mathewhe/aqua_rat huggingface dataset:
Question: A certain team has 8 members, including Joey. A three-member relay team will be selected as follows: one of the 8 members is to be chosen at random to run first, one of the remaining 7 members is to be chosen at random to run second, and one of the remaining 6 members is to be chosen at random to run third. What is the probability that Joey will be chosen to run second or third?
(A) 2/3
(B) 1/4
(C) 2/5
(D) 3/8
(E) 3/10
Rationale: Each member has an equal probability to run second (1/8) or third (1/8).
The probability that Joey runs second or third is 1/8 + 1/8 = 1/4
The answer is B.
Answer: (B) 1/4
Question: There exists exactly one positive value of k such that the line y = kx intersects the parabola
y = x2 + x + 4 at exactly one point. Compute the intersection point.
(A) (2,10)
(B) (5,10)
(C) (7,10)
(D) (3,10)
(E) (1,10)
Rationale: If the line is tangent, then we must have that x2 + x + 4 = kx has a unique solution
in x, or x2 + (1 - k)x + 4 = 0 has a unique solution. Thus, (1 - k)2- 16 = 0, or (1- k) = 4.
Therefore, k = -3 or k = 5.
Taking k = 5, we have that y = 5x intersects y = x2 + x + 4 when x = 2, and the intersection
point is (2, 10) .
correct answer A
Answer: (A) (2,10)
Question: Three friends sakthi, samy and Charlie divide $1010 amongs them in such a way that if $6, $8 and $10 are removed from the sums that sakthi, samy and Charlie received respectively, then the share of the sums that they got will be in the ratio of 4 : 8 : 6. How much did Charlie receive?
(A) $316
(B) $326
(C) $331
(D) $336
(E) $334
Rationale: Explanatory Answer
Let the sums of money received by A, B and C be x, y and z respectively.
Then x - 6 : y - 8 : z -10 is 4a : 8a : 6a
When $6, $8 and $10 are removed, we are removing a total of $24 from $1010.
Therefore, 4a + 8a + 6a = 1010 - 24 = 986
i.e., 18a = 986
or a =55 .
We know that z - 6 = 6a =6 * 55 = 330
Therefore, z = 330 + 6 = $336
The correct choice is (D)
Answer: (D) $336
Question: How many positive even integers less than 100 contain digits 5 or 9?
(A) 16
(B) 10
(C) 18
(D) 19
(E) 20
Rationale: Two digit numbers:
5 at tens place: 50,52,54,56,58
9 at tens place: 90,92,94,96,98
If 5 and 9 is at units place, the number cant be even
Total:5+5= 10
Answer B
Answer: (B) 10
Question: A particular store purchased a stock of turtleneck sweaters and marked up its cost by 20%. During the New Year season, it further marked up its prices by 25% of the original retail price. In February, the store then offered a discount of 9%. What was its profit on the items sold in February?
(A) 27.5%
(B) 30%
(C) 35%
(D) 36.5%
(E) 40%
Rationale: Assume the total price = 100x
Price after 20% markup = 120x
Price after 25%further markup = 1.25*120x = 150x
Price after the discount = 0.91*150x = 136.5x
Hence total profit = 36.5%
Option D
Answer: (D) 36.5%
Question: In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs. 2.20 per hour for regular work and Rs. 3.20 per hours for overtime. If he earns Rs. 432 in 4 weeks, then how many hours does he work for ?
(A) 160
(B) 185
(C) 190
(D) 200
(E) 210
Rationale: Suppose the man works overtime for x hours.
Now, working hours in 4 weeks = (5 x 8 x 4) = 160.
160 x 2.20 + X x 3.20 = 432
X = 25.
Hence, total hours of work = (160 + 25) = 185.
answer :B
Answer: (B) 185
Question: The sector of a circle has perimeter of 144 cm and central angle 180o. Find its radius?
