mathewhe/aqua_rat huggingface dataset:
Question: One night a certain hotel rented 1/2 of its rooms, including 2/3 of their air conditioned rooms. If 3/5 of its rooms were air conditioned, what percent of the rooms that were not rented were air conditioned?
(A) 25%
(B) 30%
(C) 35%
(D) 40%
(E) 50%
Rationale: The rooms which were not rented is 1/2
The AC rooms which were not rented is (1/3)*(3/5) = 1/5
The percentage of unrented rooms which were AC rooms is (1/5) / (1/2) = 2/5 = 40%
The answer is D.
Answer: (D) 40%
Question: Find the time between 5 and 6 o'clock when the two hands of clock are 6 minutes spaces apart.
(A) 3 2/11 minutes past 5 o'clock
(B) 6 6/11 minutes past 5 o'clock
(C) 20 8/11 minutes past 5 o'clock
(D) 4 2/11 minutes past 5 o'clock
(E) 5 2/11 minutes past 5 o'clock
Rationale: minute hand should travel 19 mis or 31 mins to have gape of 6 mins...so in case of 19 mins (19 60/55) and in case of 31 mins (31*60/55) will be the ans...for above question c is ans...i.e 20 8/11
ANSWER:B
Answer: (B) 6 6/11 minutes past 5 o'clock
Question: An unbiased die is tossed. Find the probability of getting a multiple of 1
(A) A)1/3
(B) B)2/5
(C) C)1/2
(D) D)2/3
(E) E)3/7
Rationale: Here S = {1,2,3,4,5,6}
E = event of getting a multiple of 2
E = {2,4,6}
P(E) = 3/6 = 1/2
Answer is C
Answer: (C) C)1/2
Question: lexus car agency has 162 cars.he sold some cars at 9% profit and rest at 36% profit thus he gains 17% on the sale of all his cars.the no. of cars sold at 36% profit is?
(A) 36
(B) 37
(C) 48
(D) 39
(E) 40
Rationale: ratio of 36% profit cars to 9% profit cars = 8:19
so no. of cars sold at 36% profit = 162*8/27= 48 cars
ANSWER:C
Answer: (C) 48
Question: Guy drives 60 miles to attend a meeting. Halfway through, he increases his speed so that his average speed on the second half is 16 miles per hour faster than the average speed on the first half. His average speed for the entire trip is 30 miles per hour. Guy drives on average how many miles per hour during the first half of the way?
(A) 12
(B) 14
(C) 16
(D) 24
(E) 40
Rationale: Let x be the average speed for 1st half of the distance. Then the average speed for 2nd half of the distance will be x+16
avg speed= total distance/total time
30 = 60/{(30/x) + (30/(x+16))}
Solving we get
x^2-14x-240=0
x= -10 or 24
x cant be negative hence x= 24
ANSWER:D
Answer: (D) 24
Question: A, B and C have Rs.500 between them, A and C together have Rs.200 and B and C Rs.350. How much does C have?
(A) 50
(B) 78
(C) 267
(D) 29
(E) 27
Rationale: A+B+C = 500
A+C = 200
B+C = 350
--------------
A+B+2C = 550
A+B+C = 500
----------------
C = 50
Answer: A
Answer: (A) 50
Question: What is the greatest number of three digits which is divisible by 10, 20, 30 ?
(A) 960
(B) 970
(C) 980
(D) 990
(E) 965
Rationale: Greatest number of 3 digits = 999
LCM of 10,20,30 = 60
999 ÷ 60= 16, remainder = 39
Hence, greatest number of four digits which is divisible by 10,20,30
= 999 - 39 = 960
answer : A
Answer: (A) 960
Question: If 50% of 3/5 of a number is 36, then the number is?
(A) 120
(B) 100
(C) 75
(D) 90
(E) None of these
Rationale: Let the number be x. Then 50% of 3/5 of x=36
50/100*3/5*x=36
x=(36*10/3)=120
Required number=120.
Correct Option: A
Answer: (A) 120
Question: Find the number of square tiles to cover the floor of a room measuring 5.5 m * 9.5 m leaving 0.25 m space around the room. A side of square tile is given to be 25 cms?
