mathewhe/aqua_rat huggingface dataset:
Question: What is the greatest value of n such that 18^n is a factor of 18! ?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: We know that 18 = 2 *3^2.
Hence, we need to find total number of 3s in 18! ( As out of 3 and 2 , we will have count of 3 least)
No. of 3s = 18/3 = 6/3 = 2.
Add the numbers in Bold, you will get total number of 3s = 8.
Hence, total number of 3^2 = 8/2 = 4.
Hence, answer is 4.
ANSWER:D
Answer: (D) 4
Question: In 1992 a total of 100 earthquakes occurred worldwide, some but not all of which occurred in Asia. If 10 of these earthquakes occurred in Asia, which of the following represents the ratio of the number of earthquakes that occurred in Asia to the number that did NOT occur in Asia?
(A) 1/5
(B) 1/9
(C) 1/2
(D) 1/3
(E) 1/4
Rationale: We're given a couple of facts to work with:
1) There were a total of 100 earthquakes
2) Of those earthquakes, 10 of them occurred in Asia
We're asked for the ratio of the number of earthquakes that occurred IN ASIA to the number of earthquakes that DID NOT occur in Asia.
Thus, there were 90 earthquakes that DID NOT occur in Asia....
The answer to the question is 10/90 = 1/9
Answer : B
Answer: (B) 1/9
Question: How many such 6's are there in the following number series which are followed by an even number and preceded by any odd number ? 3 6 4 5 7 6 3 5 4 3 6 4 5 6 4 1 6 3 9 6 3 4 5 6
(A) three
(B) one
(C) two
(D) four
(E) none
Rationale: 3 6 4
3 6 4
5 6 4
so three times
ANSWER:A
Answer: (A) three
Question: A train leaves Delhi at 11 a.m. at a speed of 30 kmph. Another train leaves at 2 p.m. at a speed of 40 kmph on the same day and in the same direction. How far from Delhi, will the two trains meet?
(A) 360
(B) 288
(C) 600
(D) 888
(E) 121
Rationale: D = 30 * 3 = 90
RS = 40 – 30 = 10
T = 90/10 = 9
D = 40 * 9 = 360 km
Answer: A
Answer: (A) 360
Question: In a family 11 people eat only vegetarian, 6 people eat only non veg., 9 people eat both veg and non veg.. How many people eat veg in the family?
(A) 20
(B) 11
(C) 9
(D) 31
(E) 21
Rationale: Total people eat veg = only veg + both veg and non veg
Total= 11+9= 20
Answer = A
Answer: (A) 20
Question: 30 pens and 75 pencils were purchased for 450. If the average price of a pencil was 2.00, find the average price of a pen.
(A) 10
(B) 11
(C) 12
(D) 13
(E) 14
Rationale: Since average price of a pencil = 2
∴ Price of 75 pencils = 150
∴ Price of 30 pens = (450 – 150) = 300
∴ Average price of a pen = 360⁄60 = 10
Answer A
Answer: (A) 10
Question: A, Band C enter into partnership. A invests 3 times as much as B and B invests two-third of what C invests. At the end of the year, the profit earned is Rs. 8800. What is the share of B ?
(A) 1100
(B) 800
(C) 1400
(D) 1200
(E) 1600
Rationale: Let C's capital = Rs. x. Then, B's capital = Rs. (2/3)x
A’s capital = Rs. (3 x (2/3).x) = Rs. 2x.
Ratio of their capitals = 2x : (2/3)x :x = 6 : 2 : 3.
Hence, B's share = Rs. ( 8800 x (2/11))= Rs. 1600.
Answer is E
Answer: (E) 1600
Question: A car covers a distance of 624 km in 4 hours. Find its speed?
(A) 104
(B) 277
(C) 156
(D) 269
(E) 213
Rationale: 624/4 = 156 kmph
Answer:C
Answer: (C) 156
Question: Shop Offered 32% offer for every Shirt, Smith bought a shirt at Rs. 650. and What was the shop's original selling Price?
