mathewhe/aqua_rat huggingface dataset:
Question: The true discount on Rs. 1760 due after a certain time at 12% per annum is Rs. 160. The time after which it is due is :
(A) 6 months
(B) 8 months
(C) 9 months
(D) 10 months
(E) None
Rationale: Solution
P.W = Rs. (1760 - 160) = Rs. 1600.
∴ S.I on Rs.1600 ar 12% is Rs. 160.
∴ Time = 100 x 160/1600x12 ) = 5/6years = ( 5/6x12 ) months = 10 months.
Answer D
Answer: (D) 10 months
Question: A train 800 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?
(A) 532 m
(B) 537 m
(C) 500 m
(D) 846 m
(E) 536 m
Rationale: Speed = 78 * 5/18 = 65/3 m/sec.
Time = 1 min = 60 sec.
Let the length of the train be x meters.
Then, (800 + x)/60 = 65/3
x = 500 m.
Answer:C
Answer: (C) 500 m
Question: Amithab's average expenditure for the January to June is Rs. 4200 and he spends Rs.1200 in January and Rs.1500 in july.The average expenditure for the months of febraury to July is
(A) Rs. 4250
(B) Rs. 4228
(C) Rs. 4128
(D) Rs. 4988
(E) Rs. 4192
Rationale: Amithab's total expenditure for Jan - June = 4200 x 6 = 25200
Expenditure for Feb - June = 25200-1200 = 24000
Expenditure for the months of Feb - July = 24000 + 1500 =25500
The average expenditure = {25500}/{6}=4250
Answer: A
Answer: (A) Rs. 4250
Question: A taxi driver states that his cab number is divisible by the no 2,3,4,5,6 with a remainder of 1 and when the number is divided by 11 it does not give any remainder
(A) 101
(B) 11
(C) 121
(D) 111
(E) 131
Rationale: on finding the LCM of 2,3,4,5 & 6 we get the value as 60 ,on adding 1 to 60 satisfy the first condition
Now 61 not divisible by 11
Then multiply 60 by 2,
we get 120: 120+1, 121 is exactly divisible by 11
ANSWER:C
Answer: (C) 121
Question: Company S produces two kinds of radios: basic and deluxe. Of the radios produced by Company S last month, 2/3 were basic and the rest were deluxe. If it takes 7/5 as many hours to produce a deluxe radio as it does to produce a basic radio, then the number of hours it took to produce the deluxe radio last month was what fraction of the total number of hours it took to produce all the radios?
(A) 7/17
(B) 2/3
(C) 8/17
(D) 6/17
(E) 3/4
Rationale: No of basic radios was 2/3 of total and # of deluxe radios was 1/3 of total, let's assume total=12, then Basic=8 and Deluxe=4.
Now, if time needed to produce one Deluxe rdio is 1 unit than time needed to produce one Basic radio would be 7/5 units. Total time for Basic would be 8*1=8 and total time for Deluxe would be 4*7/5=28/5 --> total time for both of them would be 8+28/5 -->68/5 deluxe/total=28/5 / 68/5 = 28/68 =7/17
Answer: A.
Answer: (A) 7/17
Question: A train 100 meters long completely crosses a 300 meters long bridge in 12 seconds. What is the speed of the train is?
(A) 32 kmph
(B) 76 kmph
(C) 120 kmph
(D) 43 kmph
(E) 40 kmph
Rationale: S = (100 + 300)/12
= 400/12 * 18/5
= 120
Answer:C
Answer: (C) 120 kmph
Question: John has on his shelf four books of poetry, four novels, and two reference works. Suppose from these ten books, we were to pick two books at random. What is the probability that we pick one novel and one reference work?
(A) 1/2
(B) 2/5
(C) 3/10
(D) 7/20
(E) probability= 8/45
Rationale: For the denominator, we are going to pick two books from among ten total: a combination of two from ten. Again, we will use the formula:
nC2 = n(n-1)/2
which, for profound mathematical reasons we need not address here, is also the formula for the sum of the first (n – 1) positive integers. Here
10C2=10(9)/2=5*9=45
That’s the total number of pairs of books we could pick from the ten on the shelf. That’s our denominator.
