mathewhe/aqua_rat huggingface dataset:
Question: X can do a piece of work in 40 days. He works at it for 8 days and then Y finished it in 16 days how long will they work together take to complete the work?
(A) 13 1/3
(B) 15
(C) 20
(D) 56
(E) 57
Rationale: Explanation:
Work done by x in 8 days= 8/40 = 1/5
remaining work= 4/5
4/5 work is done by Y in 16 days
whole work is done by Y in 16*5/4 = 20 days
X’s 1 day work =1/40
Y’s 1 day work =1/20
(X+Y)’s 1 day work=1/40 +1/20 = 3/40 = 13 1/3
Answer: Option A
Answer: (A) 13 1/3
Question: A man engaged a servant on the condition that he would pay him Rs.900 and a uniform after one year service. He served only for 9 months and received uniform and Rs.650, find the price of the uniform?
(A) 377
(B) 197
(C) 187
(D) 100
(E) 822
Rationale: Explanation:
9/12 = 3/4 * 900 = 675
650
-------------
25
1/4 -------- 25
1 --------- ? => Rs.100
Answer: D
Answer: (D) 100
Question: A man can row his boat with the stream at 16 km/h and against the stream in 8 km/h. The man's rate is?
(A) 4 kmph
(B) 2 kmph
(C) 7 kmph
(D) 8 kmph
(E) 3 kmph
Rationale: DS = 16
US = 8
S = ?
S = (16 - 8)/2 = 4 kmph
Answer:A
Answer: (A) 4 kmph
Question: A man’s speed with the current is 18 km/hr and the speed of the current is 2.5 km/hr. the man’s speed against the current is :
(A) 8.5 km/hr
(B) 9.5 km/hr
(C) 13 km/hr
(D) 12.5 km/hr
(E) None of these
Rationale: Solution
Man's rate in still water = (18-2.5) km/hr = 15.5 km/hr.
Man's rate against the current = (15.5-2.5) km/hr = 13 km/hr Answer C
Answer: (C) 13 km/hr
Question: 130kg of an alloy A is mixed with 160 kg of alloy B. If alloy A has lead and tin in the ratio 2:3 and alloy B has tin and copper in the ratio 3:4, then the amount of tin in the new alloy is?
(A) 140.6kg
(B) 145.3kg
(C) 146.5kg
(D) 110.8kg
(E) 114kg
Rationale: Quantity of tin in 130kg of A = 130*3/5 = 78kg
Quantity of tin in 160kg of B = 160*3/7 = 68.5kg
Quantity of tin in the new alloy = 78+68.5 = 146.5kg
Answer is C
Answer: (C) 146.5kg
Question: A train 150 meters long takes 6 seconds to cross a man walking at 5 kmph in the direction opposite to that of the train. Find the speed of the train.
(A) 45 kmph
(B) 50 kmph
(C) 85 kmph
(D) 60 kmph
(E) 70 kmph
Rationale: Explanation:
Let the speed of the train be x kmph.
Speed of the train relative to man = (x + 5) kmph = (x + 5) ×5/18 m/sec.
Therefore 150/((x+5)×5/18)=6 <=> 30 (x + 5) = 2700 <=> x = 85
Speed of the train is 85 kmph.
Answer: Option C
Answer: (C) 85 kmph
Question: A natural number has exactly 10 divisors including 1 and itself.how many distint prime factors this natural number will have?
(A) 37
(B) 29
(C) 27
(D) 99
(E) 11
Rationale: Answer:D
Answer: (D) 99
Question: If there are 86 workers in a factory, and on a certain day, 72 were present. Calculate the percentage that showed up for work? (round to the nearest tenth).
(A) 82.7%
(B) 81.7%
(C) 83.7%
(D) 89.7%
(E) 88.7%
Rationale: 72/86*100=83.72
83.7%
correct answer C
Answer: (C) 83.7%
Question: Anthony and Cindy were each given x dollars in advance to perform at a community festival. Anthony eventually performed on all 14 days of the festival, while Cindy performed on 7 fewer days than Anthony performed. If Cindy gives Anthony y dollars of her advance payment so that they would have each received the same daily rate, what was Anthony paid in advance, in terms of y?
