mathewhe/aqua_rat huggingface dataset:
Question: A certain hall contains two cuckoo clocks. If the first clock chirps 20 times per hour and the second clock chirps 10 times per hour, and both clocks chirp for the first time at 2:03 PM, at what time will the first clock have chirped three times as many times as the second clock can chirp per hour?
(A) 2:30 PM
(B) 2:45 PM
(C) 3:00 PM
(D) 3:15 PM
(E) 3:30 PM
Rationale: The question is asking when the first clock will have chirped 30 times (3*10 chirps).
The first clock chirps once every 3 minutes.
If the first chirp is at 2:03, then the 30th chirp is at 90 minutes after 2:00.
The answer is E.
Answer: (E) 3:30 PM
Question: A man goes downstream at 11 kmph, and upstream8 kmph. The speed of the stream is
(A) 1.5kmph
(B) 4kmph
(C) 16kmph
(D) 2.5kmph
(E) 26kmph
Rationale: Speed of the stream = 1/2(11-8)kmph
=1.5kmph.
correct option :A
Answer: (A) 1.5kmph
Question: How many integers between 100 and 170, inclusive, cannot be evenly divided by 3 nor 5?
(A) 36
(B) 38
(C) 40
(D) 42
(E) 44
Rationale: The total numbers between 100 and 170, inclusive, is 71.
3*34=102 and 3*56=168 so the number of multiples of 3 is 23.
5*20=100 and 5*34=170 so the number of multiples of 5 is 15.
However, the multiples of 15 have been counted twice.
15*7=105 and 15*11=165 so the number of multiples of 15 is 5.
Thus the total number is 71-23-15+5=38.
The answer is B.
Answer: (B) 38
Question: A chemical supply company has 60 liters of a 30% HNO3 solution. How many liters of pure undiluted HNO3 must the chemists add so that the resultant solution is a 50% solution?
(A) 12
(B) 15
(C) 20
(D) 24
(E) 30
Rationale: 60 liters of a 30% HNO3 solution means HNO3 = 18 liters in 60 liters of the solution.
Now, let x be the pure HNO3 added.
As per question,
18 + x = 50% of (60 + x)
or x =24. Hence, D
Answer: (D) 24
Question: On an order of 5 dozen boxes of a consumer product, a retailer receives an extra dozen free. This is equivalent to allowing him a discount of?
(A) 16 2/37%
(B) 16 2/3%
(C) 16 6/3%
(D) 12 2/3%
(E) 16 3/3%
Rationale: Clearly, the retailer gets 1 dozen out of 6 dozens free.
Equivalent discount = 1/6 * 100 = 16 2/3%.Answer: C
Answer: (C) 16 6/3%
Question: How many 4 digit number contain number 2 ?
(A) 3168
(B) 3268
(C) 3368
(D) 3468
(E) 3568
Rationale: total 4 digit no. = 9*10*10*10 = 9000
not containing 2 = 8*9*9*9 = 5832
total 4 digit number contain 2 = 9000 - 5832 = 3168
ANSWER:A
Answer: (A) 3168
Question: Denise is trying to open a safe whose combination she does not know. IF the safe has 4000 possible combinations,and she can try 50 different possibilities,what is the probability that she does not pick the one correct combination.
(A) 1
(B) 0.9875
(C) 0.8875
(D) 3/160
(E) 0
Rationale: If Denise does not pick the correct combination in first 50 try, then the correct combination is one of remaining 3950. So Probability = 3950/4000 = 0.9875.
answer is B
Answer: (B) 0.9875
Question: The ratio of male to female in a class is 3:3. the career preference of the students in the class are to be represented in a circle graph. If the area of the graph allocated to each career preference is to be proportional to the number of students who have that career preference, how many degrees of the circle should be used to represent a career that is preferred by one third of the males and two-third of the females in the class?
(A) a)160 degree
(B) b) 168 degree
(C) c)191 degree
(D) d)180 degree
(E) e)204 degree
Rationale: here is my approach => males => 3x and females =3x => total =6x
now 6x=> 360
therefore 3x => 180 degree .