Now, the numerator. We want one novel and one reference work. Well, there are four novels and two reference works, so by the FCP, the number of ways we can pick this is 4 x 2 = 8. That’s the total possible number of pairs involving exactly one of these four novels and exactly one of these two reference works. That’s our numerator.
probability = 8/45
Answer = E
Answer: (E) probability= 8/45
Question: One student to pass the subject as probability 1/4. another man to get driving licence and student passed subject probability 1/6. find the probability man get driving licence.
(A) 1/3
(B) 2/3
(C) 4/3
(D) 5/3
(E) 1/4
Rationale: Let the probability of the man get driving licence is x.
so, 1/4 * x = 1/6
x = 2/3.
ANSWER:B
Answer: (B) 2/3
Question: In how many ways can be 5 boys and 5 girls sit around circular table so that no two boys sit next to each other?
(A) (5!)^2
(B) (6!)^2
(C) 5!4!
(D) 11!
(E) (5!)^2*6!
Rationale: first fix one boy and place other 4 in alt seats so total ways is 4!
now place each girl between a pair of boys... total ways of seating arrangement of girls 5!
total is 5!*4!
ANS C
Answer: (C) 5!4!
Question: R is the set of all positive integers x such that x^2 is a multiple of both 27 and 375. Which of the following integers must be a divisor of every integer x in R?
I. 9
II. 15
III. 27
(A) I only
(B) II only
(C) I and II only
(D) I and III only
(E) I, II, and III
Rationale: Ans: C
R->{x} where x^2 is a multiple of both 27 and 375 means 3^3 and (5^3)*3
means x must contain 3^2 and 5^2
so with these conditions we know that 9=3^2 and 15=3*5 both have required factors for the divisibility of lowest int for x which is 9*25
but 27 is not a divisor because it can't divide 9*25 fully.
so Ans : C
Answer: (C) I and II only
Question: A waiter's salary consists of his salary and tips. During one week his tips were 5/4 of his salary. What fraction of his income came from tips ?
(A) 4/9
(B) 5/4
(C) 5/8
(D) 5/9
(E) 6/9
Rationale: Income = salary (s) +tips = s + s*5/4 = s*9/4
Tips = s*5/4
fraction of his income came from tips = (s*5/4)/(s*9/4)= 5/9
ANSWER:D
Answer: (D) 5/9
Question: What will come in place of (a) in the following expression?
a - 796.21 + 498.05 = 215.50 – 300.01
(A) 431.65
(B) 488.6
(C) 388.67
(D) 431.2
(E) 488.61
Rationale: Explanation:
a - 796.21 + 498.05 = 215.50 - 425.01
a = 413.65
ANSWER: A
Answer: (A) 431.65
Question: Mangala completes a piece of work in 30 days, Raju completes the same work in 45 days. If both of them work together, then the number of days required to complete the work is
(A) 18 days
(B) 6 days
(C) 8 days
(D) 10 days
(E) 11 days
Rationale: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days.
That is, the required No. of days = 30 × 45/75 = 18 days.
Answer : A
Answer: (A) 18 days
Question: In what time will a train 120 m long cross an electric pole, it its speed be 144 km/hr?
(A) 2.5
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: Speed = 144 * 5/18 = 40 m/sec
Time taken = 120/40 = 3 sec.
Answer: Option B
Answer: (B) 3
Question: 4 liters of a 20 percent solution of alcohol in water are mixed with 5 liters of a 10 percent alcohol in water solution. What is the percentage of alcohol in the new solution?
(A) 14.4%
(B) 14.8%
(C) 15.2%
(D) 15.6%
(E) 16.0%
Rationale: The total amount of alcohol is 0.2(4) + 0.1(5) = 1.3 liters.
The percentage is 1.3 / 9 = 13 / 90 which is about 14.4%
The answer is A.