(A) 955
(B) 550
(C) 600
(D) 700
(E) 750
Rationale: SP* (68/100) = 650
SP= 9.55 * 100 => CP = 955
Answer:A
Answer: (A) 955
Question: A Booster pump can be used for filling as well as for emptying a tank. The capacity of the tank is 2400 m3. The emptying capacity of the tank is 10 m3 per minute higher than its filling capacity and the pump needs 8 minutes lesser to empty the tank than it needs to fill it. What is the filling capacity of the pump?
(A) 18
(B) 50
(C) 34
(D) 69
(E) 59
Rationale: Let, the filling capacity of the pump be x m3/min
Then, emptying capacity of the pump=(x+10) m3/min.
So,2400/x – 2400/(x+10) = 8
on solving x=50.
ANSWER:B
Answer: (B) 50
Question: If 0.75 : x :: 5 : 8, then x is equal to:
(A) 120
(B) 12
(C) 1.2
(D) 0.12
(E) 0.012
Rationale: ((x) x 5) = (0.75 x 8)
= x = 6/5
= 1.20
Answer is C.
Answer: (C) 1.2
Question: If a student loses 5 kilograms, he will weigh twice as much as his sister. Together they now weigh 116 kilograms. What is the student's present weight in kilograms?
(A) 76
(B) 77
(C) 78
(D) 79
(E) 80
Rationale: Let x be the weight of the sister.
Then the student's weight is 2x+5.
x + (2x+5) = 116
3x = 111
x = 37 kg
Then the student's weight is 79 kg.
The answer is D.
Answer: (D) 79
Question: A trader mixes 80 kg of tea at 15 per kg with 20 kg of tea at cost price of 20 per kg. In order to earn a profit of 25%, what should be the sale price of the mixed tea?
(A) 23.75
(B) 22
(C) 20
(D) 19.20
(E) None of these
Rationale: C.P. of mixture = 80×15+20×20/80+20=16
∴ S.P. = (100+25)/100×16=20
Answer C
Answer: (C) 20
Question: If x = 1 + √2, then what is the value of x4 - 4x3 + 4x2 + 5?
(A) -1
(B) 0
(C) 6
(D) 2
(E) 3
Rationale: Answer
x = 1 + √2
∴ x4 - 4x3 + 4x2 + 5 = x2(x2 - 4x + 4) + 5
= x2(x - 2)2 + 5
= (1 + √2)2(1 + √2 - 2)2 + 5
=(√2 + 1)2 (√2 - 1)2 + 5
=[(√2)2 - (1)2]2 + 5
=(2 - 1)2 =1 + 5=6
Correct Option: C
Answer: (C) 6
Question: When I add 4 times my age 4 years from now to 5 times my age 5 years from now, I get 10 times my current age. How old will I be 3 years from now?
(A) 42 years
(B) 41 years
(C) 43 years
(D) 40 years
(E) 45 years
Rationale: Let x= current age 4(x+4)+5(x+5)=10x ;so x=R 41 years
Answer C
Answer: (C) 43 years
Question: If one-third of one-fourth of a number is 15, then three-tenth of that number is:
A. 35
(A) 23
(B) 87
(C) 26
(D) 54
(E) 01
Rationale: Explanation:
The number is 1/3 of 1/4 is =15 then 1/3 × 1/4 = 15
Number is 180 then 180 × 3/10 = 54
Answer: D
Answer: (D) 54
Question: Mangala completes a piece of work in 10 days, Raju completes the same work in 15 days. If both of them work together, then the number of days required to complete the work is?
(A) 5 days
(B) 6 days
(C) 7 days
(D) 8 days
(E) 9 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 = 10 Ã— 15/25 = 6 days.
B)
Answer: (B) 6 days
Question: In a garden, there are 10 rows and 15 columns of mango trees. The distance between the two trees is 2 metres and a distance of one metre is left from all sides of the boundary of the garden. The length of the garden is
(A) 20 m
(B) 30 m
(C) 24 m
(D) 26 m
(E) 28 m
Rationale: Explanation:
Each row contains 15 plants.
There are 14 gapes between the two corner trees (14 x 2) metres and 1 metre on each side is left.
Therefore Length = (28 + 2) m = 30 m.
Answer: B
Answer: (B) 30 m
Question: If x and y are integers and x + y = 5, which of the following must be true?