P.S => 3x is nothing but total number of students with the given prefee
aNSWER D
Answer: (D) d)180 degree
Question: A boat whose speed is 15 k/hr in still water goes 30 k/he downwards and come back in total 4 hr 30 min what is the speed of stream in k/hr ?
(A) 1km/hr
(B) 2km/hr
(C) 3km/hr
(D) 4km/hr
(E) 5km/hr
Rationale: If the speed of stream=x
Speed in downstream=15+x , Speed in Upstream=15-x,
Total time=4 hr 30 min=9/2 hr
[30/(15+x) + 30/(15-x)]=9/2,Solving x=5
x=5km/hr
ANSWER:E
Answer: (E) 5km/hr
Question: Find the odd man out
4, 9, 16, 25, 36, 50, 64, 81
(A) 4
(B) 9
(C) 25
(D) 36
(E) 50
Rationale: as 50 is only odd number.
ANSWER:E
Answer: (E) 50
Question: 16 men can complete a piece of work in 25 days. In how many days can 20 men complete that piece of work?
(A) 33
(B) 77
(C) 20
(D) 99
(E) 71
Rationale: 16 * 25 = 20 * x => x
= 20 days
Answer: C
Answer: (C) 20
Question: Of all the players in a professional baseball league, 1/2 are foreign-born, including 1/3 of the pitchers. If 3/4 of the players are pitchers, what percentage of the players who are not pitchers are foreign-born?
(A) 100%
(B) 75%
(C) 66 2/3%
(D) 50%
(E) 25%
Rationale: Assume that the total number of players is 100.
1/2 are foreign born, so 50 are foreign born. 75 players are pitchers out of which 1/3 are foreign born. 25 players are foreign born and pitchers. The other 25 who are foreign born are thus not pitchers.
Thus out of 25 non pitchers, 25 are foreign born. Answer: A - 100%
ANSWER:A
Answer: (A) 100%
Question: Murali travelled from city A to city B at a speed of 40 kmph and from city B to city C at 60 kmph. What is the average speed of Murali from A to C given that the ratio of distances between A to B and B to C is 2 : 3?
(A) 17 kmph
(B) 50 kmph
(C) 18 kmph
(D) 17 kmph
(E) 11 kmph
Rationale: Let the distances between city A to B and B to C be 2x km and 3x km respectively.
Total time taken to cover from A to C
= (2x)/40 + (3x)/60 = (6x + 6x)/120 = 12x/120 = x/10 Average speed = (2x + 3x)/(x/10)
= 50 kmph.
Answer:B
Answer: (B) 50 kmph
Question: A lemonade stand sold only small and large cups of lemonade on Tuesday. 3/5 of the cups sold were small and the rest were large. If the large cups were sold for 7/3 as much as the small cups, what fraction of Tuesday's total revenue was from the sale of large cups?
(A) (a) 14/23
(B) (b) 7/15
(C) (c) 10/21
(D) (d) 17/35
(E) (e) 1/2
Rationale: This problem is very good example how easy and quick plug-in method might be.
Let the total # of cups be 10.
# of small cups sold 3/5*10=6;
# of large cups sold 10-6=4;
Let the price of small cup be $6, then the price of larges cup would be 7/3*6=$14;
Revenue from small cups: 6*$6=$36;
Revenue from large cups cups: 4*$14=$56;
Fraction of total revenue from large cups: 56/(36+56)=14/23.
Answer: A.
Answer: (A) (a) 14/23
Question: A monkey start climbing up a tree 17 ft tall.Each hour it hops 3 ft and slips back 2 ft. How much time would it take the monkey to reach the top.
(A) 15 hrs
(B) 18 hrs
(C) 19 hrs
(D) 17 hrs
(E) 16 hrs
Rationale: if monkey hops 3ft and slips back 2ft in a hour, it means the monkey hops (3ft-2ft)= 1ft/hr.
similarly in 14hrs it wil be 14ft.
Bt since the height of the tree is 17ft, so if the monkey hops up the tree in the next hr i.e 15th hr then it reaches at the top of the tree.
hence it takes 15 hrs for monkey to reach at the top
ANSWER:A
Answer: (A) 15 hrs
Question: If x is an integer, which of the following is a possible value of K=(x^2 +2x – 7)/9?