Answer: (A) 14.4%
Question: Amit and Ian paint a wall in alternating shifts. First Amit paints alone, then Ian paints alone, then Amit paints alone, etc. During each of his shifts, Amit paints 1/2 of the remaining unpainted area of the wall, while Ian paints 1/3 of the remaining unpainted area of the wall during each of his shifts. If Amit goes first, what fraction of the wall's area will remain unpainted after Amit has completed his 3th shift?
(A) 1/17
(B) 1/54
(C) 1/81
(D) 1/162
(E) 1/216
Rationale: Fraction of area unpainted after FIRST shift of Amit = 1-(1/2) = 1/2
Fraction of area unpainted after FIRST shift of Ian = (1/2)-(1/3)(1/2) = (2/3)(1/2)
Fraction of area unpainted after SECOND shift of Amit = (1/2)(2/3)(1/2)
Fraction of area unpainted after SECOND shift of Ian = (2/3)(1/2)(2/3)(1/2)
Fraction of area unpainted after THIRD shift of Amit = (1/2)(2/3)(1/2)(2/3)(1/2)=1/18
Answer: option A
Answer: (A) 1/17
Question: Company P had 15 percent more employees in December than it had in January. If Company P had 490 employees in December, how many employees did it have in January?
(A)  391
(B)  426
(C)  410
(D)  423
(E)  445
Rationale: D = number of employees in December
J = number of employees in January
J x 1.15 = D
J x 1.15 = 490
J = 490/1.15
J = 49,000/115 = 426
Thus B is the correct answer.
Answer: (B)  426
Question: Today is Tuesday. A person wants to meet a lawyer and as that lawyer is busy he asks him to come three days after the before day of the day after tomorrow? On which day the lawyer asks the person to come?
(A) Saturday
(B) MONDAY
(C) TUESDAY
(D) WEDNESDAY
(E) FRIDAY
Rationale: Today is Tuesday
after three days--->Friday
now, (Friday)after before day--->Thursday
then, (Thursday)day after tomorrow--->Saturday
ANSWER:A
Answer: (A) Saturday
Question: Two vessels A and B contain milk and water mixed in the ratio 8:5 and 5:2 respectively. The ratio in which these two mixtures be mixed to get a new mixture containing milk and water in the ratio 9:4
(A) 2:7
(B) 5:2
(C) 3:5
(D) 5:7
(E) 6:7
Rationale: Soln:-
Required Ratio = (5/7−9/13)/(9/13−8/13)
= 2/7
Answer: A
Answer: (A) 2:7
Question: There are 6 magazines lying on a table; 3 are fashion magazines and the other 3 are sports magzines. If 2 magazines are to be selected at random from the 8 magazines, what is the probability that at least one of the fashion magazine will be selected?
(A) 4/5
(B) 8/9
(C) 4/6
(D) 1/2
(E) 3/6
Rationale: 1- (3c2/6c2) = 1-1/5 = 4/5
Answer : A
Answer: (A) 4/5
Question: Two employees X and Y are paid a total of Rs. 660 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.150
(B) s.200
(C) s.250
(D) s.350
(E) s.300
Rationale: Let the amount paid to X per week = x
and the amount paid to Y per week = y
Then x + y = 660
But x = 120% of y = 120y/100 = 12y/10
âˆ´12y/10 + y = 660
â‡’ y[12/10 + 1] = 660
â‡’ 22y/10 = 660
â‡’ 22y = 6600
â‡’ y = 6600/22 = 600/2 = Rs.300
E
Answer: (E) s.300
Question: A certain sum of money at simple interest amounted Rs.850 in 10 years at 3% per annum, find the sum?
(A) 651.85
(B) 652.85
(C) 653.85
(D) 654.85
(E) 655.85
Rationale: 850 = P [1 + (10*3)/100]
P = 653.85
Answer: C
Answer: (C) 653.85
Question: A person can swim in still water at 4 km/h. If the speed of water 2 km/h, how many hours will the man take to swim back against the current for 14km?
