mathewhe/aqua_rat huggingface dataset:
Question: Andy solves problems 80 to 125 inclusive in a Math exercise. How many problems does he solve?
(A) 53
(B) 52
(C) 51
(D) 46
(E) 49
Rationale: 125-80+1= 52
'D' is the answer
Answer: (D) 46
Question: Kamal was 4 times as old as his son 8 years ago. After 8 years, Kamal will be twice as old as his son. Find out the present age of Kamal.
(A) 30
(B) 35
(C) 40
(D) 45
(E) 50
Rationale: Let age of the son before 8 years =x
Then, age of Kamal before 8 years ago =4x
After 8 years, Kamal will be twice as old as his son
⇒4x+16=2(x+16)⇒x=8
Present age of Kamal
=4x+8=4×8+8=40
Answer is C.
Answer: (C) 40
Question: How long does a train 110 m long running at the speed of 72 km/hr takes to cross a bridge 175 m length?
(A) 12.9 sec
(B) 12.1 sec
(C) 17.9 sec
(D) 16.8 sec
(E) 14.25 sec
Rationale: Speed = 72 * 5/18 = 20 m/sec
Total distance covered = 110 + 175 = 285 m.
Required time = 285/20 = 14.25 sec.
Answer: E
Answer: (E) 14.25 sec
Question: Pipe A can fill a tank in 4 hours. Due to a leak at the bottom, it takes 8 hours for the pipe A to fill the tank. In what time can the leak alone empty the full tank?
(A) 13
(B) 17
(C) 18
(D) 8
(E) 12
Rationale: Let the leak can empty the full tank in x hours 1/4 - 1/x = 1/8
=> 1/x = 1/4 - 1/8 = (2 - 1)/8 = 1/8
=> x = 8.
Answer: D
Answer: (D) 8
Question: Train A travelling at 63 kmph takes 27 to sec to cross Train B when travelling in opposite direction whereas it takes 162 seconds to overtake it when travelling in the same direction. If the length of train B is 500 meters, find the length of Train A.
(A) 400 m
(B) 810 m
(C) 500 m
(D) 310 m
(E) 210 m
Rationale: DETAILED SOLUTION
Let the length of Train A be x meters
Let speed of Train B be y kmph
Relative distance = Relative speed * time taken to cross/overtake
Crossing scenario:
Relative speed of 2 trains = 63 + y
Time taken to cross = 27 sec or 27/3600 hrs
Relative distance between 2 trains = Length of Train A + length of train B = (x + 0.5) km
Therefore, x + 0.5 = (63 + y) * 27 / 3600 ----- (1)
Overtaking scenario:
Relative speed of 2 trains = 63 – y
Time taken to overtake = 162 sec or 162/3600 hrs
Relative distance between 2 trains = x + 0.5
Therefore, x + 0.5 = (63 – y) * 162/3600 --- (2)
From (1) and (2), solve for y.
(63 + y) * 27 = (63 – y) * 162
27y + 162 y = 63*162 – 63 *27
189y = 63 * 135 or y = 45 kmph
Substitute in (2) to get x.
x + 0.5 = (63 – 45) * 162/3600
Or x = 0.31 km or 310 meters
CORRECT ANSWER D
Answer: (D) 310 m
Question: What is the total number of integers between 200 and 500 that are divisible by 25?
(A) 20
(B) 25
(C) 14
(D) 15
(E) 18
Rationale: 125, 150, 175, ..., 450,475
This is an equally spaced list; you can use the formula:
n = (largest - smallest) / ('space') + 1 = (475- 125) / (25) + 1 = 350/25 + 1 = 14+ 1 = 15
Answer is D
Answer: (D) 15
Question: If Rs.400 amount to Rs.540 in 4 years, what will it amount to in 6 years at the same rate % per annum?
(A) s.575
(B) s.595
(C) s.590
(D) s.610
(E) s.585
Rationale: 80 = (400*4*R)/100
R = 8.75%
I = (400*6*8.75)/100 = 210
400 + 210 = 610
ANSWER:D
Answer: (D) s.610
Question: A car runs 10,000 miles using 5 tyres interchangeably. to have equal worn out by all tyres,how many miles each tyre should have run?