(A) -2.4
(B) 0.268
(C) 1.166 repeating
(D) 4.555 repeating
(E) 8.125
Rationale: x is an integer, which of the following is a possible value of K=(x^2 +2x – 7)/9?
Used process of elimination
A. -2.4
when this is multiplied by 9, x is not an integer
B. 0.268
when this is multiplied by 9, x is not an integer
C. 1.166 repeating
when this is multiplied by 9, x is not an integer
D. 4.555 repeating
E. 8.125
when this is multiplied by 9, x is not an integer
Answer choice D seems to fit.D
Answer: (D) 4.555 repeating
Question: Of the 550 people attending a conference, 300 have signed up for the Marketing workshop and 400 have signed up for the Accounting workshop. If 110 of the people attending did not sign up for either workshop, then the number of people who signed up for both the Marketing and the Accounting workshops is:
(A) 245
(B) 260
(C) 275
(D) 280
(E) 300
Rationale: Since the information in the prompt refers to the 'standard' 5 groups, you can use the Overlapping Sets Formula to get to the solution:
Total = Gp.1 + Gp.2 - Both + Neither
550 = 300 + 400 - Both + 110
550 = 810 - Both
Both = 260
Final Answer:
B
Answer: (B) 260
Question: A spends 90% of his salary and B spends 85% of his salary. But savings of both are equal. Find the income of B, if sum of their incomes is Rs. 5000.
(A) 2000
(B) 2400
(C) 2125
(D) 2400
(E) None
Rationale: Explanation:
Let the incomes of A and B are x, y respectively.
Savings of A = (100 - 90)% (x) = 10% (x)
Savings of B = (100 - 85)% (y) = 15% (y)
Given, both saves equal amount.
Therefore, 10% (x) = 15% (y) ⇒xy=15%/10%=3/2
Therefore, x : y = 3 : 2
Hence, B's salary = 2/(2+3) x 5000 = Rs. 2000.
Correct Option: A
Answer: (A) 2000
Question: A box contain a certain number of balls, marked successively from 1 to n. If there are 55 different ways that two balls can be selected from the box such that the ball with number 3 marked on it is not selected, then what is the value of n?
(A) 6
(B) 8
(C) 9
(D) 12
(E) 14
Rationale: Total ways of selecting 2 balls out of n balls = nC2
We're told that one balls marked as 3 cannot be selected.
So total number of balls left now = (n-1)
Hence total ways of selecting 2 balls out of (n-1) balls = (n-1)C2
Given that (n-1)C2 = 55
So, [(n-1)(n-2)]/[2 * 1] = 55
So, n^2-3n+2 = 110
So, n^2-3n-108 = 0
So, n = 12 or -9 (rejected)
Hence option 4.
ANSWER:D
Answer: (D) 12
Question: What is the tens digit of 6^19?
(A) 1
(B) 3
(C) 5
(D) 7
(E) 9
Rationale: The tens digit of 6 in integer power starting from 2 (6^1 has no tens digit) repeats in a pattern of 5: {3, 1, 9, 7, 5}:
The tens digit of 6^2=36 is 3.
The tens digit of 6^3=216 is 1.
The tens digit of 6^4=...96 is 9.
The tens digit of 6^5=...76 is 7.
The tens digit of 6^6=...56 is 5.
The tens digit of 6^7=...36 is 3 again.
etc...
19 has the form 5n+4, so the tens digit of 6^19 is 9.
The answer is E.
Answer: (E) 9
Question: A and B entered into partnership with capitals in the ratio 4 : 5. After 3 months, A withdrew ¼ of his capital and B withdrew 1/5 of his capital. At the end of 10 months, the gain was Rs. 760. What is A's share in the profit?