(A) 3
(B) 6
(C) 8
(D) 9
(E) 7
Rationale: M = 4
S = 2
US = 4 - 2 = 2
D = 14
T = 14/2 = 7
Answer:E
Answer: (E) 7
Question: 800 students took the test on English and Maths. 35% students failed in english and 45% failed in maths. 40% of those who passed in maths also passed in english, then how many students failed in both ?
(A) 162
(B) 138
(C) 16
(D) 38
(E) 12
Rationale: Passed in english = 65%
Passed in maths = 55%
Passed in both = 40% of 55% = 2/5 * (55%) = 22%
Passed in (English + Maths - Both + Neither) = 100%
65 + 55 - 22 + Neither = 100
Neither = 100 - 98 = 2% = 0.02 * 800 = 16
Answer: C
Answer: (C) 16
Question: If the selling price of 50 articles is equal to the cost price of 25 articles, then the loss or gain percent is:
(A) 45%
(B) 23%
(C) 20%
(D) 60%
(E) 50%
Rationale: C.P. of each article be Re. 1.
Then, C.P. of 50 articles = Rs. 50;
S.P. of 50 articles = Rs. 25.
Loss % = 25/50 * 100 = 50%
ANSWER E
Answer: (E) 50%
Question: 3 women and a few men participated in a chess tournament. Each player played two matches with each of the other players. If the number of matches that men played among themselves is 78 more than those they played with the women, how many more men than women participated in the tournament?
(A) 20
(B) 15
(C) 11
(D) 10
(E) 19
Rationale: Let x be the number of men.
Number of matches men play among themselves is 2*(xC2)
Number of matches men play with women is 2*(3x)
2*(xC2) - 2*(3x) =78
x=13
Difference between men and women is 13-3=10.
ANSWER D
Answer: (D) 10
Question: A train 110 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: Speed of train relative to man = (60 + 6) km/hr = 66 km/hr
[66 * 5/18] m/sec = [55/3] m/sec.
Time taken to pass the man = [110 * 3/55] sec = 6 sec
Answer: Option B
Answer: (B) 6
Question: In the infinite sequence 50, 60, 70, 80, 90, . . . , where each term is 10 greater than the previous term, the 100th term is
(A) 1330
(B) 1807
(C) 1910
(D) 1040
(E) 2060
Rationale: T(n) = a + (n-1) d
Here d =10, a=50, n=100
Solving we get T(n) = 1040.
Answer: D
Answer: (D) 1040
Question: If C.P. of 26 books is equal to S.P of 30 books , then your gain or loss is ?
(A) 23 1/3 gain %
(B) 30 10/23 loss %
(C) 13 1/3 loss %
(D) 30 1/3 loss %
(E) 40 1/3 loss %
Rationale: Say the cost price of 26 books is $26 so $1 for a book.
The cost of 30 books would be $30, and the selling price of 30 books would be 26$, hence the loss = ($30 - $26)/$30 = ~13.3%.
Answer: C.
Answer: (C) 13 1/3 loss %
Question: Beth received 3/12 of the votes cast in a certian election. What franction of the other votes cast would she have needed in order to have received 1/2 of the votes cast?
(A) 1/5
(B) 2/7
(C) 3/9
(D) 7/20
(E) 1/2
Rationale: Let the total votes be 12. Beth received 3 votes, other votes 12-3=9. In order to have received 1/2 of the votes she needed 6 votes so 3 more, which is 3/9 of the other votes.
Answer: C.
Answer: (C) 3/9
Question: Four barrels of water have an average capacity of 8 gallons. What is the maximum possible capacity of the smallest barrel Y if the median is 10 gallons?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Suppose 4 barrels are B1, B2, B3, B4 in ascending capacity.
(B1+B2+B3+B4)/4 = 8
B1+B2+B3+B4=32
median is 10 ....... as the no. of terms are even i.e 4, median = (B2+B3)/2
==> B2+B3 = 20
now we have B1+B4 = 32-20 =12
Only the following possible cases can be there :
1,9,11,11
1,10,10,11
2,10,10,10
Max value of smallest barrel Y= 2
Answer: (B) 2
Question: A circular grass lawn of 35 metres in radius has a path 7 metres wide running around it on the outside. Find the area of path.