(A) 422
(B) 476
(C) 429
(D) 428
(E) 720
Rationale: Floor area to be covered by tiles = 5 * 9 = 45
tiles area = 0.25 * 0.25 =0.0625
No. of tiles = 45/0.0625 = 720
Answer : E
Answer: (E) 720
Question: $500 will become $1000 in 4 years find the rate of interest?
(A) A)10%
(B) B)20%
(C) C)25%
(D) D)30%
(E) E)50%
Rationale: SI = simple interest = A-P = 1000-500 = $500
R = 100SI/PT = 100*500/500*4 =25%
Answer is C
Answer: (C) C)25%
Question: If a is positive and a4-62a2+1 = 0, find the value of a3+(1/a3)
(A) 424
(B) 648
(C) 392
(D) 488
(E) None
Rationale: Explanation :
Given a4-62a2+1 = 0
Dividing by a2
a2-62+(1/a2) = 0 => a2+(1/a2) = 62
=> a2+(1/a2)+2 = 64 => (a+(1/a))2 = 64
Hence a+(1/a) = 8 or -8
Since a>0 so a+(1/a) = 8
Now (a+(1/a))3 = a3+(1/a3)+3(a+(1/a))
=> 512 = a3+(1/a3)+24
=> a3+(1/a3) = 488
Answer : D
Answer: (D) 488
Question: The fourth proportional to 4, 7, 16 is:
(A) 20
(B) 22
(C) 24
(D) 26
(E) 28
Rationale: Let the fourth proportional to 4, 7, 16 be x.
Then, 4 : 7 : 16 : x
4x = (7 x 16)
x =	(7 x 16)/4
x=112/4 =28
Answer: Option E
Answer: (E) 28
Question: If x and y are integers and x=50y + 29, which of the following must be odd?
(A) xy
(B) x + y
(C) 3X-1
(D) 3x-1
(E) X+2Y
Rationale: x = 50y + 69, since y is integer, 50y will always be even hence 50y + 69 will be odd hence x = odd
you don't know whether Y is even or odd, so you need to try.
A: odd * even = even ; odd*odd= odd ->not true
B: odd + odd = even ; odd+even = odd -> not true
E: odd + 2*odd = odd ; odd + 2*even = odd -> TRUE, stop here.
D: EVEN , C--EVEN
Answer E
Answer: (E) X+2Y
Question: If (x^2 + 2x - 9)/2 ≤ x -4, then x could be represented by which of the following?
(A) − 4 ≤ x ≤ − 3
(B) − 4 ≤ x ≤ 3
(C) -1 ≤ x ≤ 1
(D) − 3 ≤ x ≤ 4
(E) 3 ≤ x ≤ 4
Rationale: IMO C is correct answer
solving through eqautions
x^2 +2x-9<= 2x-8
(x+1)(x-1)<=0
Answer: (C) -1 ≤ x ≤ 1
Question: How long will it take a train travelling at 78kmph to pass an electric pole if the train is 110 meters in lenght?
(A) 2.07
(B) 3.07
(C) 5.07
(D) 4.07
(E) 2
Rationale: Sol.
Speed = [ 78x5/18] m/sec =21.7 m / sec.
Time taken = (110/21.7)sec =5.07 sec.
Answer C
Answer: (C) 5.07
Question: One fast typist type some matter in 5hrs and another slow typist type the same matter in 8hrs. If both do combine in how much time they will take to finish.
(A) 10 hr 4 mins
(B) 1 hr 4 mins
(C) 2 hr 4 mins
(D) 3 hr 4 mins
(E) 1 hr 14 mins
Rationale: Fast's 1 hr work = 1/5
slow's 1 hr work = 1/8
1/5 + 1/8 = 13/40
they ll finish in 40/13hrs= 3 1/13 ==> 3 hr 4 mins
ANSWER:D
Answer: (D) 3 hr 4 mins
Question: The ratio of three numbers is 5:3:4 and their sum is 108. The second number of the three numbers is?
(A) 24
(B) 27
(C) 29
(D) 32
(E) 33
Rationale: 5:3:4
Total parts = 12
12 parts --> 108
1 part ---->9
The second number of the three numbers is = 3
3 parts ----> 27
B
Answer: (B) 27
Question: A number consists of 3 digits whose sum is 10. The middle digit is equal to the sum of the other two and the number will be increased by 99 if its digits are reversed. The number is:
(A) 251
(B) 253
(C) 255
(D) 257
(E) 260
Rationale: Let the middle digit be x.