(A) 2y
(B) 3y
(C) 5y
(D) 6y
(E) 10y
Rationale: Anthony performed for 14 days meansw Cindy performed for(14-7)=7 days.
If Cindy gives y dollars to Anthony their Daily rate will be equal.It means
(x+y)/14=(x-y)/7
Solving we get, x=3y
Now Anthony's Advance is x=3y .So answer should be B.
Answer: (B) 3y
Question: A computer system uses alphanumeric case sensitive characters for its passwords. When the system was created it required users to create passwords having 4 characters in length. This year, it added the option of creating passwords having 5 characters in length. Which of the following gives the expression for the total number of passwords the new computer system can accept?
Assume there are 52 unique alphanumeric case sensitive characters.
(A) 63^4
(B) 62^5
(C) 62(62^4)
(D) 53(52^4)
(E) 63(62^6)
Rationale: Total number of passwords = number of 4 character password +number of 5 character password
= 52^4 + 52^5 (Since there is no limitation on repetition , each character can be chosen in 52 ways )
=52^4(1+ 52)
=52^4 * 53
Answer D
Answer: (D) 53(52^4)
Question: A boat moves upstream at the rate of 1 km in 20 minutes and down stream 1 km in 12 minutes. Then the speed of the current is :
(A) 1 kmph
(B) 2 kmph
(C) 3 kmph
(D) 2.5 kmph
(E) 3.5 kmph
Rationale: Rate upstream = (1/20 *60) = 3 kmph
Rate dowm stream = 1/12 * 60 = 5 kmph
Rate of the current = ½ (5-3) = 1 kmph
ANSWER:A
Answer: (A) 1 kmph
Question: What decimal of an hour is a second
(A) .0028
(B) .0027
(C) .0026
(D) .0025
(E) None of these
Rationale: Explanation:
1/(60*60) = 1/3600 = .0027
Option B
Answer: (B) .0027
Question: In a tea factory,one half of the workers are above 50 years,quarter are between 50 to 45 years,one-fifth are between 45 to 35 years and other 30 workers are below 20 years. How many workers total are there in the factory?
(A) 250
(B) 366
(C) 400
(D) 500
(E) 600
Rationale: 1/2x + 1/4x +1/5x = 19/20x
Remaining 1/20 x= 30
x= 30*20= 600
E is the answer.
Answer: (E) 600
Question: Find the odd man out
253, 136, 352, 323, 631, 244
(A) 323
(B) 136
(C) 352
(D) 631
(E) 531
Rationale: The sum all three digits comes to 10 except 323
ANSWER:A
Answer: (A) 323
Question: 6x − 12 = 6y
5y + 5x = 10
Which of the following is the number of solutions to the system of equations shown above?
(A) More than three
(B) Exactly three
(C) Exactly two
(D) Exactly one
(E) None
Rationale: 6x − 12 = 6y
=> 6x - 6y = 12
=> x- y =2 -- 1
5y + 5x = 10
=>x + y = 2 -- 2
From equation 1 and 2 , we get
2x = 4
=> x=2
y=0
Therefore , the given system will have Exactly one solution
D
Answer: (D) Exactly one
Question: Andy has grades of 84, 65, and 76 on three math tests. What grade must he obtain on the next test to have an average of exactly 80 for the four tests?
(A) 80
(B) 85
(C) 90
(D) 95
(E) 98
Rationale: (84 + 65 + 76+ x) 4 = 80
(4)(80) = 225 + x
320 = 225 + x
( 320-225) (225-225)
95 = x
ANSWER :D
Answer: (D) 95
Question: 81,162,49,98,25,50,66
(A) 126
(B) 127
(C) 129
(D) 128
(E) 132
Rationale: 81*2=162
49*2=98
25*2=50
66*2=132
ANSWER:E
Answer: (E) 132
Question: A rectangular table seats 5 people on each of two sides, with every person directly facing another person across the table. If ten people choose their seats at random, what is probability that any two of them directly face other?
(A) 1/56
(B) 1/8
(C) 1/7
(D) 1/9
(E) 4/7
Rationale: A B C D E
------------
| TABLE |
------------
F G H I J
A to J are 10 people.