(A) 1694 m2
(B) 1700 m2
(C) 1598 m2
(D) 1500 m2
(E) None of thes
Rationale: Radius of a circular grass lawn (without path) = 35 m
∴ Area = πr2 = π(35)2
Radius of a circular grass lawn (with path)
= 35 + 7 = 42 m
∴ Area = πr2 = π(42)2
∴ Area of path = π(42)2 – π(35)2
= π(422 – 352) = π( 42 + 35)(42 – 35)
Answer A
Answer: (A) 1694 m2
Question: X starts a business with Rs.45000. Y joins in the business after 3 months with Rs.30000. What will be the ratio in which they should share the profit at the end of the year?
(A) 1:2
(B) 2:1
(C) 1:3
(D) 3:1
(E) 4:2
Rationale: Explanation:
Ratio in which they should share the profit
= Ratio of the investments multiplied by the time period
=45000Ã—12:30000Ã—9=45Ã—12:30Ã—9=3Ã—12:2Ã—9=2:1
ANSWER IS B
Answer: (B) 2:1
Question: In how many ways can three boys can be seated on five chairs?
(A) 30
(B) 40
(C) 60
(D) 80
(E) 90
Rationale: There are three boys.
The first boy can sit in any of the five chairs (5 ways).
5
Now there are 4 chairs remaining. The second boy can sit in any of the four chairs (4 ways).
5 4
Now there are 3 chairs remaining. The third boy can sit in any of the three chairs (3 ways).
5 4 3
Hence, total number of ways in which 3 boys can be seated on 5 chairs
=5×4×3=60
ANSWER C 60
Answer: (C) 60
Question: The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 600 resolutions?
(A) 844.8 m
(B) 704 m
(C) 774 m
(D) 714 m
(E) 744 m
Rationale: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 600 resolutions.
= 600 * 2 * 22/7 * 22.4 = 84480 cm
= 844.8 m
Answer:A
Answer: (A) 844.8 m
Question: We have a 630 ml of mixture of milk and water in the ratio 7:2. How much water must be added to
make the ratio 7:3?
(A) 70 ml
(B) 60 ml
(C) 80 ml
(D) 50 ml
(E) None of these
Rationale: Explanation :
concentration of water in mixture1 = 2/9 (Since the ratio of milk and water = 7:2) ---item(1)
concentration of water in pure water= 1 ---item(2)
Now the above mentioned items are mixed to form a mixture2 where milk and water ratio = 7: 3
=>concentration of water in mixture2 = 3/10
By the rule of alligation, we have
concentration of water
in mixture1 : 2/9 concentration of water
in pure water : 1
Mean concentration
3/10
1 - 3/10 = 7/10 3/10 - 2/9 = 7/90
=> Quantity of mixture1 : Quantity of water = 7/10 : 7/90 = 1/10 : 1/90 = 1 : 1/9
Given that Quantity of mixture1 = 630 ml
=> 630 : Quantity of water = 1 : 1/9
⇒Quantity of water = 630×19=70 ml
Answer : Option A
Answer: (A) 70 ml
Question: When the integer y is divided by 12, the remainder is 3. Which of the following, when divided by 12, will have a remainder of 6 ?
I. 2y
II. 6y
III. 4y + 6
(A)  I only
(B)  II only
(C)  III only
(D)  I and II only
(E)  I, II, and III
Rationale: is it E.
y = 12*a + 3
2y = 12*2*a + 6
6y = 12*6*a + 18 ( 18 = 12+6)
4y + 6 = 12*4*a + 18 (18 = 12 + 6)
Answer: (E)  I, II, and III
Question: How many 5 letter words ( with or without meaning) can be formed using all the following 5 letters P,Q,R,V,and T so that letter P is to the left of letter R?
(A) 90
(B) 60
(C) 120
(D) 144
(E) 160
Rationale: Two positions can be selected out of 5 positions in 5C2 ways = 10 ways.
And the remaining 3 letters can be placed in 3 posions in 3! Ways = 6 ways.
