C) 16 2/3%
(D) 12 2/3%
(E) 16 1/3%
Rationale: X=100	y=135
135------35
100-------? => 25 5/27%
Answer:B
Answer: (B) 25 5/27%
Question: The value of a 10.5% stock, in which an income of Rs.756 is derived by investing Rs.9000, brokerage being% is :
(A) Rs. 113.5
(B) Rs. 120
(C) Rs. 124.75
(D) Rs. 137.5
(E) Rs. 145.8
Rationale: For an income of Rs.756, investment = Rs.9000
For an income of Rs., investment = = Rs.125
For a Rs.100 stock, investment = Rs.125.
Market value of Rs. 100 stock = = Rs. 124.75
C
Answer: (C) Rs. 124.75
Question: There are 2 sections A and B in a class, consisting of 16 and 14 students respectively. If the average weight of section A is 20kg and that of section B is 25kg, Find the average of the whole class?
(A) 33.5kg
(B) 37.25kg
(C) 42.45kg
(D) 55.12kg
(E) 29.78kg
Rationale: Total weight of 36+44 students = 16*20 + 14*25 = 670
Average weight of the class is = 670/20 = 33.5 kg
Answer is A
Answer: (A) 33.5kg
Question: A jar full of whiskey contains 40% alcohol. A part of this whisky is replaced by another containing 19%
alcohols and now the percentage of alcohol was found to be 26%. The quantity of whisky replaced is
(A) 43
(B) 34
(C) 32
(D) 23
(E) 38
Rationale: Explanation :
Concentration of alcohol in 1st Jar = 40%
Concentration of alcohol in 2nd Jar = 19%
After the mixing, Concentration of alcohol in the mixture = 26%
By the rule of alligation,
Concentration of alcohol in 1st Jar Concentration of alcohol in 2nd Jar
40% 19%
Mean
26%
7 :14
Hence ratio of 1st and 2nd quantities = 7 : 14 = 1 : 2
Answer : Option D
Answer: (D) 23
Question: Two trains of length 300 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 90 kmph. In how much time will the trains cross each other?
(A) 87/7 sec
(B) 80/7 sec
(C) 80/9 sec
(D) 80/5 sec
(E) 15 sec
Rationale: Relative speed = (54 + 90)* 5/18 = 8 * 5 = 40 mps.
The time required = d/s = (100 + 300 + 200)/40
= 600/40 = 15 sec.
Answer: E
Answer: (E) 15 sec
Question: A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. How far is the place?
(A) 2.89
(B) 2.88
(C) 2.85
(D) 2.84
(E) 2.82
Rationale: M = 6
S = 1.2
DS = 6 + 1.2 = 7.2
US = 6 - 1.2 = 4.8
x/7.2 + x/4.8 = 1
x = 2.88
Answer:B
Answer: (B) 2.88
Question: By selling an umbrella for Rs. 300, a shop keeper gains 20%. During a clearance sale, the shopkeeper allows a discount of 10% on the marked price. His gain percent during the sale is?
(A) 5%
(B) 2%
(C) 8%
(D) 3%
(E) 4%
Rationale: Marked price = Rs. 300
C.P. = 100/120 * 300 = Rs. 250
Sale price = 90% of Rs. 300 = Rs. 270
Required gain % = 20/250 * 100 =8%.
Answer: C
Answer: (C) 8%
Question: There are 6 multiple choice questions in an examination. How many sequences of answers are possible, if the first three questions have 4 choices each and the next three have 5 each?
(A) 4576
(B) 7200
(C) 6300
(D) 4500
(E) 8000
Rationale: Here we have to perform 6 jobs of answering 6 multiple choice questions. Each of the first three questions can be answered in 4 ways and each one of the next three can be answered in 5 different ways. So, the total number of different sequences = 4 × 4 × 4 × 5 × 5 × 5 = 8000
Ans: E
Answer: (E) 8000
Question: A company has issued 500 preferred shares and 400 common shares both of par value Rs. 100 each. The dividend on a preferred share and a common share is 8% and 12%, respectively. The company had a total profit of 150000 rupees out of which some amount was kept in reverse fund and the remaining disturbed as dividend. Find the amount kept in reserve fund.
(A) 141000
(B) 141500
(C) 141300
(D) 141250
(E) 141200
Rationale: Face value of each preferred share = 100
Dividend per preferred share = 100×8/100
Total dividend in all preferred shares = (500×100×8)/100=Rs.4000
Face value of each common share = 100
Dividend per common share = 100×12/100
Total dividend in all common shares = 400×100×12/100 = Rs.4800
Total dividend = Rs.4000 + Rs.4800 = Rs.8800
amount kept in reserve fund = Rs.150000 - Rs.8800 = Rs.141200
Answer is E.
Answer: (E) 141200
Question: A waitress's income consists of her salary and tips.During one week ,her tips were 11/4 of her salary.What fraction of her income for the week came from tips?