(A) x and y are consecutive integers.
(B) If x < 0, then y > 0.
(C) If x > 0, then y < 0.
(D) Both x and y are even.
(E) Both x and y are less than 5.
Rationale: Notice that the question asks which of the following MUST be true, not COULD be true.
Given: x + y = 5
A. x and y are consecutive integers: not necessarily true, for example x=1 and y=4;
B. If x < 0, then y > 0: if x is negative then y must be positive in order x+y to be positive, so this statement must be true;
C. If x > 0, then y < 0: not necessarily true, for example x=1 and y=4;
D. Both x and y are even: never true, as the sum of two even numbers is even and can not equal to odd number 5;
E. Both x and y are less than 5: not necessarily true, for example x=6 and y=-1;
Answer: B.
Answer: (B) If x < 0, then y > 0.
Question: Sam is training for the marathon. He drove 12 miles from his home to the Grey Hills Park and then ran 5 miles to Red Rock, retraced his path back for 2 miles, and then ran 3 miles to Rock Creek. If he is then n miles from home, what is the range of possible values for n?
(A) 1 ≤ n ≤23
(B) 3 ≤ n ≤21
(C) 6 ≤ n ≤18
(D) 5 ≤ n ≤19
(E) 9 ≤ n ≤15
Rationale: ANSWER: C To find the maximum and minimum range for his distance from home, assume that he traveled either directly toward his home or directly away from his home. The range then is between 12+5-2+3=18 for the maximum, and 12-5+2-3=6 for the minimum, so C is the answer
Answer: (C) 6 ≤ n ≤18
Question: 8 litres are drawn from a cask full of wine and is then filled with water. This operation is performed three more times. The ratio of the quantity of wine now left in cask to that of the water is 16 : 65. How much wine the cask hold originally ?
(A) 18 litres of wine
(B) 24 litres of wine
(C) 32 litres
(D) 42 litres
(E) None
Rationale: Solution
Let the quantity of the wine in the cask originally be x litres
then, quantity of wine left in cask after 4 operations
= [x(1- 8/x)4] litres.
Therefore x(1- 8/x)4 / x = 16/81 =› (1- 8/x)4 = (2/3)2
=› (x - 8 / x) = 2/3 =› 3x - 24 = 2x =› x = 24.
Answer B
Answer: (B) 24 litres of wine
Question: The sides of a cube are in the ratio 1:2 the ratio of their volume is?
(A) 1:6
(B) 1:4
(C) 1:0
(D) 1:2
(E) 1:1
Rationale: 1:4
Answer:B
Answer: (B) 1:4
Question: It takes a boat 3 hours to travel down a river from point A to point B, and 5 hours to travel up the river from B to A. How long would it take the same boat to go from A to B in still water?
(A) 1h 15m
(B) 6h 35m
(C) 3h 45m
(D) 2h 49m
(E) 4h 40m
Rationale: Let: S be the speed of the boat in still water, r be the rate of the water current and d the distance between A and B.
d = 3(S + r) : boat traveling down river
d = 5(S - r) : boat traveling up river
3(S + r) = 5(S - r)
r = S / 4 : solve above equation for r
d = 3(S + S/4) : substitute r by S/4 in equation B
d / S = 3.75 hours = 3 hours and 45 minutes.
correct answer is :C) 3h 45m
Answer: (C) 3h 45m
Question: Find the ones digit of 73^300
(A) 3
(B) 5
(C) 6
(D) 7
(E) 10
Rationale: Cyclicity of 3 is 3,9,7,1after 4 multiplication again the cycle repeats.
So divide 330 by 4 and we get 87 as quotient and 2 as remainder. So cycle will run for 87 times and then 2 times more. So pick up the 2nd item from the cycle.
Hence Answer E.
Answer: (E) 10
Question: If the mean of numbers 28, x, 42, 78 and 104 is 62, then what is the mean of 128, 255, 280, 511, 1023 and x?
(A) 395
(B) 375.8
(C) 355
(D) 415
(E) 365
Rationale: The mean of numbers 28, x, 42, 78 and 104 is 62: 28+x+42+78+104=62*5 --> x=58;
So, the mean of 128, 255, 511, 1023 and x is (128+255+280+511+1023+58)/6=375.8.