(A) 5000
(B) 8000
(C) 4000
(D) 3000
(E) 7000
Rationale: for 5 tyres running interchangeably 10,000 miles the car runs
for 1 tyre=10000/5=2000
as you all know i suppose the car has 4 tyre
to have equal worn out by 4 tyres we need=2000*4=8000
ANSWER:B
Answer: (B) 8000
Question: The salaries of A, B, C are in the ratio 2:3:5. If the increments of 15%, 10% and 20% are allowed respectively in their salaries, then what will be the new ratio of their salaries?
(A) 23:33:62
(B) 23:33:68
(C) 23:33:60
(D) 23:32:60
(E) 23:23:60
Rationale: Let A = 2k, B = 3k and C = 5k
A's new salary = 115/100 of 2k = 23/10 k
B's new salary = 110/100 of 3k = 33/10 k
C's new salary = 120/100 of 5k = 6k
New ratio = 23k/10 : 33k/10 : 6k = 23:33:60
Answer:C
Answer: (C) 23:33:60
Question: 600 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) 60
(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 * 600 = 12
Answer: E
Answer: (E) 12
Question: If
1 = 5
2 = 10
3 = 15
4 = 20
5 = 25
6 = 30
Then 25 = ?
Hint: Its a logic Riddle not a mathematical riddle
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: E
5
As stated
5=25 => 25=5
Answer is E
Answer: (E) 5
Question: Robert is traveling from one end of a forest to the other. In order to find his way back, he is leaving morsels of bread in the following pattern: 2 morsels of milk, 3 morsels of white, and 1 morsel of rye. The pattern repeats after he leaves the morsel of rye. If Robert drops 2,000 morsels of bread, what are the last 3 morsels of bread that he drops?
(A) rye − milk − milk
(B) milk − milk − white
(C) white − rye − milk
(D) white − white − white
(E) white − white − rye
Rationale: In a single round Robert drops 6 morsels.
Remainder (2000/6) = 2
Final action = 2 drops of milk --> Options B, C, D and E can be eliminated
Answer: A
Answer: (A) rye − milk − milk
Question: Over a three-week period, the price of an ounce of gold increased by 25% in the first week, decreased by 40% in the following week, and increased by 20% in the third week. If the price of gold was G dollars per ounce at the beginning of the three weeks, what was the price at the end of the three weeks?
(A) 0.75G
(B) 0.8G
(C) 0.85G
(D) 0.9G
(E) 0.95G
Rationale: After 3 weeks, the price was 1.2*0.6*1.25*G=0.9G
The answer is D.
Answer: (D) 0.9G
Question: Ashok and Pyarelal invested money together in a business and share a capital of Ashok is 1/9 of that of Pyarelal.if the incur a loss of Rs 2000 then loss of Pyarelal?
(A) 1600
(B) 1700
(C) 1800
(D) 1900
(E) 1000
Rationale: Let the capital of Pyarelal be x, then capital of Ashok=x/9
So ratio of investment of Pyarelal and Ashok = x : x/9 =9x : x
Hence out of the total loss of 2000, loss of Pyarelal= 2000*9x/10x=1800
ANSWER:C
Answer: (C) 1800
Question: 2,300 has how many positive divisors?
(A) 12
(B) 15
(C) 18
(D) 24
(E) 30
Rationale: By factorization, we can write 2300 as 2300=2^2*5^2*23.
The number of factors is (2+1)(2+1)(1+1) = 18
The answer is C.
Answer: (C) 18
Question: Every student at Larcy School is in at least one of three clubs: horseback riding, embroidery, and country dancing, which are the only clubs in existence at the school. The ratio of the number of students in exactly two clubs to the number of students in exactly one club is 4:3, while the ratio of the number of students in exactly two clubs to the number of students in at least two clubs is 5:7. Which of the following could be the total number of students at Larcy School?