(A) 25 cm
(B) 32 cm
(C) 14 cm
(D) 28 cm
(E) 21 cm
Rationale: Let the radius is x cm
Perimeter of the sector = length of the arc + 2(radius)
144= (180/360 * 2 * 22/7 * x) + 2(x)
144= 22x/7 + 2x
144= 36x/7
36x= 1008
x = 28
Answer: D
Answer: (D) 28 cm
Question: 78654 * 9999
(A) 784598562
(B) 765858254
(C) 784569825
(D) 786461346
(E) None of these
Rationale: Explanation:
78654 * (10000 - 1)
= 786540000 - 78654
= 786461346
Option D
Answer: (D) 786461346
Question: 6 workers should finish a job in 8 days. After 3 days came 4 workers join them. How many days C do they need to finish the same job?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: Let Rate of one worker be R
=> (6*R)*8 = 1 (Rate * Time = work)
=> R = 1/48
=> Work remaining after 3 days
1 - (3*6)/48 = 30/48
After 4 ppl joined in
((6+4)*Time)/48 = 30/48
Time C= 3 days to finish the task
IMO A
Answer: (A) 3
Question: A reduction of 20% in the price of salt enables a lady to obtain 10kgs more for Rs.100, find the original price per kg?
(A) 2 3/2
(B) 2 2/3
(C) 2.5
(D) 3
(E) 1
Rationale: 100*(20/100) = 20 --- 10
? --- 1 => Rs.2
100 --- 80
? --- 2 => Rs.2.5
ANSWER:C
Answer: (C) 2.5
Question: If a train, travelling at a speed of 90 kmph, crosses a pole in 5 sec, then the length of train is?
(A) 125 m
(B) 104 m
(C) 140 m
(D) 152 m
(E) 150 m
Rationale: D = 90 * 5/18 * 5 = 125 m
ANSWER A
Answer: (A) 125 m
Question: Out of 9 persons, 8 persons spent Rs. 30 each for their meals. The ninth one spent Rs. 20 more than the average expenditure of all the nine. The total money spent by all of them was
(A) Rs. 292.50
(B) Rs. 297.50
(C) Rs. 298
(D) Rs. 298.50
(E) None of these
Rationale: Explanation:
Let the average expenditure be Rs. x Then,
9x = [8× 30 + (x + 20)] ⇔9x = x + 260 ⇔ x = 32.50
Total money spent = 9x = Rs. (9 x 32.5O) = Rs 292. 50 Answer: A
Answer: (A) Rs. 292.50
Question: Find the average of first 3 multiples of 5?
(A) 10
(B) 15
(C) 12.5
(D) 13
(E) 21
Rationale: average = (5+10+15)/3 = 10
Answer is A
Answer: (A) 10
Question: The amounts of time that three secretaries worked on a special project are in the ratio of 2 to 3 to 5. If they worked a combined total of 110 hours, how many hours did the secretary who worked the longest spend on the project?
(A) 80
(B) 55
(C) 56
(D) 16
(E) 14
Rationale: 10x = 110
=> x = 11
Therefore the secretary who worked the longest spent 11 x 5 = 55 hours on the project
Option (B)
Answer: (B) 55
Question: Ten coins are tossed simultaneously. In how many of the outcomes will the third coin turn up a head?
(A) 2(10)
(B) 2(9)
(C) 3 * 2(8)
(D) 3 * 2(9)
(E) None of these
Rationale: Explanatory Answer
When a coin is tossed once, there are two outcomes. It can turn up a head or a tail.
When 10 coins are tossed simultaneously, the total number of outcomes = 210
Out of these, if the third coin has to turn up a head, then the number of possibilities for the third coin is only 1 as the outcome is fixed as head.
We need to find out what happens to the remaining 9 coins?
The remaining 9 coins can turn up either a head or a tail. Each of the 9 coins has 2 possibilities.
Number of outcomes for the remaining 9 coins = 2(9)
∴ the number of outcomes in which the 3rd coin turns a head = 1 * 2(9) = 2(9).
Choice D
Answer: (D) 3 * 2(9)
Question: What is the value of the following series 1/7 + 2/7^2 + 1/7^3 +2/7^4 + 1/7^5 +.......