Then, 2x = 10 or x = 5. So, the number is either 253 or 352.
Since the number increases on reversing the digits, so the hundred's digits is smaller than the unit's digit.
Hence, required number = 253.
Option B
Answer: (B) 253
Question: From below option 22 is divisible by which one?
(A) A)3
(B) B)4
(C) C)11
(D) D)9
(E) E)7
Rationale: 22/11 = 2
C
Answer: (C) C)11
Question: A sum of money is distributed among A,B,C,D in the proportion of 6:4:8:5. If C gets $3000 more than D, what is the B's share?
(A) $2000
(B) $6000
(C) $1000
(D) $4000
(E) $5000
Rationale: Let the shares of A,B,C,D are 6x,4x,8x,5x
8x-5x = 3000
3x = 3000,X=1000
B's share = 4x = $4000
Answer is D
Answer: (D) $4000
Question: The difference in compound interest earned on a deposit (compounded annually) in year 1 and year 2 is $ 40. Had the interest rate been three times its present value, the difference a would have been how much?
(A) 40/3
(B) 40
(C) 120
(D) 360
(E) 420
Rationale: CASE 1:
Deposit = $x;
Rate of increase = r.
Interest yearned in 1 year = xr. Deposit in 1 year = x + xr.
Interest yearned in 2 year = (x + xr)r.
The difference a= (x + xr)r - xr = xr^2 = 40.
CASE 2:
Deposit = $x;
Rate of increase = 3r.
Interest yearned in 1 year = x(3r). Deposit in 1 year = x + 3xr.
Interest yearned in 2 year = (x + 3xr)3r.
The difference = (x + 3xr)3r - 3xr = 9xr^2. Since from CASE 1 we know that xr^2 = 40, then 9xr^2 = 9*40 = 360.
Answer: D.
Answer: (D) 360
Question: A student has to select 3 subject out of 6 subjects M,B,H,U,L. If he has chosen M, what is the probability of B being chosen ?
(A) 2/5
(B) 1/5
(C) 3/5
(D) 7/5
(E) None of these
Rationale: Explanation :
Out of 6 subjects, one subject M has already been chosen. Ramaining 2 subjects are to be choden from rest (6-1) i.e 5 subjects.
Without restriction, no. of selections = 5C2.
With restriction, no. of selection of B from rest 4 subject = 4C1.
=> Probability
= Selections with restriction / Selections without restriction
= 4C1 / 5C2 .
= 2 / 5.
Hence, the probability of subject B being chosen is 2 / 5.
Answer : A
Answer: (A) 2/5
Question: If a man walks at the rate of 4 kmph, he misses a train by only 6 min. However, if he walks at the rate of 5 kmph he reaches the station 6 minutes before the arrival of the train. The distance covered by him to reach the station is
(A) 3 km
(B) 4 km
(C) 5 km
(D) 6 km
(E) 7 km
Rationale: Let the distance covered be d and time taken to reach the station in time t
d/4 = t+6/60---(1)
d/5 = t-6/60---(2)
(1)-(2) gives
d/4 - d/5 = (6+6)/60
d/20 = 12/60
d = 12*20/60
=4 km
ANSWER:B
Answer: (B) 4 km
Question: If x is equal to the sum of the integers from 40 to 60, inclusive, and y is the number of even integers from 40 to 60, inclusive, what is the value of x + y?
(A) 1021
(B) 1041
(C) 1061
(D) 1081
(E) 1101
Rationale: x = 40 + 41 +...+ 60 = 21(50) = 1050
y = 11
x+y = 1061
The answer is C.
Answer: (C) 1061
Question: A store reported total sales of $480 million for February of this year. If the total sales for the same month last year was $320 million, approximately what was the percent increase in sales?
(A) 2%
(B) 17%
(C) 50%
(D) 65%
(E) 83%
Rationale: New Value – Old Value)/Old Value x 100
We are given:
February sales this year = 480 million
February sales last year = 320 million
We need to determine the percent increase between sales from last year to sales this year.