(A) 310
(B) 330
(C) 370
(D) 350
(E) None of these
Rationale: Explanation :
Ratio of the initial capital of A and B = 4 : 5
Hence we can take the initial capitals of A and B as 4x and 5x respectively
Ratio in which profit will be divided
= (4x*3) + (3/4)*(4x)*7 : (5x*3)+ (4/5)*(5x)*7
= 12+21 : 15+28
= 33 : 43
A's share = 760 * 33/76 = 330.Answer : Option B
Answer: (B) 330
Question: A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that exactly three bulbs are good
(A) 20/63
(B) 4/56
(C) 8/7
(D) 6/9
(E) 4/9
Rationale: Explanation:
Required probability = (âµCâ‚ƒ . â´Câ‚)/â¹Câ‚„ = (10 * 4)/126 = 20/63
Answer: A
Answer: (A) 20/63
Question: Two men and three women working 7 hours a day finish a work in 5 days. Four men and four women working 3 hours a day complete the work in 7 days. The number of days in which only 7 men working 4 hours a day will finish the work is?
(A) 5 days
(B) 8 days
(C) 6 days
(D) 3 days
(E) 2 days
Rationale: 2M + 3W ----- 35 h
4M + 4W ------- 21 h
7M -------? d
70M + 105W = 84M +84M
21W = 14M => 2M = 3W
4 * 35 = 7 * x => x = 20 hours
20/4 = 5 days
Answer: A
Answer: (A) 5 days
Question: The ratio of a compound, by weight, consisting only of substances x, y, and z is 4:6:10,
respectively. Due to a dramatic increase in the surrounding temperature, the composition of the
compound is changed such that the ratio of x to y is halved and the ratio of x to z is tripled. In the
changed compound, if the total weight is 232 lbs, how much does substance x weigh?
(A) 48
(B) 36
(C) 24
(D) 12
(E) 10
Rationale: x:y=4:6
if the ratio is halevd then x:y=2:6
The old ratio of x to z was 4:10. If this ratio is tripled, then the new ratio of x to z is 12:10.
x:y=2:6=12:36 ( multiplied the ration with 6/6 to have a common co eff x in both the rations x:y and x:z)
so x:y:z= 12:36:10
and we know x + y + z = 232 lbs
from the ratio of x ,y and z we have x=12k y=36k z=10K
put it in the equation we have 12k+36k+10k=232
k=4
Hence x=12(4)=48
Ans A
Answer: (A) 48
Question: Two cars start together in the same direction from the same place. The first goes with uniform speed of 10 kmph. The second goes at a speed of 8 kmph in the first hour and increases its speed by 1/2 kmph each succeeding hours. After how many hours will the second car overtake the first, if both cars go non stop?
(A) 8 hours
(B) 7 hours
(C) 6 hours
(D) 9 hours
(E) None
Rationale: Explanation :
The second car overtake the first car in x hours
Distance covered by the first car in x hours = Distance covered by the second car in x hours
10x = x/2[2a + (x-1)d] 10x = x/2[2*8 + (x-1)1/2] x = 40 -31 = 9
Answer – D
Answer: (D) 9 hours
Question: What is the smallest of six consecutive odd integers whose average (arithmetic mean) is z + 2?
(A) z - 5
(B) 3
(C) z - 3
(D) z
(E) z + 1
Rationale: Since the numbers are consecutive odd integers, mean = median = 3rd integer + 4th integer /2
And 1st integer= 3rd integer- 4
let's say 3rd integer = n and 4th integer = n+2
2n+2/2= z+2
n= z+1
1st integer= z+1-4= z-3
C is the answer
Answer: (C) z - 3
Question: Rahul went to a shop and bought things worth Rs. 25, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
(A) Rs. 16.80
(B) Rs. 15
(C) Rs. 18
(D) Rs. 19
(E) Rs. 19.70
Rationale: Total cost of the items he purchased = Rs.25
Given that out of this Rs.25, 30 Paise is given as tax
=> Total tax incurred = 30 Paise = Rs.30100
Let the cost of the tax free items = x
Given that tax rate = 6%
âˆ´ (25âˆ’30100âˆ’x)6100=30100â‡’6(25âˆ’0.3âˆ’x)=30â‡’(25âˆ’0.3âˆ’x)=5
x=25âˆ’0.3âˆ’5
=19.70
correct answer - E
Answer: (E) Rs. 19.70
Question: How many kg of pure salt must be added to 100kg of 10% solution of salt and water to increase it to a 35% solution?