(A) 6/49
(B) 8/49
(C) 11/49
(D) 13/49
(E) 9/49
Rationale: it can be written as
{ 1/7(1 + 1/7^2 + 1/7^4 +....) } + { 2/7^2 (1+ 1/7^2 +7^4 +.....) }
which can b further written as
=(1+ 1/7^2 +7^4 +.....)(1/7 + 2/7^2)
=(1+0.02+0.0004+......)(9/49)
~(1)(9/49)
=9/49
ANSWER:E
Answer: (E) 9/49
Question: How many liters of water must be evaporated from 50 liters of a 3 percent sugar solution to get a 5 percent sugar solution?
(A) 2
(B) 4
(C) 6
(D) 10
(E) 20
Rationale: 3% sugar solution means that currently there are 1.5 Liters of sugar and this amount must be 5% of a reduced final amount (50-x)
1.5=0.05*(50-x)
0.05x=1
x=20
Answer E
Answer: (E) 20
Question: 12*18*6 is the volume of some material. How many cubes of edge 3 can be insert into it?
(A) 48
(B) 49
(C) 50
(D) 51
(E) 52
Rationale: no. of such cubes = volume of material / volume of one cube
(12*18*6)/(3*3*3)= 48
ANSWER:A
Answer: (A) 48
Question: The vertices of a rectangle in the standard (x,y) coordinate place are (0,0), (0,4), (10,0) and (10,4). If a line through (1,1) partitions the interior of this rectangle into 2 regions that have equal areas, what is the slope of this line?
(A) 1/2
(B) 1/3
(C) 1/4
(D) 1/5
(E) 1/6
Rationale: We should know that a rectangle can be divided into two equal areas by a straight line only when the straight line passes through the center of the rectangle.
The center of the rectangle is the point (5,2).
The slope of line passing through points (1,1) and (5,2) = (2-1)/(5-1) = 1/4
The answer is C.
Answer: (C) 1/4
Question: A(n+1)=1+(1/A(n)) and A(1)=1. What is the value of A(10)?
(A) 89/55
(B) 91/57
(C) 93/59
(D) 95/61
(E) 97/63
Rationale: A(n+1)=1+(1/A(n))
A(1) = 1
A(2) = 2
A(3) = 3/2
A(4) = 5/3
A(5) = 8/5
A(6) = 13/8
A(7) = 21/13
A(8) = 34/21
A(9) = 55/34
A(10) = 89/55
The answer is A.
Answer: (A) 89/55
Question: Eleven people are planning to share equally the cost of a rental van. If one person withdraws from the arrangement and the others share equally the cost of the rental van, then the share of each of the remaining people will increase by...?
(A) 1/10
(B) 1/9
(C) 1/8
(D) 11/10
(E) 10/9
Rationale: Let P = total cost of the rental van.
The original share per person is P/11.
The new share per person is P/10.
P/10 = P/11 * 11/10 = (1 + 1/10)*original share
The answer is A.
Answer: (A) 1/10
Question: A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office. In how many ways can the company assign 3 employees to 6 different offices?
(A) 501
(B) 60
(C) 117
(D) 110
(E) 216
Rationale: Each of three employee can be assigned to either of offices, meaning that each has 2 choices --> 6*6*6=6^3=216.
Answer: E.
Answer: (E) 216
Question: Which of the following numbers completes
the sequence 3, 8, 14, 21, 29, 38, 48, 59, 71 ___?
(A) 35
(B) 36
(C) 37
(D) 84
(E) 99
Rationale: The numbers increase at a somewhat steady rate, so you have to figure out how much
you have to add to each number to produce the next in the sequence: 3 + 5 = 8; 8 + 6 = 14;
14 + 7 = 21; 21 + 8 = 29, and so on. The rule for the sequence is to add successively larger
numbers to each number; therefore, the next number is 71 + 13 = 84.
correct answer D)84
Answer: (D) 84
Question: The population of a town is 8000. It decreases annually at the rate of 20% p.a. What will be its population after 2 years?