Thus, the new value = 480 million and the old value = 320 million. Let’s plug them into our percent change formula.
(New Value – Old Value)/Old Value x 100
[(480 – 320)/320] x 100
= 50%.
The answer is C.
Answer: (C) 50%
Question: In a river flowing at 2 km/hr, a boat travels 32 km upstream and then returns downstream to the starting point. If its speed in still water be 6 km/hr, find the total journey time.
(A) 10 hours
(B) 12 hours
(C) 14 hours
(D) 16 hours
(E) None of these
Rationale: Explanation :
speed of the boat = 6 km/hr
Speed downstream = (6+2) = 8 km/hr
Speed upstream = (6-2) = 4 km/hr
Distance travelled downstream = Distance travelled upstream = 32 km
Total time taken = Time taken downstream + Time taken upstream
= (32/8) + (32/4) = (32/8) + (64/8) = (96/8) = 12 hr. Answer : Option B
Answer: (B) 12 hours
Question: Two numbers are respectively 20% and 50% more than a third number. What percentage is the first of the second?
(A) 25%
(B) 60%
(C) 80%
(D) 55%
(E) 74%
Rationale: Required answer = (100+x)/(100+y)*100 = 120*100/150 = 80%
Answer is C
Answer: (C) 80%
Question: mr. depak has $419,574 in his bank account. What is the least amount of money (in whole number of dollars) that he must add to his account if he wants to split this money evenly among her six best friends?
Options:
(A) $1
(B) $2
(C) $3
(D) $4
(E) $0
Rationale: To find the least amount deepak should add to his saving account to split the money evenly among his 6 best friends,
he needs to make the total divisible by 6
Simply add the individual digits of the total = 4+1+9+5+7+4 = 30
If you add 0 , the number is divisible by 0 (30+ 0)
Correct Option : E
Answer: (E) $0
Question: If n is a natural number, then (6n2 + 6n) is always divisible by?
(A) 6 only
(B) 6 and 12 both
(C) 12 only
(D) 6 or 12 only
(E) None
Rationale: (6n2 + 6n) = 6n(n + 1), which is always divisible by 6 and 12 both, since n(n + 1) is always even.
B)
Answer: (B) 6 and 12 both
Question: what should be the rate of interest to become a sum five times of itself in 8 years?
(A) 50
(B) 40
(C) 30
(D) 20
(E) 10
Rationale: let the sum x,after 8 years it should 5x.4x is the interest.
4x=x*r*8/100
r=4*100/8=50%
answer A
Answer: (A) 50
Question: A company has 3 directors and 4 managers. How many different committees with 5 people can be chosen having at least 1 director?
(A) 500
(B) 720
(C) 4500
(D) 25
(E) 21
Rationale: atleast one means exactly one and more than one.
different committees with 5 people can be chosen having at least 1 director is
(3c1*4c4) + (3c2*4c3) + (3c3*4c2) = 21;
Hence E.
Answer: (E) 21
Question: A farmer has an apple orchard consisting of Fuji and Gala apple trees. Due to high winds this year 10% of his trees cross pollinated. The number of his trees that are pure Fuji plus the cross-pollinated ones totals 221, while 3/4 of all his trees are pure Fuji. How many of his trees are pure Gala?
(A) 22
(B) 33
(C) 55
(D) 77
(E) 39
Rationale: Let f = pure fuji , g = pure gala and c - cross pollinated.
c = 10% of x where x is total trees.
c = .1x
also 3x/4 = f and c+f = 221 => .1x + 3/4x = 221 => x = 260
260 - 221 = pure gala = 39.
E
Answer: (E) 39
Question: If the average (arithmetic mean) of a and b is 115, and the average of b and c is 160, what is the value of a − c?
(A) −220
(B) −100
(C) −90
(D) 135
(E) It cannot be determined from the information given
Rationale: Question: a - c = ?
(a + b)/ 2 =115 ===> a + b = 230
(b + c)/2 = 160 ===> b + c = 320
(a + b) - (b + c) = 230 - 320 ===> a + b - b - c = - 90 ===> a - c = - 90
Answer: C
Answer: (C) −90
Question: x<3y<0 which of the following is the greatest?