Prob to select any 1 person = 1
Prob to select the person opposite to the chosen person = 1/9
For ex. If we select A as the person than prob of choosing F is 1/9.
Hence, answer will be D.
Answer: (D) 1/9
Question: A box contains 4 red balls and 4 black balls. One by one, every ball is selected at random without replacement. What is the probability that the fourth ball selected is black?
(A) 1/4
(B) 1/2
(C) 1/2
(D) 5/8
(E) 2
Rationale: My complicated version of your simple approach
Let the 4 black balls be BBBBand 4 Red Balls be RRRR
They can be arranged in 8 slots _ _ _ _ _ _ _ _
in (8!)/ (4!x4!)
If the fourth slot is Black ball then the arrangement will be to fill
_ _ _ B _ _ _ _
we have 7 slots and 3 Black (BBB) and 4 Red (RRRR)
They can be arranged in (7!)/ (4!x3!)
Hence required probability = [(8!)/ (4!x4!)]/[(7!)/ (4!x3!)]
=2
E
Answer: (E) 2
Question: Due to 10% decrease in the price of sugar and John can buy 5kg more sugar in Rs100 , then find the CP of sugar?
(A) Rs. 2(1/9)
(B) Rs. 2(2/9)
(C) Rs. 2(1/3)
(D) Rs. 3(2/5)
(E) Rs. 3(1/7)
Rationale: Here r = 10 % ,x = 100 and A = 5 kg
Actual price of sugar = 10*100/((100-10 )*5) = Rs. 2(2/9)
B
Answer: (B) Rs. 2(2/9)
Question: In 1990 the budgets for projects Q and V were $620,000 and $780,000, respectively. In each of the next 10 years, the budget for Q was increased by $30,000 and the budget for V was decreased by $10,000. In which year was the budget for Q equal to the budget for V ?
(A)  1992
(B)  1993
(C)  1994
(D)  1995
(E)  1996
Rationale: Let the no of years it takes is x.
620+30x = 780-10x --> 40x = 160 and x=4.
Thus, it happens in 1994.
C.
Answer: (C)  1994
Question: Income and expenditure of a person are in the ratio 5 : 4. If the income of the person is Rs. 17000, then find his savings?
(A) 3600
(B) 3400
(C) 3608
(D) 3602
(E) 3603
Rationale: Let the income and the expenditure of the person be Rs. 5x and Rs. 4x respectively.
Income, 5x = 17000 => x = 3400
Savings = Income - expenditure = 5x - 4x = x
So, savings = Rs. 3400.
Answer:B
Answer: (B) 3400
Question: A 600 meter long train crosses a signal post in 40 seconds. How long will it take to cross a 3 kilometer long bridge, at the same speed?
(A) 4 min
(B) 2 min
(C) 8 min
(D) 9 min
(E) 3 min
Rationale: S = 600/40 = 15 mps
S = 3600/15 = 240 sec = 4 min.Answer: A
Answer: (A) 4 min
Question: Convert the 13/36 m/s into kilometers per hour?
(A) 2.9
(B) 2.2
(C) 1.3
(D) 1.2
(E) 1.8
Rationale: 13/36 m/s = 13/36 * 18/5 = 13/10 = 1.3 kmph.
Answer: C
Answer: (C) 1.3
Question: There are 8 boxes numbered from 1 to 8. Either a red ball or a green ball will be placed in each box in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. How many different ways can this be done?
(A) 32
(B) 34
(C) 36
(D) 38
(E) 40
Rationale: 1 green ball: 8 ways
2 green balls: 7 ways
3 green balls: 6 ways
4 green balls: 5 ways
5 green balls: 4 ways
6 green balls: 3 ways
7 green balls: 2 ways
8 green balls: 1 way
The total number of ways is 8*9/2=36
The answer is C.
Answer: (C) 36
Question: If 7^t is a factor of the product of the integers from 1 to 100, inclusive, what is the largest value of t?