(A) 63
(B) 69
(C) 74
(D) 82
(E) 86
Rationale: total number of students at Larcy School The answer is 86 or any multiple of 43.E
Answer: (E) 86
Question: If x = 3p, where p is a prime number greater than 2, how many different positive even divisors does x have, including x?
(A) 0
(B) 1
(C) 2
(D) 3
(E) It cannot be determined from the information given
Rationale: p is prime greater than 2 thus p is odd
3p is odd
Thus no even factors
Ans:A
Answer: (A) 0
Question: Three bells commence tolling together and toll at intervals of 2, 4, 6 seconds respectively. In 10 minutes, how many times do they toll together ?
(A) 51
(B) 52
(C) 53
(D) 54
(E) 55
Rationale: LCM of 2, 4, 6 is 12.
So, after each 12 seconds, they would toll together.
Hence, in 10 minutes, they would toll 10*60 seconds / 12 seconds = 50 times
But then the question says they commence tolling together. So, they basically also toll at thebeginning(0second).
So, total tolls together = 50+1 = 51
Answer: A
Answer: (A) 51
Question: One-third of Ramani’s savings in National Savings Certificate is equal to one-half of his savings in Public Provident Fund. If he has 150000 as total savings, how much he saved in Public Provident Fund?
(A) 60000
(B) 50000
(C) 90000
(D) 30000
(E) None of these
Rationale: Ratio of Ramani’s savings in NSC and PPF = 3: 2
His savings in PPF = 2⁄5 × 150000 = 60000
Answer A
Answer: (A) 60000
Question: Stock / Number of shares
V ------------ 68
W ---------- 112
X ------------ 56
Y ------------ 94
Z ------------ 45
The table shows the number of shares of each of the 5 stocks owned by Mr Sami. If Mr. Sami was to sell 20 shares of Stock X and buy 27 shares of stock Y, what would be the increase in the range of the numbers of shares of the 5 stocks owned by Mr. Sami?
(A) 4
(B) 6
(C) 9
(D) 18
(E) 20
Rationale: Based on the original number of shares, the range would be: 112 - 45 = 67
However, the prompt tells us that two of the values in the table are going to change. After the changes, the values will be:
V 68
W 112
X 36
Y 121
Z 45
Now the range is 121 - 36 = 85
The INCREASE in the range requires us to compare thenewrange to theoldrange: 85 - 67 = 18
D
Answer: (D) 18
Question: Swetha takes a trip and drives 8 hours from Town A to Town C at a rate of 40 miles per hour. On her way back, Swetha drives 30 miles per hour and stops in Town Y which is midway between Town A and Town C. How many hours does it take Swetha to drive from Town C to Town B?
(A) 1.01
(B) 1.25
(C) 1.53
(D) 5.33
(E) 2.0
Rationale: distance from A to C =8 hr* 40 mph= 320 miles
hence distance from B to C= 1/2*320=160
time=160/30=5.33 hrs
IMO: D
Answer: (D) 5.33
Question: The value of a machine depreciates at 20% per annum. If its present value is Rs. 1,50,000, at what price should it be sold after two years such that a profit of Rs. 22,000 is made?
(A) 328897
(B) 120000
(C) 118000
(D) 277768
(E) 188871
Rationale: The value of the machine after two years = 0.8 * 0.8 * 1,50,000 = Rs. 96,000
SP such that a profit of Rs. 22,000 is made = 96,000 + 24,000 = Rs. 1,18,000
Answer: C
Answer: (C) 118000
Question: In each term of a sequence, 12 is added to get the next term. If the first term is 5, what is the forty-fifth term?
(A)  533
(B)  595
(C)  513
(D)  562
(E)  531
Rationale: 1rst term + 44 terms = 5 + 12+12+12+12+12+12+12+...+12 (44 times)
5 + (12 x 44) = 5 + 528 = 533
Answer A
Answer: (A)  533
Question: A two digit number is 18 less than the sum of the squares of its digits. How many such numbers are there?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: suppose the digit 10x+y.
so, 10x+y=x^2+y^2-18
=>(x-6)(x-4)=(y-7)(-y-6)
so conddition satisfied for x=6,4 and y=7 so no of digit 2. 67,47.