(A) x+2y
(B) -2x+y
(C) 3x-y
(D) -(2x+2y)
(E) x-y
Rationale: Plugging in -1 for both x and y we get
A. x+2y =-3
B. -2x+y =1
C. 3x-y =-2
D. -(2x+2y) =4
E. x-y =0
Answer: D
Answer: (D) -(2x+2y)
Question: If i walk with 30 miles/hr i reach 1 hour before and if i walk with 20 miles/hr i reach 1 hour late.Find the distance between 2 points and the exact time of reaching destination is 11 am then find the speed with which it walks.
(A) 120 MILES
(B) 130 MILES
(C) 140 MILES
(D) 150 MILES
(E) 160 MILES
Rationale: LET ORIGINAL SPEED BE V AND TIME TAKEN BE T...
AS DISTANCE BETWEEN TWO POINTS IS CONSTANT,
30*(T-1)=20*(T+1)=V*T
HENCE, V=24MILE/HR
T=5 HRS
DISTANCE BETWEEN TWO POINTS IS 120 MILES
ANSWER:A
Answer: (A) 120 MILES
Question: A man by motorcycle goes from Delhi to Bharatpur , a distance of 192 km, at an average speed of 32 kmph. Another man starts from Delhi by car 2.5 h after the motorcyclist starts and reaches Bharatpur half an hour late. What is the ratio of person on the motorcycle to the person going by car ?
(A) 1:2
(B) 2:3
(C) 10:27
(D) 5:4
(E) 4:5
Rationale: A man by motorcycle goes from Delhi to bharatpur
The time take by the motorcyclist = 192/32 = 6 hours
Another man start from Delhi be car after 2.5 hour the man starts = 6 - 2.5 = 3.5
and the man on can reaches half and hour late which is = 3.5 + .5 = 4
Thus, the ratio between motorcycle to car is 4:6
or, 2:3.
ANSWER:B
Answer: (B) 2:3
Question: A, B and C can do a piece of work in 4 days, 6 days and 8 days respectively. How long will they taken, if all the three work together?
(A) 2
(B) 4
(C) 5
(D) 1 11/13
(E) 9
Rationale: 1/4 + 1/6 + 1/8 = 13/24 => 24/13 => 1 11/13 days
Answer: D
Answer: (D) 1 11/13
Question: A man sitting in a train which is traveling at 50 kmph observes that a goods train, traveling in opposite direction, takes 9 seconds to pass him. If the goods train is 150 m long, find its speed.
(A) 20 km/hr
(B) 10 km/hr
(C) 15 km/hr
(D) 18 km/hr
(E) 19 km/hr
Rationale: speed of train = 50 kmph = 50*5/18 = 250/18 m/sec
relative speed =(250/18)+x where x is speed of goods train
then
150/((250/18)+x) = 9
solving it, we get
x= 50/18 m/sec = 10 km/hr
ANSWER:B
Answer: (B) 10 km/hr
Question: If x=-2, which of the following is(are) true?
I. x^2=-|x| II |x|=-x III x/-3 = -2/3
(A) II only
(B) I only
(C) III only
(D) I,II only
(E) II, III only
Rationale: I. x^2=-|x| -2^2 = - |-2| Not true
II |x|=-x |-2| =-( -2 ) true
III x/-3 = -2/3 Not true
Answer : A
Answer: (A) II only
Question: During a certain two-week period, 70 percent of the movies rented from a video store were comedies, and of the remaining movies rented, there were 5 times as many dramas as action movies. If no other movies were rented during that two-week period and there were A action movies rented, then how many comedies, in terms of A, were rented during that two-week period?
(A) A/14
(B) 5A/7
(C) 7A/5
(D) 14A
(E) 35A
Rationale: Total movies = 100.
Comedies = 70.
Action + Drama = 30. Since there were 5 times as many dramas as action movies, then Action + 5*Action = 30 --> Action = A = 5.
Comedies = 70 = 14A.
Answer: D.
Answer: (D) 14A
Question: Ana is 5 years more than Jack. The sum of their ages is 29. Find the ages of Ana
(A) 13
(B) 14
(C) 15
(D) 16
(E) 17
Rationale: Let Jack's age = x
And Ana's age, y = x+5---->(1)
Sum of their ages, x+y = 29----->(2)
substitute equation 1 in 2,
x+(x+5)=29
2x+5=29
2x=29-5
2x=24 ==>x=12(Jack's age)
Substitute x value in equation 1,
y= x+5
y= 12+5
y=17(Ana's age)
ANSWER:E
Answer: (E) 17
Question: find the last 3 digit of 443^443.