(A) 12
(B) 13
(C) 14
(D) 15
(E) 16
Rationale: So the question just means that we have to find all the multiples t of 7 between 1 to 100
So there are 14 multiples of 7 ( 7 - 98)
But 49 and 98 contain two 7's as factors
so we have to add 14 + 2 = 16
E
Answer: (E) 16
Question: Difference between the length & breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is?? We have: (l - b) = 23 and 2(l + b) = 206 or (l + b) = 103?
(A) 2500 m^2
(B) 2510 m^2
(C) 2520 metre sq
(D) 2540 m^2
(E) 2590 m^2
Rationale: Solving the two equations, we get: l = 63 and b = 40.
Area = (l x b) = (63 x 40) m2 = 2520 m^2
C
Answer: (C) 2520 metre sq
Question: The number of ways in which one or more balls can be selected out of 10 white, 9 green and 7 blue balls is
(A) 892
(B) 881
(C) 891
(D) 879
(E) None of these
Rationale: The required number of ways
= (10 + 1)(9 + 1)(7 + 1) - 1 = 879.
Answer D
Answer: (D) 879
Question: A necklace is made by stringing N individual beads together in the repeating pattern green bead, white bead, yellow bead, red bead, and blue bead. If the necklace design begins with a green bead and ends with a yellow bead, then N could equal
(A) 55
(B) 65
(C) 75
(D) 68
(E) 85
Rationale: Recognize that we are going to have to look for an answer thats a multiple of 5, plus 3.
Mutliple of 5 because there are 5 beads in the pattern, and plus 3 because the bead ends on yellow, which is 3 into the pattern.
I just went through all the answer choices, and only E fits. 5x13 = 65, and 65+3=68
Answer : D
Answer: (D) 68
Question: the sides of a triangle are in the ratio 3:5:7.if the pereimeter is 60 cms,the longest side is
(A) 7
(B) 30
(C) 28
(D) 25
(E) 16
Rationale: 3x+5x+7x=60
15x=60
x=4
longest side=7*4=28
ANSWER:C
Answer: (C) 28
Question: There are 6 equally spaced points A,B,C,D,E and F marked on a circle with radius R. How many convex pentagons of distinctly different areas can be drawn using these points as vertices?
(A) 6P5
(B) 1
(C) 5
(D) None of these
(E) Cannot be determined
Rationale: Solution:
Since, all the points are equally spaced; hence the area of all the convex pentagons will be same.
Answer: Option D
Answer: (D) None of these
Question: If in a kindergarten class, there are five children 3 feet 4 inches tall (indicated by notation 3'4"), two children 4'3" tall and thirteen children 2'4" tall, which of the following is the median height of the children?
(A) 2'2"
(B) 2'4"
(C) 3'3"
(D) 3'4"
(E) 4'3
Rationale: Total number of children in class = 20
so median must be between 10th and 11th child when they are arranged in ascending order.
When arranged in ascending order 5th and 6th child will have the height of 3'4"
so required median height = (2'4"+2'4")/2 = 2'4"
Ans:Option B
Answer: (B) 2'4"
Question: Find the odd man out
2, 7, 32, 157, 782, 3907, 17251
(A) 7
(B) 32
(C) 157
(D) 3907
(E) 17251
Rationale: 1*5-3 = 2
2*5-3 = 7
7*5-3 = 32
32*5-3 = 157
157*5-3 = 782
782*5-3 = 3907
3907*5-3= 19532
ANSWER:E
Answer: (E) 17251
Question: Find the ratio between whole surfaces of a sphere and a hemisphere?
(A) 4:3
(B) 3:4
(C) 3:2
(D) 5:2
(E) 4:6
Rationale: 4 Ï€r2 : 3 Ï€r2 => 4:3
ANSWER A
Answer: (A) 4:3
Question: At a meeting of the 5 Joint Chiefs of Staff, the Chief of Naval Operations does not want to sit next to the Chief of the National Guard Bureau. How many ways can the 5 Chiefs of Staff be seated around a circular table?