ANSWER:B
Answer: (B) 2
Question: The average age of a class of 32 students is 16 yrs. if the teacher's age is also included, the average increases by one year. Find the age of the teacher
(A) 30 Years
(B) 31 Years
(C) 32 Years
(D) 34 Years
(E) 49 Years
Rationale: Total age of students is 32X16 = 512 Years
Total age inclusive of teacher = 33X (16+1) = 561
So, Teacher's age is 561-512 = 49 Yrs
There is a shortcut for these type of problems
Teacher's age is 16+(33X1) = 49 Years
E
Answer: (E) 49 Years
Question: City A and City B are 140 miles apart. Train C departs City A, heading towards City B, at 4:00 and travels at 40 miles per hour. Train D departs City B, heading towards City A, at 5:30 and travels at 20 miles per hour. The trains travel on parallel tracks. At what time do the two trains meet?
(A) 5:00
(B) 7:30
(C) 6:00
(D) 6:30
(E) 7:00
Rationale: Train C has traveled 20 mi in the half hour before Train D has started its journey.
140-20=120
40+20 =60 mph
120 mi/ 60 mph = 2 hrs
5:30pm + 2 hrs = 7:30pm
Answer:
B. 7:30
Answer: (B) 7:30
Question: A and B can do a piece of work in 6 days, B and C in 8 days, C and A in 12 days. How long will C take to do it?
(A) 48 days
(B) 55 days
(C) 24 days
(D) 33 days
(E) 40 days
Rationale: 2c = 1/8 + 1/12 – 1/6= 1/24
c = 1/48 => 48 days
Answer: A
Answer: (A) 48 days
Question: If x^2 + 9/x^2 = 10, what is the value of x - 3/x
(A) 36
(B) 25
(C) 2
(D) 5
(E) 3
Rationale: To find : x-3/x. Let it be t.
=> x-3/x = t
=> (x^2 + 9/x^2) - 2*x*3/x = t^2 (Squaring both sides).
=> (10) - 2*3 = 4
=> t^2 = 4. Thus t=2 or t=-2.
Answer C
Answer: (C) 2
Question: A man sells a horse for Rs.2000 and loss something, if he had sold it for Rs.3100, his gain would have been double the former gain. Find the cost price of the horse?
(A) 1025
(B) 1225
(C) 1000
(D) 1100
(E) 1200
Rationale: CP = SP + 1CP = SP - g
2000 + x = 3200- 2x
3x = 1200 => x = 400
CP = 800 + 400 = 1200
Answer: E
Answer: (E) 1200
Question: When asked what the time is,a person answered that the amount of time left is 3/5 of the time already completed.what is the time.
(A) 2 PM
(B) 9 PM
(C) 3 PM
(D) 8 PM
(E) 6 PM
Rationale: A day has 24 hrs. Assume x hours have passed. Remaining time is (24 - x)
24−x=3/5x⇒x=15
Time is 3 PM
Answer:C
Answer: (C) 3 PM
Question: Four people need to cross a dark river at night.
* They have only one torch and the river is too risky to cross without the torch.
* If all people cross simultaneously then torch light wont be sufficient.
* Speed of each person of crossing the river is different.cross time for each person is 1 min, 2 minutes, 7 minutes and 10 minutes.
What is the shortest time needed for all four of them to cross the river ?
(A) 16 minutes
(B) 17 minutes
(C) 18 minutes
(D) 19 minutes
(E) 20 minutes
Rationale: Solution:
17 min
The initial solution most people will think of is to use the fastest person as an usher to guide everyone across. How long would that take? 10 + 1 + 7 + 1 + 2 = 21 minutes. Is that it? No. That would make this question too simple even as a warm up question.
Let's brainstorm a little further. To reduce the amount of time, we should find a way for 10 and 7 to go together. If they cross together, then we need one of them to come back to get the others. That would not be ideal. How do we get around that? Maybe we can have 1 waiting on the other side to bring the torch back. Ahaa, we are getting closer. The fastest way to get 1 across and be back is to use 2 to usher 1 across. So let's put all this together.