(A) 5100
(B) 5120
(C) 5200
(D) 5400
(E) 5500
Rationale: Formula :
( After =100 denominator
Ago = 100 numerator)
8000 × 80/100 × 80/100 = 5120
B)
Answer: (B) 5120
Question: A bat is bought for Rs.200 and sold at a gain of 20% find its selling price
(A) A)Rs.460/-
(B) B)Rs.270/-
(C) C)Rs.280/-
(D) D)Rs.240/-
(E) E)Rs.520/-
Rationale: 100 % ------> 200 (100 * 2 = 200)
120 % ------> 240 (120 * 2 = 240)
Selling price = Rs.240/-
Answer : D
Answer: (D) D)Rs.240/-
Question: To reach her destination, Jeanette must drive 90 miles. If she drives 3 miles every 7 minutes, how much time will it take her to reach her destination?
(A) 2 hours and 2 minutes
(B) 54 minutes
(C) 2 hours and 10 minutes
(D) 2 hours and 12 minutes
(E) 2 hours and 15 minutes
Rationale: 3 minute for 5 miles how much for 90? minutes for 1(3/5) mile multiplied by 90 miles.
3*90/5= 54> 54 min answer is B
Answer: (B) 54 minutes
Question: Find the smallest number of six digits exactly divisible by 25,35,45 and 15.
(A) 100555
(B) 100775
(C) 100885
(D) 100995
(E) 100665
Rationale: Smallest number of six digits is 100000.
Required number must be divisible by L.C.M. of 25,35,45,15 i.e 1575,
On dividing 100000 by 1575,we get 800 as remainder.
Therefore, Required number = 100000 +( 1575 â€“ 800 ) = 100775.
Answer is B.
Answer: (B) 100775
Question: Convert 500 miles to KM?
(A) 600KM
(B) 700KM
(C) 800KM
(D) 900KM
(E) 1000KM
Rationale: 800KM
500*1.6=800
Answer:C
Answer: (C) 800KM
Question: The sides of a triangle are in the ratio 5: 12: 13 and its perimeter is 180 m, its area is?
(A) 90
(B) 882
(C) 277
(D) 261
(E) 281
Rationale: 5x + 12x + 13x = 180 => x = 6
a = 30, b = 72, c = 78
S = (30 + 72 + 78)/2 = 90
Answer: A
Answer: (A) 90
Question: A is twice as good workman as B, and together they complete a work in 12 days. In how many days can the work be complete by B alone?
(A) 36 days
(B) 65 days
(C) 45 days
(D) 75 days
(E) 95 days
Rationale: B=3A
36 days
A
Answer: (A) 36 days
Question: On a race track a maximum of 5 horses can race together at a time. There are a total of 25 horses. There is no way of timing the races. What is the minimum number T of races we need to conduct to get the top 3 fastest horses?
(A) 5
(B) 7
(C) 8
(D) 10
(E) 11
Rationale: T=7 is the correct answer.
Good solution Buneul.B
Answer: (B) 7
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. 110.75
(B) Rs. 115.75
(C) Rs. 124.75
(D) Rs. 125
(E) Rs. 126
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: How much time does a train 225 metres long running at 90 km/hr take to pass a pole?
(A) 7.9s
(B) 2.5s
(C) 7.5s
(D) 9s
(E) 7.4s
Rationale: Explanation:
90 km/hr = 90 * 5/18 = 25 m/s
Speed = distance/time; v = d/t
25 = 225/t
t = 9s
ANSWER: D
Answer: (D) 9s
Question: X is an even number and( Y +2) is a positive odd number. Which of the following expressions cannot be even?
(A) X^5
(B) X^4
(C) X^3
(D) X^2
(E) Y+2
Rationale: Y+2 WILL BE ODD
E
Answer: (E) Y+2
Question: John has exactly 31 pens, and each pen is either bule, black, or red. If he has 5 more black pens than red pens, and twice as many blue pens as black pens, how many blue pens does john has ?
(A) 15
(B) 18
(C) 20
(D) 22
(E) 17
Rationale: x = the number of blue pens
y = the number of black pens
z = the number of red pens
From the first sentence we have
Equation #1: x + y + z = 31
...he has 5 more black pens than red pens...
Equation #2: y = 5 + z
...twice as many blue pens as black pens...
Equation #3: x = 2y
Solve equation #1 for z: z = y - 5
Now, we can replace both x and z with y in Equation #1
2y + y + (y - 5) = 31
4y - 5 = 31
4y = 36
y = 9
There are 9 black pens. This is 5 more than the number of red pens, so z = 4. Hence the answer is. x = 18, and just for check 18 + 9 + 4 = 31.