(A) 120
(B) 480
(C) 960
(D) 2520
(E) 5040
Rationale: Bunuel, I'm also a little confused with the number of arrangements of n distinct objects in a circle. Why is it given by (n-1)!. In theveritasanswer they say:answer D (2520), should be the number of ways to arrange all 7 without the seating restriction given. Is this incorrect?D
Answer: (D) 2520
Question: How much time will it take for an amount of 600 to yield 81 as interest at 4.5% per annum of simple interest?
(A) 3 years
(B) 4 years
(C) 6 years
(D) 5 years
(E) 7 years
Rationale: Time = (100 x 81)/(600 x 4.5) years = 3 years.
answer A
Answer: (A) 3 years
Question: In Kaya's teacher's desk there are 9 pink highlighters, 8 yellow highlighters, and 5 blue highlighters. How many highlighters are there in all?
(A) 11
(B) 22
(C) 77
(D) 33
(E) 88
Rationale: Add the numbers of highlighters.
9 + 8 + 5 =22.
Answer is B.
Answer: (B) 22
Question: Calculate 469138 x 9999 = ?
(A) 4586970843
(B) 4686970743
(C) 4690910862
(D) 4586870843
(E) NONE
Rationale: Answer
469138 x 9999 = 469138 x (10000-1)
= 4691380000 - 469138
= 4690910862.
Option: C
Answer: (C) 4690910862
Question: A rectangular box measures internally 1.6m long, 1m broad and 60cm deep. The number of cubical box each of edge 20cm that can be packed inside the box is:
(A) 30
(B) 60
(C) 90
(D) 120
(E) 140
Rationale: Explanation:
Number of blocks =(160x100x60/20x20x20)=120
Answer: D
Answer: (D) 120
Question: Free notebooks were distributed equally among children of a class. The number of notebooks each child got was one-eighth of the number of children. Had the number of children been half, each child would have got 16 notebooks. Total how many notebooks were distributed ?
(A) 256
(B) 512
(C) 432
(D) 352
(E) 640
Rationale: Let total number of children be x.
Then, x *(1/8)x =(x/2)x 16
x = 64.
Number of notebooks =(1/8)x^2 =(1/8)x 64 x 64= 512.
Answer is B.
Answer: (B) 512
Question: A mixture contains alcohol and water in the ratio 4 : 3. If 5 litres of water is added to the mixture, the ratio becomes 4: 5. Find the quantity of alcohol in the given mixture
(A) 10 litres
(B) 20 litres
(C) 30 litres
(D) 5 litres
(E) 14 litres
Rationale: Let the quantity of alcohol and water be 4x litres and 3x litres respectively
4x/(3x+5)=4/5 20x=4(3x+5)8x=20 x=2.5
Quantity of alcohol = (4 x 2.5) litres = 10 litres.
ANSWER A 10 litres
Answer: (A) 10 litres
Question: What is the least number should be added to 1056, so the sum of the number is completely divisible by 25?
(A) 19
(B) 20
(C) 32
(D) 41
(E) 53
Rationale: (1056 / 25) gives remainder 6
19 + 6 = 23, So we need to add 19
A
Answer: (A) 19
Question: If a : b = 2 : 3, find the value of (3a + 5b) : (3a – b)
(A) 2 : 7
(B) 7 : 1
(C) 2 : 5
(D) 4 : 9
(E) None of these
Rationale: Explanation:
Given: a/b = 2/3
(3a + 5b) / (3a – b)
= [3(a/b) +5] / [3(a/b) – 1]
= [3(2/3) +5] / [3(2/3) – 1]
= 7/1
ANSWER: B
Answer: (B) 7 : 1
Question: The size of a flat-screen tablet is given as the length of the screen’s diagonal. How many square inches greater is the screen of a square 6-inch flat-screen tablet than a square 5 -inch flat-screen tablet?
(A) 5.0
(B) 6.0
(C) 6.8
(D) 5.8
(E) 5.5
Rationale: If we take a square with side length x and draw a diagonal, we get two isosceles right triangles.