1 and 2 go cross
2 comes back
7 and 10 go across
1 comes back
1 and 2 go across (done)
Total time = 2 + 2 + 10 + 1 + 2 = 17 minutes
Answer B
Answer: (B) 17 minutes
Question: Dana borrows 6000 pounds annually for her college education. If Dana gives her parents 2% of that amount back each month, how much will she still owe her parents after three years of college?
(A) 13680
(B) 13885
(C) 14005
(D) 14280
(E) 14680
Rationale: dana borrows 6000 and returns 2% per month.
so returns 120 per month. and 1440 per year.
so dana owes 6000-1440=4560 per year.
after 3 years she will owe 13680.
Ans (A)
Answer: (A) 13680
Question: A water tank is one-fifth full.Pipe A can fill a tank in 10 minutes and pipe B can empty it in 6 minutes.If both the pipes are open,how long will it take to empty or fill the tank completely?
(A) 6 min.to empty
(B) 9 min.to empty
(C) 5 min.to empty
(D) 4 min.to empty
(E) 3 min.to empty
Rationale: Explanation:
Clearly,pipe B is faster than pipe A and so,the tank will be emptied.
part to be emptied = 1/5
part emptied by (A+B) in 1 minute=(1/6-1/10)=1/15
so, the tank will be emptied in 3 min
Answer: E
Answer: (E) 3 min.to empty
Question: The 4 sticks in a complete bag of Pick-Up Sticks are all straight-line segments of negligible width, but each has a different length: 1 inch, 2 inches, 3 inches, and 4 inches, respectively. If Tommy picks a stick at random from each of 3 different complete bags of Pick-Up Sticks, what is the probability A that Tommy CANNOT form a triangle from the 3 sticks?
(A) 11/32
(B) 13/32
(C) 15/32
(D) 17/32
(E) 19/32
Rationale: In order to form a triangle, the sum of two sides must be greater than the third side.
So we can choose the combination of numbers which will NOT result in a triangle.
Favorable outcomes:
1,1,4 (4>1+1): 3 ways of arriving at this (1,1,4), (1,4,1), (4,1,1) or
1,2,4 (4>1+2): 6 ways of arriving at this (1,2,4), (1,4,2), (2,1,4), (2,4,1), (4,1,2), (4,2,1) which is same as 3!
1,3,4 (4=1+3): 6 ways of arriving at this
2,2,4 (4=2+2): 3 ways of arriving at this
1,1,3 (3>1+1): 3 ways of arriving at this
1,2,3 (3=1+2): 6 ways of arriving at this
1,1,2 (2+1+1): 3 ways of arriving at this
Overall favourable outcomes: 30
Total outcomes: 4*4*4 = 64 (4 ways of choosing a stick from each of the 3 bags)
Probability A that a triangle is not formed = 30/64 = 15/32
C is the correct option here.
Answer: (C) 15/32
Question: The average of marks obtained by 120 boys was 40. If the average of marks of passed boys was 39 and that of failed boys was 15, the number of boys who passed the examination is?
(A) 100
(B) 110
(C) 125
(D) 130
(E) 145
Rationale: Let the number of boys who passed = X.
Then, 39 x X + 15 x (120 - X) = 120 x 40
24X = 4800 - 1800
=> X = 3000/24
X = 125
Hence, the number of boys passed = 125.
ANSWER:C
Answer: (C) 125
Question: (A% of 2B + B% of A) is equal to ?
(A) A% of B
(B) B% of A
(C) 3% of AB
(D) AB% of 3
(E) None
Rationale: Answer
A% of 2B + B% of A =2AB/100 + AB/100
= 23AB/100 = 3% of AB
Correct Option: C
Answer: (C) 3% of AB
Question: If 18 is 15 percent of 30 percent of a certain number, what is the number?