(A) 1/9
(B) 1/6
(C) 1/3
(D) 4/9
(E) 11/15
Rationale: Her tips were 11/4 of her salary.
Let's say her salary =$4
This mean her tips = (11/4)($4) =$11
So, her TOTAL INCOME =$4+$11=$15
What fraction of her income for the week came from tips
$11/$15 =11/15
= E
Answer: (E) 11/15
Question: If the sum of one-third and one-half of a number exceeds two-third of a number by 5, the number is
(A) 30
(B) 32
(C) 36
(D) 40
(E) 50
Rationale: Explanation:
Let the number be x. Then,
x/3 + x/2 = 2x/3 + 5
= 5x/6 - 2x/3 = 5
= x/6 = 5
= x = 30
Answer: Option A
Answer: (A) 30
Question: What least number mustbe subtracted from 427398 so that remaining no.is divisible by 15
(A) 3
(B) 4
(C) 6
(D) 7
(E) 8
Rationale: Explanation:
On dividing 427398 by 15 we get the remainder 3, so 3 should be subtracted
Answer: Option A
Answer: (A) 3
Question: The distance between two cities A and B is 330 Km. A train starts from A at 8 a.m. and travel towards B at 60 km/hr. Another train starts from B at 9 a.m and travels towards A at 75 Km/hr. At what time do they meet?
(A) 10 a.m
(B) 10.30 a.m
(C) 11 a.m
(D) 11.30 a.m
(E) None of these
Rationale: Explanation:
Suppose they meet x hrs after 8 a.m
then,
[Distance moved by first in x hrs] + [Distance moved by second in (x - 1) hrs] = 330.
Therefore, 60x + 75(x - 1) = 330.
=> x = 3.
So,they meet at (8 + 3) i.e, 11a.m.
Answer: C
Answer: (C) 11 a.m
Question: A man gets a simple interest of Rs.800 on a certain principal at the rate of 5% p.a in two years. Find the compound interest the man will get on twice the principal in two years at the same rate.
(A) Rs.500
(B) Rs.250
(C) Rs.5012.50
(D) Rs.5062.50
(E) 410
Rationale: Let the principal be Rs.P
S.I at 5% p.a in 8 years on Rs.P = Rs.800
(P)(8)(5)/100 = 800
P = 2000
C.I on Rs.2P i.e., Rs.4000 at 5% p.a in two years
=4000{ [1 + 5/100]2 - 1} = 4000{ 212 - 202 /202}
= Rs.410
ANSWER:E
Answer: (E) 410
Question: How should we mix two rice packets to get one 1kg packet priced at Rs 8 when the prices of 1 kg packets of the two types are Rs 7.1 and Rs 9.2.
(A) 4:3
(B) 4:7
(C) 4:9
(D) 4:2
(E) 4:1
Rationale: Explanation:
No explanation is available for this question!
ANSWER: A
Answer: (A) 4:3
Question: If DON is coded as 18 and MASS is coded as 29 Then KING is coded as
(A) 21
(B) 20
(C) 19
(D) 17
(E) None
Rationale: KING = 11+9+14+7=41 i.e (4*4)+(1*1)=17
MASS = 13+1+19+19=52 i.e (5*5)+(2*2)=29
DON = 4+14+15=33 i.e(3*3)+(3*3)=18
ANSWER:D
Answer: (D) 17
Question: A reduction of 30% in the price of oil enables a house wife to obtain 9kgs more for Rs.900, what is the reduced price for kg?
(A) 72
(B) 27
(C) 40
(D) 30
(E) 20
Rationale: 900*(30/100) = 270 ---- 9
? ---- 1 => Rs.30
Answer:D
Answer: (D) 30
Question: A company bought for its 7 offices 2 computers of brand N and 4 computers of brand M. In how many ways could computers be distributed among the offices if each office can have only 1 computer.
(A) 196
(B) 105
(C) 256
(D) 292
(E) 312
Rationale: This problem has to do withcombinations. Here's the general idea: if you have a set of n elements, and you are going to choose r of them (r < n), then the number of combinations of size r one could choose from this total set of n is:
# of combinations = nCr = (n!)/[(r!)((n-r)!)]
where n! is the factorial symbol, which means the product of every integer from n down to 1. BTW, nCr is readn choose r.
In this problem, let's consider first the three computers of brand M. How many ways can three computer be distributed to seven offices?
# of combinations = 7C4 = 35
There are 35 different ways to distribute three computers to 7 offices. (The massive amount of cancelling that occurred there is very much typical of what happens in the nCr formula.)
One we have distributed those three M computers, we have to distribute 2 N computers to the remaining four offices. How many ways can two computer be distributed to four offices?
# of combinations = 3C2 = 3
For each of the 35 configurations of distributing the M computers, we have 3 ways of distributing the N computers to the remaining offices. Thus, the total number of configurations is 35*3 = 105. Answer choice =B
Answer: (B) 105