If we focus on one such right triangle, we see that the legs have length x.
square 6-inch flat-screen television
The diagonal (hypotenuse) = 6
So, we can apply the Pythagorean Theorem to get x² + x² = 6²
Simplify: 2x² = 6²
Divide both sides by 2 to get: x² = 6²/2
Since the area of the square = x², we can see that the area of this square is 6²/2
square 5-inch flat-screen television
The diagonal (hypotenuse) = 5
So, we can apply the Pythagorean Theorem to get x² + x² = 5²
Simplify: 2x² = 5²
Divide both sides by 2 to get: x² = 5²/2
Since the area of the square = x², we can see that the area of this square is 5²/2
DIFFERENCE IN AREAS =6²/2-5²/2
= (6²- 5²)/2 = (36-25)/2 =11/2=5.5
E
Answer: (E) 5.5
Question: A train passes a man standing on the platform. If the train is 160 meters long and its speed is 72 kmph, how much time it took in doing so?
(A) 6 Â½ sec
(B) 6 Â½ sec
(C) 9 Â½ sec
(D) 8 sec
(E) 7 Â½ sec
Rationale: D
8 sec
D = 160
S = 72 * 5/18 = 20 mps
T = 160/20 = 8 sec
Answer: (D) 8 sec
Question: Sarah invested $38,700 in an account that paid 6.2% annual interest, compounding monthly. She left the money in this account, collecting interest for three full years. Approximately how much interest did she earn in the last month of this period?
(A) $239.47
(B) $714.73
(C) $2793.80
(D) $7,888.83
(E) $15,529.61
Rationale: 1% of 38700 is 387
6% is approximately 2400
At the end of first year, total amount = 38700+2400 = 41000 (approx)
At the end of second year, total amount = 41000+2400 (6% of 41000 works out to approximately the same) = 43400 (approx)
So total earnings for third year cannot be more than 6% of 43400 i.e at max $3000
So monthly earning has to be in the range of 250.
Answer is A
Answer: (A) $239.47
Question: There is a 35 cm line marked at each centimeter and an insect is placed at every centimeter. 9 frogs are trained to jump a constant distance. The first one jumps 2 cm in every leap, the second one jumps 3 cm and so on until the 9th one jumps 10 cm in every leap and they eat any insect that is available at that spot. If all of them start from start line and finish the entire 35 cm, how many insects were still left after the race was over?
(A) 0
(B) 4
(C) 6
(D) 7
(E) 10
Rationale: Only the prime numbers greater than 10 and less than 35 were left.
That is 11, 13, 17, 19, 23, 29, and 31.
The total is 7.
The answer is D.
Answer: (D) 7
Question: If 4 gallons of gasoline are added to a tank that is already filled to 3/4 of its capacity, the tank is then filled to 9/10 of its capacity. How many gallons does the tank hold?
(A)  20
(B)  24
(C)  36
(D)  40
(E)  60
Rationale: Let the Capacity of the tank=C
(3/4)C + 4= (9/10)C
=>(9/10)C - (3/4)C = 4
=>(3/20)C = 4
=>C = (4*20)/3 = 26.66
Number of gallons of gasoline that the tank currently holds = 3/4*C +4 = 19.99+4 = 23.99=24
Answer B
Answer: (B)  24
Question: A man has Rs. 800 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
(A) 370
(B) 380
(C) 220
(D) 900
(E) 150
Rationale: Let number of notes of each denomination be x.
Then, x + 5x + 10x = 800 16x = 800 x = 50.
Hence, total number of notes = 3x = 150.
Answer:E
Answer: (E) 150
Question: Find the area of circle whose radius is 7m?
(A) 121 sq m
(B) 184 sq m
(C) 174 sq m
(D) 124 sq m
(E) 154 sq m
Rationale: the area of circle =pie* r^2
=22/7 * 7 * 7 = 154 sq m
ANSWER:E
Answer: (E) 154 sq m
Question: A man sold two similar houses each for Rs. 1,00,000 one at a gain of 20% and another at a loss of 20%. What is net gain or loss?
(A) 4%
(B) 6%
(C) 5%
(D) 3%
(E) 2%
Rationale: Explanation :
Solution: Here always net loss of (20/100)^2 % = 4%.
Answer : A
Answer: (A) 4%
Question: A started a business with an investment of Rs. 70000 and after 6 months B joined him investing Rs. 120000. If the profit at the end of a year is Rs. 65000, then the share of B is?