Answer = 18,(B)
Answer: (B) 18
Question: A person purchased a TV set for Rs. 16000 and a DVD player for Rs. 6250. He sold both the items together for Rs. 31150. What percentage of profit did he make?
(A) 16%
(B) 87%
(C) 40%
(D) 17%
(E) 18%
Rationale: The total CP = Rs. 16000 + Rs. 6250 = Rs. 22250 and SP
= Rs. 31150
Profit(%) = (31150 - 22250)/22250 * 100
= 40%
Answer:C
Answer: (C) 40%
Question: If x is an integer and |1-x|<2 then which of the following must be true?
(A) x is not a prime number
(B) x^2+x is not a prime number
(C) x is positive
(D) Number of distinct positive factors of x+2 is a prime number
(E) x is not a multiple of an odd prime number
Rationale: 1−x|<2 = -2<(1-x)<2
= -3<-x<1
= 3>x>-1
So x can hold values of 0,1 & 2 to satisfy the condition. Now we can evaluate the choices.
A) 1 & 2 primes, so incorrect
B) 1^2+1=2 is a prime, so incorrect
C) 0 is not +ve, So incorrect
D) x+2= 2,3,or 4, here 2 has 2 factor(prime), 3 has 2 factor (prime) & 4 has 3 factors (prime). Hence correct choice.
E) 2 is multiple of 1. So incorrect.
Hence Answer D.
Answer: (D) Number of distinct positive factors of x+2 is a prime number
Question: From the integer n, if n*n*n is odd, then what is true from below options?
(A) n is odd and n*n is even
(B) n is odd
(C) n*n is even
(D) n*n is odd
(E) n is even
Rationale: n is odd and n*n is even
Option A
Answer: (A) n is odd and n*n is even
Question: If four students are made to sit in a row, then 6 don't have seats. If 6 students are made to sit in a row, then one row is empty. How many students have to sit a row such that each row has equal number of students and all students are seated?
(A) 0
(B) 1
(C) 4
(D) 5
(E) 9
Rationale: Let there be a rows.
Then 4a + 6 = 6(a-1) [equating the number of students]
=> a= 6
and total number of students = 30
Therefore 5 students much sit in each row such that each row has an equal number of students and all students are seated.
Option (D)
Answer: (D) 5
Question: At Joes Steakhouse the hourly wage for a chef is 20% greater than that of a dishwasher, and the hourly wage of a dishwasher is half as much as the hourly wage of a manager. If a managers wage is $10.50 per hour, how much less than a manager does a chef earn each hour?
(A) $1.40
(B) $2.40
(C) $3.40
(D) $4.40
(E) $4.30
Rationale: Manager wages per hour = $10.50
Dishwasher wages per hour = half of manager's wages. = 1/2($10.50) ==> $5.25
Chef wages per hour = 20% greater than Dishwasher wages
--> 20% of $5.25 = (20*($5.25)) /100
--> ($95)/100
--> $0.95
Therefore,
Chef wages per hour = $5.25 + $0.95 ==> $6.20
Difference of wages between manager and chef = $10.50 - $6.20 ==> $4.30
ANSWER:E
Answer: (E) $4.30
Question: A person can walk at a constant rate of 8mph and can bike at a rate of 32mph. If he wants to travel 80 miles in 4 hours using bike and walking at their constant rates, how much distance would he require to walk?
(A) 20
(B) 30
(C) 48
(D) 60
(E) 72
Rationale: Total distance = 80
Distance = Speed * Time
Walking speed = s1 = 8
Walking time = t1
Bike speed = s2 = 32
Time traveled in bike = t2
d1 + d2 = 80
s1t1 + s2t2 = 80
8*t1 + 32*t2 = 80
t1 + 4*t2 = 10 ----- (1)
Given: t1 + t2 =4 ----- (2)
(1) - (2) -->3 t2 = 6 , t2=2 and t1 = 8 - 2 = 6
Walking distance = s1*t1 = 8*6 = 48
Answer: C
Answer: (C) 48
Question: The slant height of a cone is 14 cm and radius of the base is 12cm, find the curved surface of the cone.