(A) A)6.7
(B) B)38.5
(C) C)9.6
(D) D)12.5
(E) E)7.9
Rationale: Amount salt in 100kg solution = 10*100/100 = 10 kg
Let x kg of pure salt be added
then(10+x)/(100+x)=35/100
200+20x=700+7x
13x = 500
x = 28.5
Answer is B
Answer: (B) B)38.5
Question: If each digit in the set A = {1, 2, 3, 4, 5, 6, 7, 8, 9} is used exactly once, in how many ways can the digits be arranged?
(A) 356,580
(B) 358,680
(C) 360,780
(D) 362,880
(E) 364,980
Rationale: 9! = 362,880
The answer is D.
Answer: (D) 362,880
Question: A and B can do a piece of work in 4 days, B and C in 6 days, C and A in 3 days. How long will C take to do it?
(A) 8 days
(B) 10 days
(C) 12 days
(D) 4 days
(E) 12 days
Rationale: 2c = 1/6 + 1/3 – 1/4 = 1/4
c = 1/8 => 8 days
Answer:A
Answer: (A) 8 days
Question: What is the time required for a bike to cover a distance of 450 km with a speed of 90 kmh?
(A) 5 hours
(B) 3 hours
(C) 8 hours
(D) 6 hours
(E) 4 hours
Rationale: Time= Distance / Speed
Time = 450 / 90 = 5
Answer: A
Answer: (A) 5 hours
Question: The circumference of the front wheel of a cart is 30 ft long and that of the back wheel is 32 ft long. What is the distance traveled by the cart, when the front wheel has done five more revolutions than the rear wheel?
(A) 20 ft
(B) 25 ft
(C) 750 ft
(D) 900 ft
(E) 2400 ft
Rationale: Point to note: Both the wheels would have traveled the same distance.
Now consider, no. of revolutions made by back wheel as x, which implies that the number of revolutions made by the front wheel is (x+5).
Equating the distance traveled by front wheel to back wheel: (x+5)*30 = x * 32. (Formula for calculating the distance traveled by each wheel is: # of revolutions * circumference.)
Solving this eqn. gives x=75.
Sub x=75 either in (x+5)*30 or in x * 32 to get the distance, which is 2400. So the correct choice is E.
Answer: (E) 2400 ft
Question: A person covers a distance in 18 minutes. If runs at a speed of 12 km per hour on an average. Find the speed at which he must run to reduce the time of journey to 5 minutes.
(A) 18 m/s
(B) 4 m/s
(C) 12 m/s
(D) 10 m/s
(E) 5 m/s
Rationale: Explanation:
T = 18 m
Spees = 12 kmph
= 12 x 5/18 = 10/3 m/s
Let new speed be "x"
18 x (10/3) = 5x
x = 12 m/s
Answer: Option C
Answer: (C) 12 m/s
Question: If x is 50 percent greater than 88, then x =
(A) 68
(B) 132
(C) 86
(D) 105.6
(E) 108
Rationale: x=88*1.5=132
So the answer is B.
Answer: (B) 132
Question: A cycle is bought for Rs.900 and sold for Rs.1080, find the gain percent?
(A) 77%
(B) 20%
(C) 87%
(D) 55%
(E) 66%
Rationale: 900 ---- 180
100 ---- ? => 20%
Answer: B
Answer: (B) 20%
Question: A university cafeteria offers 22 flavors of pizza - Hawaiian and vegetarian. If a customer has an option (but not the obligation) to add extra cheese, mushrooms or both to any kind of pizza, how many different pizza varieties are available ?
(A) 41
(B) 8
(C) 12
(D) 4
(E) 32
Rationale: 2 flavours * 2 choices = 2C1*2C1 = 2*2=4=D
Answer: (D) 4
Question: In a question on division with zero remainder, a candidate took 12 as divisor instead of 21. The quotient obtained by him was 35. The correct quotient is:
(A) 15
(B) 18
(C) 20
(D) 22
(E) 24
Rationale: Number = (35 * 12) = 420
Correct quotient = 420/21 = 20
C
Answer: (C) 20
Question: If x and y are positive integers that have remainders of 2 and 5, respectively, when divided by 7, which of the following could be the sum of x and y?