(A) 306
(B) 307
(C) 308
(D) 309
(E) 310
Rationale: power is 443
=>443/4 rem=3
so,443^3=86938307
last 3 digit=307
ANSWER:B
Answer: (B) 307
Question: A man can row downstream at 18 kmph and upstream at 10 kmph. Find the speed of the man in still water and the speed of stream respectively?
(A) 2
(B) 9
(C) 7
(D) 4
(E) 3
Rationale: Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively.
Given x + y = 18 --- (1)
and x - y = 10 --- (2)
From (1) & (2) 2x = 28 => x = 14, y = 4.
Answer:D
Answer: (D) 4
Question: A man had a stock of 500 books in his bookshop. He sold 25 on Monday, 50 on Tuesday 30 on Wednesday, 100 on Thursday and 150 on Friday. What percentage of the books were not sold?
(A) 8%
(B) 10%
(C) 29%
(D) 44%
(E) 16%
Rationale: Let N be the total number of books sold. Hence
N = 25 + 50 + 30 + 100 + 150= 355
Let M be the books NOT sold
M = 500 - N = 500- 355 = 145
Percentage
Books not sold / total number of books = 145/500 = 0.29= 29%
correct answer C
Answer: (C) 29%
Question: If a and b are consecutive integers (b>a), which of the following statements could be false? 1. a+b is an even number. 2. ab is even number 3. (a + b) is always an odd number.
(A) II only
(B) II,III only
(C) I only
(D) I,II only
(E) III only
Rationale: odd* even = even
odd+even = odd
Answer : C
Answer: (C) I only
Question: In his pocket, a boy has 3 red marbles, 6 blue marbles, and 6 green marbles. How many will he have to take out of his pocket to ensure that he has taken out at least one of each color?
(A) 12
(B) 13
(C) 14
(D) 15
(E) 16
Rationale: The worst case scenario would be that he has taken 6 blue and 6 green, a total of 12 marbles, and still doesn't have 3 distinct colors. But the next draw, marble number 13, will surely be red as only the red marbles are left in his pocket.
The answer is B.
Answer: (B) 13
Question: by what least number 4320 be multiplied to obtain a number which is a perfect cube ?
(A) 25
(B) 50
(C) 70
(D) 30
(E) 60
Rationale: Solution
Clearly, 4320 = 23 * 33 * 22 * 5.
to make it a perfect cube, it must be multiplied by 2 * 52 i.e., 50 .
Answer B
Answer: (B) 50
Question: If w > a and L < a, which of the following cannot be true?
(A)  d + L = 14
(B)  d - L = 7
(C)  d - L = 1
(D)  a - w = 9
(E)  a + d = 9
Rationale: Is the answer D?
If w>a, then w-a>0 (always positive). The converse would be a-w<0 (always negative). Option D states that a-w=9, which can never be true.
Answer: (D)  a - w = 9
Question: In a garden, there are 12 rows and 14 columns of mango trees. The distance between two trees is 2metres and a distance of one metre is left from all sides of the boundary of the garden. The length of the garden is
(A) 20m
(B) 22m
(C) 24m
(D) 26m
(E) 28m
Rationale: Each row contains 14 plants.
Leaving 2 corner plants, 12 plants in between have (12 x 2) metres & 1 metre on each side is left.
Length = (24 + 2) m = 26m.
ANSWER:D
Answer: (D) 26m
Question: Average monthly income of a family of 4 earning members was Rs. 735. One of the earning members died and therefore, the average income came down to Rs 550. The income of the deceased was?
(A) Rs. 692.80
(B) Rs. 820
(C) Rs. 990
(D) Rs. 1385
(E) None
Rationale: Answer
Income of the deceased = Total income of 4 members - total income of remaining 3 members.
= 735 x 4 - 550 x 3 Rs.
= 1290 Rs.
Correct Option: E
Answer: (E) None
Question: Given a spinner with four sections of equal size labeled T, B, C, and D, what is the probability of NOT getting an T after spinning the spinner two times?