(A) 150
(B) 170
(C) 48
(D) 528
(E) 600
Rationale: π * 12*14 =528
Answer:D
Answer: (D) 528
Question: 4 dice are thrown simultaneously on the board. Find the probability show the same face.
(A) 1/114
(B) 2/117
(C) 1/216
(D) 2/111
(E) 3/111
Rationale: The total number of elementary events associated to the random experiments of throwing four dice simultaneously is:
=6×6×6×6=64=6×6×6×6=64
n(S)=64n(S)=64
Let XX be the event that all dice show the same face.
X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}
n(X)=6n(X)=6
Hence required probability,
=n(X)n(S)=664=n(X)n(S)=664
=1/216
C
Answer: (C) 1/216
Question: Mr. Smitherly leaves Cedar Rapids at 8:00 a.m. and drives north on the highway at an average speed of 50 km per hour. Mr. Dinkle leaves Cedar Rapids at 8:30 a.m. and drives north on the same highway at an average speed of 75 km per hour. Mr. Dinkle will
(A) overtake Mr. Smitherly at 9:30 a.m.
(B) overtake Mr. Smitherly at 10:30 a.m.
(C) overtake Mr. Smitherly at 11:00 a.m.
(D) be 30 miles behind at 8:35 a.m.
(E) never overtake Mr. Smitherly
Rationale: After thirty minutes, Mr. Smitherly is ahead by 25 km.
Mr. Dinkle gains on Mr. Smitherly 25 km each hour.
1 hour after 8:30 a.m., Mr. Dinkle will catch Mr. Smitherly.
The answer is A.
Answer: (A) overtake Mr. Smitherly at 9:30 a.m.
Question: Suppose that f(x) is a function such that for every real number x,i)f(x)+f(1-x) = 15 and (ii) f(1+x) = 3+f(x). Then f(x)+f(-x)
must equal
(A) 8
(B) 9
(C) 10
(D) 11
(E) 12
Rationale: Since (ii) holds for every real number x, it will remain valid if we replace x with
-x. Therefore, f(1-x) = 3+f(-x). Now, from (i), 15 = f(x)+f(1-x) = f(x)+3+f(-x)
so that f(x) + f(-x) = 15-3 = 12. (Observe that f(x) = 3x + 4 satisfies the conditions
in the problem.)
correct answer E
Answer: (E) 12
Question: What's 8 x 600?
(A) 4,800
(B) 4,600
(C) 4,400
(D) 5,400
(E) 6,800
Rationale: A. 4,800
Answer: (A) 4,800
Question: Water consists of hydrogen and oxygen, and the approximate ratio, by mass, of hydrogen to oxygen is 2:16. Approximately how many grams of hydrogen are there in 171 grams of water?
(A) 11
(B) 13
(C) 15
(D) 17
(E) 19
Rationale: (2/18)*171 = 19 grams
The answer is E.
Answer: (E) 19
Question: Running at the same constant rate, 6 identical machines can produce a total of 270 pens per minute. At this rate, how many pens could 10 such machines produce in 4 minutes?
(A) 1500
(B) 1545.6
(C) 1640.33
(D) 1800
(E) None of these
Rationale: Explanation :
Let the required number of bottles be x.
More machines, More bottles (Direct Proportion)
More minutes, More bottles (Direct Proportion)
machines 6:10|
|::270:x
time 1:4 |
=> 6 * 1 * x = 10 * 4 * 270
=> x = (10 * 4 *270)/6
=> x = 1800
Answer : D
Answer: (D) 1800
Question: The length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 588 sq m, then what is the breadth of the rectangular plot?
(A) 16
(B) 17
(C) 18
(D) 19
(E) 14
Rationale: Let the breadth of the plot be b m.
Length of the plot = 3 b m
(3b)(b) = 588
3b2 = 588
b2 = 196
b = 14 m.
Answer: Option E
Answer: (E) 14
Question: If (5^9)(9^5)=3(15^x), what is the value of x?