(A) 16
(B) 19
(C) 40
(D) 49
(E) 72
Rationale: Minimum value of x = 9 and y = 12=>
x + y = 21 ( Divisible by 7 )
So, The correct answer choice will be one that will be divisible by 7..
Among the given options only (D) satisfies, hence answer must be (D)
Answer: (D) 49
Question: The ratio between the present ages of P and Q is 6:7. If Q is 4 years old than P, what will be the ratio of the ages of P and Q after 4 years
(A) 7:8
(B) 7:9
(C) 7:6
(D) 7:2
(E) 7:5
Rationale: Let P age and Q age is 6x years and 7x years.
Then 7x - 6x = 4 <=> x = 4
So required ratio will be (6x+4): (7x+4) => 28:32 => 7:8
Answer: A
Answer: (A) 7:8
Question: If x^2 = 111, which of the following is closest to a potential value of x?
(A) -127
(B) -11
(C) 12
(D) 13
(E) 131
Rationale: Here the thing we must not forget is that X^even has two potential solutions
=> x =+- √111 => +- 11
this value is closer to -11
Hence B is correct.
Answer: (B) -11
Question: A box contains 5 green balls, 4 red balls and 6 white balls. A ball is drawn at random from the box. What is the probability that the ball drawn is either red or green?
(A) 2/3
(B) 1/4
(C) 3/5
(D) 1/2
(E) 2/5
Rationale: Total number of balls = 4+5+6 = 15
n(s)=15
E1 = event of drawing a red ball = 4/15
E2 = event of drawing a green ball = 5/15
P(E1)+P(E2) = (4/15)+(5/15) = 9/15 = 3/5
Answer is C
Answer: (C) 3/5
Question: There are some pigeons and hares in a zoo. If heads are counted, there are 200. If legs are counted, there are 580. The number of hares in the zoo is?
(A) 20
(B) 82
(C) 90
(D) 37
(E) 37
Rationale: 200*2 = 400
580
-----
180
1----2
?----180 = 90
Answer:C
Answer: (C) 90
Question: Mona and Donald fly to Rome for the weekend. They take cash only in notes of $10 and notes of €10. Mona carries three times the amount of euros Donald carries. She also carries as many dollars as Donald carries. The number of €10 notes they take is double the number of $10 notes they take. If Donald carries a total of 30 notes (of either $10 or €10,) then what is the total number of notes (of either $10 or €10,) they take?
(A) 70
(B) 80
(C) 100
(D) 120
(E) 150
Rationale: let e10 =x no. d10 =y no. donald is having x+y notes mona carries 3x+y again x =2y or donald x+y =30
or 3y =30 y =10 ;x =20 , total notes they carry = 4x+2y = 80+20 =100
E
Answer: (E) 150
Question: An error 1% in excess is made while measuring the side of a square. What is the percentage of error in the calculated area of the square?
(A) 4.05%
(B) 4.02%
(C) 4%
(D) 3%
(E) 2.01%
Rationale: Percentage error in calculated area
=(1+1+(1Ã—1)/100)%
=2.01%
ANSWER:E
Answer: (E) 2.01%
Question: A man swims downstream 36 km and upstream 18 km taking 3 hours each time, what is the speed of the man in still water?
(A) 7
(B) 8
(C) 9
(D) 2
(E) 4
Rationale: 36 --- 3 DS = 12
? ---- 1
18 ---- 3 US = 6
? ---- 1 M = ?
M = (12 + 6)/2 = 9
Answer:C
Answer: (C) 9
Question: he ratio between the sale price and the cost price of an article is 5:6. What is the ratio between the profit and the cost price of that article?
(A) 2:6
(B) 1:8
(C) 1:6
(D) 2:1
(E) 2:5
Rationale: Let C.P. = Rs. 6x and S.P. = Rs. 5x.