So the final Answer = number of ways letters P and R can be arranged x number
of ways the other 3 letters can be arranged
Final Answer = 10 x 6 = 60 ways
B
Answer: (B) 60
Question: If s and t are positive integers such that s/t = 17.14, which of the following could be the remainder when s is divided by t ?
(A) 20
(B) 45
(C) 49
(D) 23
(E) 45
Rationale: s/t= 17.14
s = 17.14t
s = (17 + 0.14)t
s = 17t + (14/100)t
s = 17t + (7/50)t
So remainder will be multiple of 7. The only multiple of 7 is 49.
Ans. C
Answer: (C) 49
Question: A 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 24 sec. What is the length of the platform?
(A) 389 m
(B) 350 m
(C) 187.5 m
(D) 299 m
(E) 219.5 m
Rationale: Speed = 300/24 = 25/2 m/sec.
Let the length of the platform be x meters.
Then, (x + 300)/39 = 25/2
=> x = 187.5 m.
Answer:C
Answer: (C) 187.5 m
Question: How much interest will $8,000 earn in 9 months at an annual rate of 6%?
(A) $250
(B) $350
(C) $360
(D) $550
(E) $650
Rationale: Soln:-
9 months = 3/4 of year;
6% = 6/100=3/50;
$8,000(principal)*3/50(interest rate)*3/4(time)=$360.
ANSWER:C
Answer: (C) $360
Question: Today is Monday. After 61 days, it will be:
(A) Wednesday
(B) Saturday
(C) Tuesday
(D) Thursday
(E) Friday
Rationale: Each day of the week is repeated after 7 days.
So, after 63 days, it will be Monday.
After 61 days, it will be Saturday.
Answer: Option B
Answer: (B) Saturday
Question: Line k is in the rectangular coordinate system. If the c-intercept of k is -2, and the y-intercept is 3, which of the following is an equation of line k?
(A) -3c + 2y = 6
(B) 3c + 2y = -6
(C) 3c - 2y = 6
(D) 2c - 3y = 6
(E) -2c - 3y = 6
Rationale: This question can be solved in much simpler way.
To find the c intercept
Put y=0 in the equation of the line.
To find the y-intercept
Put c=0 in the equation of the line.
So
Sub c=0 in the answer choices check whether you are getting y=3.
A. -3c + 2y = 6 --- y = 3
B. 3c+ 2y = -6 --- y = -3
C. 3c - 2y = 6 ----- y = -3
D. 2c - 3y = 6 --- y = -2
E. -2c - 3y = 6 --- y =-2
Eliminate answer B,C,D and E.
So the answer is A.
Answer: (A) -3c + 2y = 6
Question: The sale price of an article including the sales tax is Rs. 616. The rate of sales tax is 10%. If the shopkeeper has made a profit of 12%, then the cost price of the article is:
(A) Rs. 500
(B) Rs. 515
(C) Rs. 550
(D) Rs. 600
(E) Rs. 700
Rationale: 110% of S.P. = 616
S.P. = (616 * 100)/110 = Rs. 560
C.P = (110 * 560)/112 = Rs. 500
ANSWER:A
Answer: (A) Rs. 500
Question: In an election between two candidates, one got 60% of the total valid votes, 30% of the votes were invalid. If the total number of votes was 9000, the number of valid votes that the other candidate got, was:
(A) 2500
(B) 2520
(C) 3000
(D) 3100
(E) None of these
Rationale: Explanation :
Number of valid votes = 70% of 9000
= 6300.
Valid votes polled by other candidates = 40% of 6300
(40/1006300)
= 2520.
Harsh Mishra a year ago
0 upvotes
Answer : B
Answer: (B) 2520
Question: Two numbers are respectively 20% and 25% more than a third number. The percentage that is first of the second is?