(A)  7
(B)  9
(C)  11
(D)  13
(E)  15
Rationale: (5^9)(9^5)=3(15^x)
=> 5^9 * 3^10 = 3 * 3^x * 5^x
=> 5^9 * 3^10 = 3^(x+1) * 5^x
Value of x = 9
Answer B
Answer: (B)  9
Question: At a special sale, 5 tickets can be purchased for the price of 3 tickets. If 5 tickets are purchased at the sale, the amount saved will be What percent of the original price of the 5 tickets?
(A) 20%
(B) 33.3%
(C) 40%
(D) 60%
(E) 66.6%
Rationale: let the price of a ticket be Rs.100, so 3 tickets cost 300 & 5 tickets cost 500
5 tickets purchased at price of 3 tickets ie., for 300, so amount saved s Rs.200,
% of 5 tickets = (200 /500)*100 =40 %
ANSWER:C
Answer: (C) 40%
Question: what is the value of (2)^-6 ?
(A) 1/62
(B) 1/64
(C) 1/65
(D) 1/66
(E) 1/67
Rationale: 2^-6= 1/(2)^6= 1/64
ANSWER:B
Answer: (B) 1/64
Question: Arun is travelling on his cycle and has calculated to reach point A at 2 pm if he travels at
10 kmph. He will reach there at 12 noon if he travels at 15 kmph. At what speed must he travel to reach A at 1 pm?
(A) 8 kmph
(B) 12 kmph
(C) 10 kmph
(D) 14 kmph
(E) 15 kmph
Rationale: Let distance be x km
travelling at 10 kmph reach at 2 pm
travelling at 15 kmph reach at 12 noon
=>time taken when travelling at 10 km - time taken when travelling at 15 km = 2 hrs
x/10 - x/15 = 2
3x-2x*30
x=60
time needed if travelled at 10kmph = 60/10 = 6 hrs=>reach at 1 pm => (6-1) = 5 hrs
req speed = 60/5 = 12 kmph
ANSWER B
Answer: (B) 12 kmph
Question: Two trains of length 100 m and 200 m are 70 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. After how much time will the trains meet?
(A) 2 sec
(B) 32/3 sec
(C) 20/7 sec
(D) 32/3 sec
(E) 53/2 sec
Rationale: They are moving in opposite directions, relative speed is equal to the sum of their speeds.
Relative speed = (54 + 72)*5/18 = 7*5 = 35 mps.
The time required = d/s = 70/35 = 2 sec.
Answer:a
Answer: (A) 2 sec
Question: rahul played weel in this season.his current batting averagge is 52.if he score 78 runs in today match.his batting average will become 54.how many matches had he played in this season.
(A) 8
(B) 12
(C) 9
(D) 6
(E) 5
Rationale: 52x+78=54(x+1)
=>2x=24
=>x=12
ANSWER:B
Answer: (B) 12
Question: How many 7-letter words can be formed using the letters of the English alphabet that contain 3 different vowels and 4 different consonants?
(A) 5!*5c2 *21c2
(B) 4!*5c2 *21c2
(C) 4!*5c3 *21c2
(D) 6!*5c3 *21c2
(E) 7!*5c3 *21c4
Rationale: combination for 3 vowels out of 5 = 5c3 ways
combination for 4 consonants of 21 = 21c4 ways
Additionally the arrangement can be = 7!
total arrangements =7!*5c3 *21c4
E
Answer: (E) 7!*5c3 *21c4
Question: A right triangle ATC has to be constructed in the xy-plane so that the right angle is at A and AT is parallel to x axis. The coordinates of A, T and C are integers and satisfy the inequalities -1 ≤ x ≤ 7 and 1 ≤ y ≤ 7. How many different triangles can be constructed with these properties?
(A) 63
(B) 336
(C) 567
(D) 3024
(E) 5040
Rationale: All the cordinates are integer hence,
possible AT values are
{-1,0}, {-1,1} ....{-1,7}: 8 ways
....
{7,-1}, {7,0} ......{7,6}: 8 ways
9*8 ways = 72
for AC values can be
{1,2}, {1,3} .... {1,7} : 6ways
......
{7,1}, {7,2} ..... {7,6} : 6 ways
7*6 = 42
Total = 72 * 42 = 3024 hence D
Answer: (D) 3024