Answer: B.
Answer: (B) 375.8
Question: What is the equation of a circle of radius 4 units centered at (3, 2)?
(A) x^2 + y^2 + 6x – 4y = 23
(B) x^2 + y^2 - 6x + 4y = 23
(C) x^2 + y^2 - 6x – 4y = 3
(D) x^2 + y^2 - 6x – 4y = - 23
(E) x^2 + y^2 + 6x + 4y = 23
Rationale: the equation of a circle with center at (a,b) and radius R is (X-a)^2+(Y-b)^2=R^2
=> answer = (X-3)^2+(Y-2)^2=4^2
solving,,we get the equation in answer choice C
Answer: (C) x^2 + y^2 - 6x – 4y = 3
Question: If green means red, red means yellow, yellow means blue, blue means orange and orange means green, what is the colour of leaf ?
(A) Red
(B) Green
(C) Yellow
(D) Orange
(E) Pink
Rationale: Explanation:
The colour of leaf is 'green' and as given 'orange' means 'green'.
so, the colour of leaf is 'red'.
Answer: D
Answer: (D) Orange
Question: A committee of 4 persons is to be formed from 3 company secretaries, 4 economists and 1 chartered accountant. What is the probability that each of the three professions is represented in the committee?
(A) 1/28
(B) 12/14
(C) 1/14
(D) 4/28
(E) 3/14
Rationale: 3/8*4/7*1/6*4! = 3/14. We are multiplying by 4! because we can choose secretary,economist, and accountant is several way:
Answer: B.
Answer: (B) 12/14
Question: How many positive integers less than 500 can be formed using the numbers 1, 2, 3 and 5 for the digits?
(A) 48
(B) 52
(C) 66
(D) 68
(E) 84
Rationale: Notice that we can find the number of 2 and 3 digit numbers by just assuming the first digit can also be zero:
0 1 1
1 2 2
2 3 3
3 5 5
Number of possibilities = 4*4*4 = 64.
Then, just add up the number of 1 digits numbers = 4, so total is 64+4 = 68.
Answer: D
Answer: (D) 68
Question: In a mixed college 160 students are there in one class. Out of this 160 students 3/4 students are girls. How many boys are there ?
(A) 40
(B) 60
(C) 80
(D) 120
(E) 140
Rationale: Total Number of Students :160
Total Girls : 160*3/4 =120
Total Boys : 160-120 = 40
Answer is A
Answer: (A) 40
Question: What is the sum of odd integers from 35 to 95, inclusive?
(A) 2,015
(B) 1,500
(C) 1,240
(D) 1,120
(E) 1,100
Rationale: Number of odd integers = (95-35)/2 + 1
= 60/2 + 1
= 31
Sum of odd integers = (35+95)/2 * 31
=2015
Answer A
Answer: (A) 2,015
Question: A boat can move upstream at 25 kmph and downstream at 37 kmph, then the speed of the current is?
(A) 5
(B) 6
(C) 7
(D) 54
(E) 3
Rationale: US = 25
DS = 37
M = (37 - 25)/2 = 6.Answer:B
Answer: (B) 6
Question: A leak in the bottom of a tank can empty the tank in 6 hrs. An pipe fills water at the rate of 4 ltrs/ minute. When the tank is full in inlet is opened and due to the leak the tank is empties in 8 hrs. The capacity of the tank is?
(A) 2345
(B) 3456
(C) 4567
(D) 4890
(E) 5760
Rationale: 1/x - 1/6 = -1/8
x = 24 hrs
24 * 60 * 4 = 5760
E
Answer: (E) 5760
Question: The market value of a 10.5% stock, in which an income of Rs. 756 is derived by investing Rs. 7000, brokerage being 1/4%, is:
(A) 96.97
(B) 114
(C) 114.75
(D) 124
(E) 124.75
Rationale: Face Value = Rs. 7000.
Dividend = 10.5%.
Annual Income = Rs. 756.
Brokerage per Rs. 100 = Rs. 0.25.
Dividend is always paid on the face value of a share.
Face Value * Dividend / (Market Value + Brokerage per Rs. 100) = Annual income.