(A) 12
(B) 687
(C) 26
(D) 96
(E) 12
Rationale: I II III
120 125 100
125----------120
100-----------? => 96%
Answer:C
Answer: (C) 26
Question: A rectangular grassy plot 110 m. by 65 m has a gravel path 2.5 m wide all round it on the inside. Find the cost of gravelling the path at 50 paise per sq. metre
(A) s425
(B) s780
(C) s880
(D) s480
(E) s980
Rationale: area of the plot=110m*65m=7150sq.m
area of plot excluding gravel=105m*60m=6300sq.m
area of gravel =7150sq.m-6300sq.m =850sq.m
cost of building it = 850sq.m*50
= 42500p
in Rs =42500/100=Rs425
ANSWER:A
Answer: (A) s425
Question: An article is bought for Rs.685 and sold for Rs.900, find the gain percent?
(A) 33 1/8%
(B) 33 8/3%
(C) 33 1/3%
(D) 31 12/31%
(E) 32 1/3%
Rationale: 685 ---- 215
100 ---- ? => 31 12/31%
Answer: D
Answer: (D) 31 12/31%
Question: 1/0.04 is equal to
(A) 25.5
(B) 2.5
(C) 25
(D) .25
(E) None of these
Rationale: Explanation:
1/0.04 = (1 * 100)/4 = 100/4 = 25
Option C
Answer: (C) 25
Question: The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder. What is the smaller number ?
(A) 226
(B) 523
(C) 775
(D) 890
(E) 270
Rationale: E
270
Let the smaller number be x. Then larger number = (x + 1365).
x + 1365 = 6x + 15
5x = 1350
x = 270
Smaller number = 270.
Answer: (E) 270
Question: All of the students of Music High School are in the band, the orchestra, or both. 70 percent of the students are in only one group. There are 111 students in the band. If 30 percent of the students are in the band only, how many students are in the orchestra only?
(A) 84
(B) 69
(C) 78
(D) 81
(E) 74
Rationale: % of students in one group only = 70%
% of students in both groups = 100 - 70 = 30%
% of students in the band only = 30%
Number of students who are in band = 111
30% + 30% = 60% = 111 Students
Finding total students:
x = (111 x 100)/60
x = 185
Students in orchestra only = 185 - 111 = 74
Answer:E
Answer: (E) 74
Question: Ayesha's father was 38 years of age when she was born while her mother was 36 years old when her brother seven years younger to her was born. What is the difference between the ages of her parents?
(A) 2 years
(B) 4 years
(C) 6 years
(D) 7 years
(E) 9 years
Rationale: Mother's age when Ayesha's brother was born = 36 years.
Father's age when Ayesha's brother was born = (38 + 7) years = 45 years.
Required difference = (45 - 36) years = 9 years.
Answer: Option E
Answer: (E) 9 years
Question: In a hostel there were 100 students. To accommodate 20 more students the average is decreased by rupees 5. But total expenditure increased by Rs.400. Find the total expenditure of the hostel now?
(A) 3800
(B) 4800
(C) 5100
(D) 5300
(E) 5400
Rationale: 100x + 400 = 12(x – 5)
x = 50
100 * 50 + 400 = 5400
E)
Answer: (E) 5400
Question: A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets Rs. 800 more than D, what is B's share?
(A) Rs. 1600
(B) Rs. 1500
(C) Rs. 2000
(D) Rs. 2500
(E) none of the above
Rationale: Let the shares of A, B, C and D be Rs. 5x, Rs. 2x, Rs. 4x and Rs. 3x respectively.
Then, 4x - 3x = 800
x = 800.
B's share = Rs. 2x = Rs. (2 x 800) = Rs. 1600.
Answer = A
Answer: (A) Rs. 1600
Question: A radio station has to choose two days of the seven in a week to broadcast a certain program, and that set will repeat each week. The program can be broadcast equally on any of the seven weekdays —- weekdays vs. weekends don’t matter at all —- nor does it matter whether the days the program airs are adjacent or not. Absolutely any two of the seven weekdays can be chosen. How many different two-day combinations of the seven weekdays can be constructed?
(A) 9
(B) 15
(C) 21
(D) 35
(E) 56
Rationale: Pick 2 days out of 7.. 7C2 = 21
Answer : C
Answer: (C) 21