(A) 15/16
(B) 9/16
(C) 1/2
(D) 1/4
(E) 1/8
Rationale: The probability of NOT getting an T after spinning the spinner two times is 3/4*3/4=9/16 (so getting any of the remaining 3 letters out of 4).
Answer: B.
Answer: (B) 9/16
Question: From the integer n, if n*n*n*n is odd, then what is true from below options?
(A) n is odd
(B) n*n is even
(C) n is odd and n*n is even
(D) n is even
(E) None
Rationale: n is odd
Option A
Answer: (A) n is odd
Question: What percentage of numbers from 1 to 70 have 1 or 9 in the unit's digit?
(A) 12 %
(B) 16 %
(C) 18 %
(D) 20 %
(E) 22 %
Rationale: Clearly, the numbers which have 1 or 9 in the unit's digit, have squares that end in the digit 1. Such numbers from 1 to 70 are 1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 59, 61, 69.
Number of such number =14
Required % = (14/70)x100 % =20 %
answer : D
Answer: (D) 20 %
Question: Find the average of first 60 natural numbers.
(A) 30
(B) 60
(C) 61
(D) 35.0
(E) 30.5
Rationale: Explanation:
Sum of first n natural numbers = n(n+1)/2
Hence, sum of first 60 natural numbers = (60 x 61)/2 = 1830
Therefore, required average of = 1830/60 =30.5
ANSWER: E
Answer: (E) 30.5
Question: If xy not equal 0 and x^2*y^2 -xy = 42, which of the following could be y in terms of x?
I. 1/2x
II. -7/x
III. 6/x
(A) II
(B) III
(C) IV
(D) II and III
(E) I &II
Rationale: x2y2 â€“ xy = 6
x2y2-xy-42 = 0
(xy-6)(xy+7)=0
xy = 6 or xy=-7
y = 6/x or y = -7/x
II and III only
D
Answer: (D) II and III
Question: In how many different number of ways 9 men and 2 women can sit on a shopa which can accommodate persons?
(A) A)160
(B) B)170
(C) C)190
(D) D)210
(E) E)1663200
Rationale: 11p7 = 11 x 10 x 9 x 8 x 7 × 6 × 5 = 1663200
Option 'E'
Answer: (E) E)1663200
Question: 2001+1015
(A) 8390
(B) 3016
(C) 2808
(D) 3890
(E) 2080
Rationale: B
Answer: (B) 3016
Question: A train running at the speed of 60 km/hr crosses a pole in 6 seconds. What is the length of the train?
(A) 186 m
(B) 100 m
(C) 872 m
(D) 150 m
(E) 765 m
Rationale: Speed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train
= (Speed x Time) = (50/3 * 6) m
= 100 m.
Answer: B
Answer: (B) 100 m
Question: A man invests 1/3rd of his income at 7%, 1/4th at 8% and the remainder of his income at 10%. If the annual profit is Rs 561. What was the initial capital?
(A) Rs 66098
(B) Rs 6608
(C) Rs 6628
(D) Rs 6600
(E) Rs 6691
Rationale: Explanation:
Let initial amount that the man invests be A
Let x be the capital
=> Profit on 1st investment + Profit on 2nd investment + Profit on 3rd investment
=> S.I. = P X R X T
=> Remainder of capital = 1 - 1/3 - 1/4 = 5/12x (x being the capital)
=> a*1/3 *7/100 + 1/4 *a * 8/100 + 5x/12*a* 10/100 = 561
Therefore, a = 6600
ANSWER: D
Answer: (D) Rs 6600
Question: A and B’s salaries together amount to Rs. 4,000. A spends 95% of his salary and B spends 85% of his. If now their savings are the same, what is A’s salary?
(A) 2777
(B) 1500
(C) 3000
(D) 2776
(E) 2881
Rationale: (5/100) A = (15/100) B
A = 3B
A + B = 4000
4B = 4000 => B = 1000
A = 3000
Answer C
Answer: (C) 3000
Question: 123 : 36 : : 221 : ?
(A) 52
(B) 69
(C) 72
(D) 25
(E) 32
Rationale: (1+2+3)^2 = 36
(2+2+1)^2 = 25
ANSWER:D
Answer: (D) 25