= 7000 * 10.5 / 756 = Market Value of Rs. 100 stock + Brokerage per Rs. 100.
= Market Value of Rs. 100 stock + Brokerage per Rs. 100 = Rs. 97.22.
= Market Value of Rs. 100 stock = Rs. 97.22 - Re. 0.25.
= Market Value of Rs. 100 stock = Rs. 96.97
answer : A
Answer: (A) 96.97
Question: Peter got a weekly raise of $680. If he gets paid every other week, write an integer describing how the raise will affect his paycheck.
(A) 860
(B) 806
(C) 608
(D) 680
(E) 850
Rationale: Let the 1st paycheck be x (integer).
Peter got a weekly raise of $ 680.
So after completing the 1st week she will get $ (x+680).
Similarly after completing the 2nd week he will get $ (x + 680) + $ 680.
= $ (x + 680 + 680)
= $ (x + 1360)
So in this way end of every week her salary will increase by (D)$ 680.
Answer: (D) 680
Question: What is the normal price of an article sold at $126 after two successive discounts of 10% and 20%?
(A) $155
(B) $165
(C) $175
(D) $185
(E) $195
Rationale: 0.8*0.9*cost price = $126
cost price = $175
The answer is C.
Answer: (C) $175
Question: If x and y are integers such that x > y, which of the following CANNOT be a positive integer?
I. y(y – x)
II. y(x – y)
III. (x - y)/(y - x)
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) II and III only
Rationale: lets see the three equations..
I. y(y – x)
if both x and y are negative number, y will be -ive and y-x, as numeric value of y will be more than x,will also be -ive... so out
II. y(x – y)
if both x and y are +ive number, y will be +ive and x-y will also be positive... so out
III. (x - y)/(y - x)
either one of the numerator and denominator will be -ive and the other +ive..
so will always be -ive
we need not see any further after checking for II as all choices except C are eliminated..
ANSWER:C
Answer: (C) III only
Question: A and B started business in partnership investing Rs. 20,000 and Rs. 15,000 respectively. After six months, C joined them with Rs. 20,000. What will be B's share in the total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business?
(A) Rs.7500
(B) Rs.7509
(C) Rs.7508
(D) Rs.7597
(E) Rs.7523
Rationale: A:B:C = (20000 * 24) : (15000 * 24) : (20000 * 18) = 4:3:3
B's share = 25000 * 3/10 = Rs.7500.
Answer: A
Answer: (A) Rs.7500
Question: A grocer has a sales of Euro 220, Euro 320, Euro 480, Euro 120and Euro 720 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Euro 920?
(A) uro 4691
(B) uro 4591
(C) uro 3591
(D) uro 7791
(E) uro 3660
Rationale: E
Euro 1860
T otal sale for 5 months = Euro (220 + 320 + 480 + 120 + 720) = Euro 1860.
Required sale = Euro [ (920 x 6) - 1860]
= Euro (5520 - 1860)
= Euro 3660.
Answer is E
Answer: (E) uro 3660
Question: In a function they are distributing noble prize. In how many ways can 3 prizes be distributed among 4 boys when No boy gets more than one prize?
(A) 12
(B) 14
(C) 17
(D) 24
(E) 27
Rationale: Sol. In this case, repetitions are not allowed. So, the first prize can be given in 4 ways. The second in 3 ways and the third in 2 ways. But fundamental principle, (4 x 3 x 2) ways = 24 ways
4: Or 4p = — 4:- 4X3X2X1- 24 ways
D
Answer: (D) 24
Question: The difference between the compound interest compounded annually and simple interest for 2 years at 20% per annum is Rs.144. Find the principal?
(A) 2277
(B) 2667
(C) 3600
(D) 2766
(E) 1811
Rationale: P = 144(100/5)2 => P = 3600
Answer: C
Answer: (C) 3600
Question: The mean of 50 observations was 39. It was found later that an observation 48 was wrongly taken as 23. The corrected new mean is
(A) 35.2
(B) 36.1
(C) 36.5
(D) 39.1
(E) None
Rationale: Sol.
Therefore correct sum
= ( 39 × 50 + 48 – 23)
= 1975.