Then, Gain = Rs. x
Required ratio = x : 6x = 1:6.
Answer:C
Answer: (C) 1:6
Question: In a class of 40 students, 12 enrolled for both English and German. 22 enrolled for German. If the students of the class enrolled for at least one of the two subjects, then how many students enrolled for only English and not German?
(A) 30
(B) 10
(C) 18
(D) 8
(E) 28
Rationale: Let A be the set of students who have enrolled for English and B be the set of students who have enrolled for German.
Then, (A U B) is the set of students who have enrolled at least one of the two subjects. As the students of the class have enrolled for at least one of the two subjects, A U B = 40
We know A U B = A + B - (A n B)
i.e, 40 = A + 22 - 12
or A = 30 which is the set of students who have enrolled for English and includes those who have enrolled for both the subjects.
However, we need to find out the number of students who have enrolled for only English = Students enrolled for English - Students enrolled for both German and English= 30 - 12 = 18.
ANSWER:C
Answer: (C) 18
Question: The population of a town is 20000. It increases annually at the rate of 20% p.a. What will be its population after 2 years?
(A) 24440
(B) 24800
(C) 28400
(D) 28800
(E) 28600
Rationale: Explanation:
Formula: (After =100 denominator
Ago = 100 numerator)
20000 * 120/100 * 120/100 = 120 * 120 * 2 = 28800
Answer: Option D
Answer: (D) 28800
Question: Simran started a software business by investing Rs. 50,000. After six months, Nanda joined her with a capital of Rs. 80,000. After 3 years, they earned a profit of Rs. 21,000. What was Simran's share in the profit?
(A) Rs. 9423
(B) Rs. 10,250
(C) Rs. 9000
(D) Rs. 14,000
(E) None of these
Rationale: Simran : Nanda = (50000 * 36) : (80000 * 30) = 3:4
Simran's share = 21000 * 3/7 = Rs. 9000
ANSWER:C
Answer: (C) Rs. 9000
Question: How many three-digit numbers ABC, in which A, B, and C are each digits, satisfy the equation 2B = A + C?
(A) 33
(B) 36
(C) 41
(D) 45
(E) 50
Rationale: Possible solutions are
Diff of 0 --
111,222,........,999 = 9
Diff of 1 --
123, 234, ....., 789 =7x2 = 14
Diff of 2 --
135, 246.......579 = 5x2 = 10
Diff of 3 --
147,258,369 = 3x2 = 6
Diff of 4 --
159 = 1x2 = 2
Last
210, 420,630,840 = 4
So total is 9+14+10+6+2+4 = 45.
ANSWER:D
Answer: (D) 45
Question: The price of a cycle is reduced by 25 % The new price is reduced by a further 20 %. The 2reductions together are equalto a single reduction of
(A) 39
(B) 45
(C) 60
(D) 56
(E) 70
Rationale: Let the original price of the cycle be 100. After the first reduction the price will be 75.
This new price is then reduced by 20% = 0.8 x 75 = 60
60 represents a reduction of 40 percent on the original.
C
Answer: (C) 60
Question: On his first day working out, Anthony did
30 push-ups. On each successive day, he
did exactly 3 more push-ups than on the
previous day. After completing his push-ups
on the 30th day, how many push-ups had
he completed on all 30 days?
(A) fewer than 500
(B) between 500 and 1,000
(C) between 1,000 and 1,500
(D) between 1,500 and 2,000
(E) more than 2,000
Rationale: Anthony completed 30 push-ups the first day, 33 the second day, 36 the third day, and
so on. Make a chart as follows:
1 2 3 4 5 . . . 10 . . . 15 . . . 20 . . . 25 . . . 30
30 33 36 39 42 57 72 87 102 117
To save time adding all these numbers, notice that the total of the first and 30th numbers
is 30 + 117 = 147. This total is the same for the 2nd and 29th, the 3rd and 28th, and so on all
the way to the 15th and 16th. Therefore, you have 15 pairings of days on which Anthony
completed 147 pushups. You can simply multiply to find the total: 147 × 15 = 2,205.
correct answer E) more than 2.000
Answer: (E) more than 2,000