(A)  9
(B)  36
(C)  40
(D)  81
(E)  400
Rationale: The math involved in this question can be 'set up' (and dealt with) in a variety of ways.
Here, if you're going to take a calculation-based approach, converting the percents to fractions would likely help you speed up (and avoid the last bit of math).
We're told that 18 is 15 percent of 30 percent of a certain number. We're asked for that number.
18 = (.15)(.3)(X)
18 = (3/20)(3/10)(X)
18 = (9/200)(X)
Since 9/200 is a relatively small fraction (it's far less than 10%), we know that 18 is LESS than 10% of X. Based on the given answer choices, there's only one number that is LARGE enough to fit that description....
Final Answer:
E
Answer: (E)  400
Question: if x+y+z =1. then xy+yz+zx is
(A) 1/2
(B) 1/3
(C) 1/4
(D) 1/5
(E) 1/6
Rationale: 1/2+1/2+0=1
xy=1/2*1/2=1/4
ANSWER:C
Answer: (C) 1/4
Question: If HARD is coded as 1357
and SOFT is coded as 2468
what will 21448 stand for?
(A) SHOOR
(B) SHOOA
(C) SHOOT
(D) SHEOT
(E) SWOOT
Rationale: HARD = 1357 => 1=H, 3=A , 5=R , 7=D
SOFT = 2468 => 2=S, 4=O , 6=F , 8=T
so, 21448 = SHOOT
ANSWER:C
Answer: (C) SHOOT
Question: A circular rim 14 inches in diameter rotates the same number of inches per second as a circular rim 35 inches in diameter. If the smaller rim makes x revolutions per second, how many revolutions per minute does the larger rim makes in terms of x ?
(A) 48pi/x
(B) 75x
(C) 48x
(D) 24x
(E) x/75
Rationale: The larger rim must circulate for the same number of inches the smaller rim does.
C = (pi)d
C(small): (pi)*14
C(large): (pi)*35
Lets say the time horizon is 60 seconds, so during that time the smaller rim covers a distance of (pi)*14*60 = (pi)*(840) inches
(pi)*(840) = (pi)*(35)(x)
pi*(24) = pi*(x)
24=x
Answer: D
Answer: (D) 24x
Question: A veterinarian surveys 26 of his patrons.He discovers that 14 have dogs, 10 have cats, and 5 have fish.Four have dogs and cats, 3 have dogs and fish, and one has a cat and fish.If no one has all three kinds of pets, how many patrons have none of these pets?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: no. of patron have dogs = 14
no. of patron have cats = 10
no. of patron have fish = 5
no. of patron have dogs and cats = 4
no. of patron have dogs and fish = 3
no. of patron have cats and fish = 1
no. of patron have all three pets = 0
no. of patron have only dogs = 7
no. of patron have only cats = 5
no. of patron have only dogs = 1
So total no. of patron have pets =7+5+1+4+3+1=21
So no. of patron don't have any pets =26-21=5
5 patrons don't have any these pets
ANSWER:C
Answer: (C) 5
Question: At a meeting of the 9 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 9 Chiefs of Staff be seated around a circular table?
(A) 120
(B) 480
(C) 960
(D) 2520
(E) 6050
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 E (6050), should be the number of ways to arrange all 7 without the seating restriction given. Is this incorrect?E
Answer: (E) 6050
Question: Find the odd man out. 1, 9, 16, 51, 121, 169, 225
(A) 169
(B) 51
(C) 16
(D) 1
(E) 121
Rationale: Explanation :
Each of the given numbers except 51 is a perfect square
Answer : Option B
Answer: (B) 51
Question: A girl scout was selling boxes of cookies. In a month, she sold both boxes of chocolate chip cookies ($1.25 each) and boxes of plain cookies ($0.75 each). Altogether, she sold 1,585 boxes for a combined value of $1,586.25. How many boxes of plain cookies did she sell?
(A) 0
(B) 233
(C) 500
(D) 695
(E) 790
Rationale: Let #plain cookies sold be X then #chocolate cookies = (total cookies-X)
Equating for X
(0.75)*X +(1.25)*(1585-X)=1586.25
=>x=790
E
Answer: (E) 790
Question: How long does a train 100 m long traveling at 60 kmph takes to cross another train of 170 m in length has a speed of 40 kmph?