Therefore correct mean
= 1975 / 50
= 39.5.
Answer E
Answer: (E) None
Question: Six students - 3 boys and 3 girls - are to sit side by side for a makeup exam. How many ways could they arrange themselves given that no two boys and no two girls can sit next to one another?
(A) 12
(B) 36
(C) 72
(D) 240
(E) 720
Rationale: in order not to have two boys or two girls next to one another, we must make an alternate sitting arrangement. (B-G-B-G-B-G) or (G-B-G-B-G-B).
Total ways = 2C1*3!*3!
=2*6*6
=72
Ans - C
Answer: (C) 72
Question: Mohit sold an article for Rs. 18000. Had he offered a discount of 19% on the selling price, he would have earned a profit of 8%. What is the cost price of the article?
(A) 13500
(B) 27767
(C) 16688
(D) 26678
(E) 19987
Rationale: Let the CP be Rs. x.
Had he offered 19% discount, profit = 8%
Profit = 8/100 x and hence his SP = x + 8/100 x = Rs. 1.08x = 18000 - 19/100(18000) = Rs. 14580
=> 1.08x = 14580
=> x = 13500
\Answer: A
Answer: (A) 13500
Question: A reduction of 25% in the price of apples would enable a man to obtain 36 more for Rs.25, what is reduced price per dozen?
(A) 2
(B) 3
(C) 6
(D) 7
(E) 10
Rationale: A
25*(25/100) = 6 --- 36
? --- 12 => Rs.2
Answer: (A) 2
Question: The average speed of a car decreased by 3 miles per hour every successive 8-minutes interval. If the car traveled 4.4 miles in the sixth 8-minute interval, what was the average speed of the car, in miles per hour, in the first 8 minute interval?
(A) 35
(B) 40
(C) 48
(D) 51
(E) 54
Rationale: (4.4 miles / 8 minutes)*60 minutes/hour = 33 mph
Let x be the original speed.
x - 5(3) = 33
x = 48 mph
The answer is C.
Answer: (C) 48
Question: Find the value of x in 3(x-8)=24
(A) 8
(B) 12
(C) 16
(D) 20
(E) 24
Rationale: 3(x-8)=24
Dividing both sides with 3 gives x-8=8
Adding both sides with 8 gives x=16
Answer: C
Answer: (C) 16
Question: Gopi gives Rs. 90 plus one turban as salary to his servant for one year. The servant leaves after 9 months and receives Rs. 65 and the turban. Find the price of the turban.
(A) 27
(B) 36
(C) 29
(D) 10
(E) 11
Rationale: Let the price of turban be x.
Thus, for one year the salary = (90 + x)
For 9 months he should earn 3434 (90 + x).
Now he gets one turban and Rs. 65.
Thus, 3434 (90 + x) = 65 + x or 270 + 3x = 260 + 4x or x = 10
Answer:D
Answer: (D) 10
Question: Three numbers are in the ratio 1 : 2 : 3 and their H.C.F. is 12. The numbers are :
(A) 4, 8, 12
(B) 5, 10, 15
(C) 10, 20, 30
(D) 12, 24, 36
(E) None of these
Rationale: Explanation:
Let the required numbers be x, 2x and 3x.
Then, their H.C.F = x. So, x = 12.
The numbers are 12, 24 and 36.
ANSWER IS D
Answer: (D) 12, 24, 36
Question: The cost per unit of electricity during a 4 year period is as follows: Year 1, $3 per unit; Year 2, $4 per unit; Year 3, $5 per unit; Year 4, $6 per unit. If a factory spent equal dollars on electricity each year, what was the average cost of a unit of electricity during the 4 year period?
(A) $4.31
(B) $4.51
(C) $4.21
(D) $5.21
(E) $5.61
Rationale: Let money spent each year = $60
Units bought first year = 20
Units bought second year = 15
Units bought third year = 12
Units bought fourth year = 10
Total number of units = 57
Total money spent = 60*4 = 240
Average = 240/57 = 4.21
Answer : C
Answer: (C) $4.21
Question: If P is a prime number greater than 3, find the remainder when P^2 + 14 is divided by 12.