(A) A)30000
(B) B)34000
(C) C)34098
(D) D)33007
(E) E)44098
Rationale: Ratio of investments of A and B is (70000 * 12) : (120000 * 6) = 7 : 6
Total profit = Rs. 65000
Share of B = 6/13 (65000)
= Rs. 30000
Answer:A
Answer: (A) A)30000
Question: If 9 spiders make 9 webs in 9 days, then how many days are needed for 1 spider to make 1 web?
(A) 5 days
(B) 7 days
(C) 8 days
(D) 9 days
(E) 6 days
Rationale: Let, 1 spider make 1 web in a days.
More spiders, Less days (Indirect proportion)
More webs, more days (Direct proportion)
Hence we can write as
(spiders)9:1
}::a:9
(webs)1:9
⇒7×1×7=1×7×a
⇒a=7
ANSWER:B
Answer: (B) 7 days
Question: A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 180 m in 18 sec. then find the length of the train?
(A) 145
(B) 180
(C) 181
(D) 184
(E) 150
Rationale: Length of the train be ‘X’
X + 120/15 = X + 180/18
6X + 720 = 5X + 900
X = 180m
Answer: Option B
Answer: (B) 180
Question: A group of 4 students bought movie tickets in one row next to each other. If Bob and Lia are in this group, what is the probability that Bob and Lia will each sit next to only one of the three other students from the group?
(A) 5.67%
(B) 16.67%
(C) 15.57%
(D) 20.25%
(E) 25.75%
Rationale: The question basically asks about the probability that Bob and Lisa sit at the ends.
The total # of sitting arrangements is 4!.
Desired arrangement is either BYZL or LYZB. Now, YZ can be arranged in 2! ways, therefore total # of favorable arrangements is 2*2!.
P=(favorable)/(total)=(2*2!)/4!=1/6.
Answer: B.
Answer: (B) 16.67%
Question: X and Y start a business with Rs.3000 and Rs.6000 respectively. Hoe should they share their profits at the end of one year?
(A) 3:1
(B) 2:1
(C) 1:2
(D) 1:3
(E) 1:4
Rationale: Explanation:
They should share the profits in the ratio of their investments.
The ratio of the investments made by X and Y =
3000 : 6000 => 1:2
Answer:C
Answer: (C) 1:2
Question: During 2001, a stock lost 80 percent of its value. During the following year, the stock's value increased by 300 percent. Which of the following is the percent change in the stock's value during those two years?
(A) 60 percent decrease
(B) 20 percent decrease
(C) 20 percent increase
(D) 60 percent increase
(E) 140 percent increase
Rationale: Let the value of the stock in 2000 be 100, then in 2001 its value would be 100*(1-80/100)=100*0.2=20 and in 2002 its value would be 20*(1+300/100)=80. Hence during those two years the value of the stock decreased from 100 to 80, so by 20%.
Answer: B.
Answer: (B) 20 percent decrease
Question: Solution Y is 30 percent liquid X and 70 percent water. If 2 kilograms of water evaporate from 6 kilograms of solution Y and 2 kilograms of solution Y are added to the remaining 4 kilograms of liquid, what percent of this new solution is liquid X?
(A) 33%
(B) 35 1/2%
(C) 37%
(D) 40%
(E) 42%
Rationale: In 8 kilograms of solution Y there are 0.3*6=1.8 kilograms of solution X;
After 2 kilograms of water are replaced by 2 kilograms of solution Y, to the existing 1.8 kilograms of solution X, 0.3*2=0.6 kilograms of solution X are added, so in the new solution of 6 kilograms there are 1.8+0.6=2.4 kilograms of solution X, which is 2.4/6*100=40% of this new solution.
Answer: D.
Answer: (D) 40%
Question: (51+ 52 + 53 + ... + 100) = ?
(A) 2525
(B) 2975
(C) 3225
(D) 3775
(E) 2753
Rationale: Explanation:
This is an A.P. in which a = 51, l = 100 and n = 50.
Sum =	n	(a + l)	=	50	x (51 + 100) = (25 x 151) = 3775.
2	2
Answer: D
Answer: (D) 3775