(A) 1.42 sec
(B) 16.8 sec
(C) 5 sec
(D) 1.68 sec
(E) 3.6 sec
Rationale: D = 100 m
S = (60+40) * 5/18 = 250/3
T = 100 * 9/250 = 3.6 sec
ANSWER:E
Answer: (E) 3.6 sec
Question: The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?
(A) 23 years
(B) 24 years
(C) 25 years
(D) 26 years
(E) None of these
Rationale: Explanation:
Let the average age of the whole team by x years.
11x - (26 + 29) = 9(x -1)
11x - 9x = 46
2x = 46
x = 23.
So, average age of the team is 23 years.
ANSWER IS A
Answer: (A) 23 years
Question: The area of a triangle is with base 4m and height 5m?
(A) 11
(B) 10
(C) 88
(D) 26
(E) 32
Rationale: 1/2 * 4 * 5 = 10 m2
Answer: B
Answer: (B) 10
Question: The ratio of number of boys and girls in a school is 2:5. If there are 420 students in the school, find the number of girls in the school?
(A) 150
(B) 250
(C) 300
(D) 370
(E) 280
Rationale: Let the number of boys and girls be 2x and 5x
Total students = 420
Number of girls in the school = 5*420/7 = 300
Answer is C
Answer: (C) 300
Question: If x is to be chosen at random from the set {1, 2, 3, 4} and y is to be chosen at random from the set {6, 7}, what is the probability that xy will be even?
(A)  1/6
(B)  1/3
(C)  1/2
(D)  2/3
(E)  5/6
Rationale: Probably the best way to solve would be to use 1 - P(opposite event) = 1 - P(odd) = 1 - P(odd)*P(odd) = 1 - 2/4*2/3 = 8/12 = 1/6
Answer: A
Answer: (A)  1/6
Question: What is the probability that when a hand of 6 cards is drawn from a well shuffled deck of 52 cards, It contains 2 Queen?
(A) 1/23445
(B) 113/22434
(C) 29187by1017926
(D) 1017926/29187
(E) None of these
Rationale: nCr = n!/(n-r)!r!
Total number of possible hands = 52C6
52C6 = (52!)/((52-6)! × 6!)
52C6 = 61075560.
Number of hands with 2 Queen and 4 non-Queen cards = 4C2 × 48C4
4C2 = (4!)/(2! × 2!) = 6.
48C4 = (48!)/(44! × 4!) = 3 × 47 × 46 × 45 = 291870
(other 2 cards must be chosen from the rest 48 cards)
P (2 Queen) = (4C2 × 48C4)/52C6 = 29187/1017926
C
Answer: (C) 29187by1017926
Question: Jake wants to invite 9 friends to his 8th birthday party. Each invitation requires 2 stamps to mail, costing 12 cents each. How much will Jake have to spend on stamps to send invitations to his 9 friends?
(A) $1.08
(B) $1.41
(C) $1.74
(D) $1.98
(E) $2.16
Rationale: 2 stamps multiplied by 12 cents = 24 cents per invitation. 24 cents multiplied by 9 invitations = 216 cents = $2.16, hence answer : E.
Answer: (E) $2.16
Question: A cycle is bought for Rs.900 and sold for Rs.1080, find the gain percent?
(A) 28%
(B) 20%
(C) 22%
(D) 16%
(E) 27%
Rationale: 900 ---- 180
100 ---- ? => 20%
Answer: B
Answer: (B) 20%
Question: Find the angle between the hour and the minute hand of a clock when the time is 3.25.
(A) 47.5
(B) 47.9
(C) 47.1
(D) 47.3
(E) 47.6
Rationale: Formula : θ=∣∣∣30h−112m∣∣∣θ=|30h−112m|
Angle = 11/2 × 25 – 30×3 = 95/2 = 47.5
Answer:A
Answer: (A) 47.5