(A) 6
(B) 1
(C) 3
(D) 8
(E) 7
Rationale: Every prime number greater than 3 can be written 6N+1 or 6N-1.
If P = 6N+1, then P^2 + 14 = 36N^2 + 12N + 1 + 14 = 36N^2 + 12N + 12 + 3
If P = 6N-1, then P^2 + 14 = 36N^2 - 12N + 1 + 14 = 36N^2 - 12N + 12 + 3
When divided by 12, it must leave a remainder of 3.
The answer is C.
Answer: (C) 3
Question: Find the odd man out. 2,4,7,10,16
(A) 11
(B) 9
(C) 10
(D) 6
(E) 14
Rationale: Explanation :
2+2=4
4+3=7
7+4=11
11+5=16
Hence, it is clear that 11 should have come instead of 10
Answer : Option A
Answer: (A) 11
Question: A team of 6 cooks is chosen from 9 men and 5 women. The team must have at least 2 men and at least 3 women. How many ways can this team be created?
(A) 140
(B) 320
(C) 560
(D) 700
(E) 1020
Rationale: Only possible combinations are a team of 2M, 4 W or 3M,3W.
Possible ways to make a team of 2M,4W = 9C2 * 5C4 =36*5 =180
Possible ways to make a team of 3M,3W = 9C3* 5C3 = 84*10 = 840
Total possible ways = 180+840 = 1020
Ans E it is.
Answer: (E) 1020
Question: The ratio between the length and the breadth of a rectangular park is 5 : 3. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 min, then thearea of the park (in sq. m) is?
(A) 124545 m
(B) 134561 m
(C) 156787 m
(D) 15450 m
(E) 150000 m
Rationale: Perimeter = Distance covered in 8 min. = 12000 x 8 m = 1600 m.
60
Let length = 5x metres and breadth = 3x metres.
Then, 2(5x + 3x) = 1600 or x = 100.
Length = 500 m and Breadth = 300 m.
Area = (500 x 300) m2 = 150000 m
E
Answer: (E) 150000 m
Question: 30 pens and 75 pencils were purchased for 510. If the average price of a pencil was 2.00, find the average price of a pen.
(A) 10
(B) 11
(C) 12
(D) cannot be determined
(E) None of the above
Rationale: Since average price of a pencil = 2
∴ Price of 75 pencils = 150
∴ Price of 30 pens = (510 – 150) = 360
∴ Average price of a pen = 360⁄60 = 12
Answer C
Answer: (C) 12
Question: The area of a square is 4096 sq cm. Find the ratio of the breadth and the length of a rectangle whose length is twice the side of the square and breadth is 24 cm less than the side of the square?
(A) 5 : 16
(B) 5 : 17
(C) 5 : 11
(D) 5 : 19
(E) 1 : 16
Rationale: Let the length and the breadth of the rectangle be l cm and b cm respectively. Let the side of the square be a cm.
a2 = 4096 = 212
a = (212)1/2 = 26 = 64
L = 2a and b = a - 24
b : l = a - 24 : 2a = 40 : 128 = 5 : 16
Answer: A
Answer: (A) 5 : 16
Question: A person is traveling at 45km/hr and reached his destiny in 5hr find the distance?
(A) A)100km
(B) B225km
(C) C)135km
(D) D)80km
(E) E)125km
Rationale: speed = 45km/hr
time = 5hr
distance = 45*5 = 225km
Answer is B
Answer: (B) B225km
Question: The captain of a cricket team of 11 members is 27 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) 20 years
(B) 21 years
(C) 22 years
(D) 23 years
(E) 24 years
Rationale: Explanation:
Let the average age of the whole team by x years.
11x â€“ (27 + 30) = 9(x -1)
11x â€“ 9x = 48
2x = 48
x = 24.
So, average age of the team is 24 years.
Answer E
Answer: (E) 24 years
Question: what is next no. 11 23 47 83 131 191 263 ???
(A) 171
(B) 347
(C) 191
(D) 201
(E) 211
Rationale: 11+12*1=23
23+12*2=47
47+12*3=83
83+12*4=131
131+12*5=191
191+ 12*6=263
263+12*7=347
ANSWER:B
Answer: (B) 347