mathewhe/aqua_rat huggingface dataset:
Question: There were P people in a room when a meeting started. Q people left the room during the first hour, while R people entered the room during the same time. What expression gives the number of people in the room after the first hour as a percentage of the number of people in the room who have been there since the meeting started?
(A) (P−Q)/(P−Q+R)
(B) 100 x (P−Q+R)/(P−Q)
(C) (P+R)/(P−Q)
(D) 100 x (P−Q)/(P−Q+R)
(E) 100 x (P+R)/(P−Q)
Rationale: Explanatory Answers
The meeting started with P people. Q left the room during the first hour.
So, (P - Q) people have been in the room since the meeting started.
This expression is obviously the denominator of the expression.
To start with there were P people, Q of whom left the room and another R joined the group.
So, the number of people in the room after the first hour = P - Q + R.
This expression is the numerator of the expression.
Required expression = 100 x (P - Q + R)/(P - Q)
Answer B
Answer: (B) 100 x (P−Q+R)/(P−Q)
Question: A store owner decided to raise the price of a particular item by exactly 10%. Of the following which is NOT the new price?
(A) $1.10
(B) $8.80
(C) $11.00
(D) $57.30
(E) $78.10
Rationale: Let price be $ 10
The store owner decided to raise the price of a particular item by exactly 10%, so the new price must be 110 *10 /100 =>11
So, The new price must be a multiple of 11
From the given options check for all the multiples of 11
Test of divisibility of 11 is
if the difference of the sum of digits at odd places and the sum of its digits at even places, is either 0 or divisible by 11, then clearly the number is divisible by 11.
A. $1.10
B. $8.80
C. $11.00
By a quick glance even a 2nd grader can eliminate options A,B and C , because they are all divisible by 11 , let with only 2 options check for the divisibility rule for options D and E
D. $57.30
Sum of even digits is 5+3 = 8
Sum of odd digits is 7 +0 = 7
Difference of the even and odd digits is 8 - 7 = 1 ; not divisible by 11
Hence this is our answer.
E. $78.10
Further inspection is not required since we have already found out the answer at (D)
Answer: (D) $57.30
Question: How many number of 3's would be used to type numbers from 1 to 700
(A) 230
(B) 240
(C) 250
(D) 260
(E) 270
Rationale: 1-99--20 (3,13,23,30,31,32,33,34,35,36,37,38,39,43,53,63,73,83,93)
likewise
100-199--20
200-299--20
300-399--120 (300-399 there is extra 100 3's)
400--499--20
500--599--20
600-700--20
20+20+20+120+20+20+20=240
ANSWER:B
Answer: (B) 240
Question: The average (arithmetic mean) of eight numbers is 49.1. If the sum of half of these numbers is 158.4, what is the average of the other half?
(A) 12.8
(B) 24.2
(C) 58.6
(D) 72.1
(E) 96.8
Rationale: arithmetic mean = sum / total numbers
sum = 49.1 * 8 = 392.8
sum of half of these numbers is 158.4. So, 4 numbers sum is 158.4. Rest 4 numbers sum = 392.8-158.4 = 234.4
Arithmetic mean of the 4 nos = 234.4/4 = 58.6
Hence, C is the answer.
Answer: (C) 58.6
Question: A number when divided by 6 leaves a remainder 3. When the square of the same number is divided by 6, the remainder is
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: Sol.
Let x = 6q + 3.
Then x2 = (6q + 3)2
= 36q2 + 36q + 9 = 6(6q2 + 6q + 1) + 3.
So, when x2 is divided by 6, remainder = 3.
Answer D
Answer: (D) 3
Question: Find the odd man out
5,15,45,60,90,180
(A) 60
(B) 180
(C) 90
(D) 5
(E) 15
Rationale: 5*3= 15
15*3 =45
45*2=90
90*2=180
180*2=360
ANSWER:A
Answer: (A) 60
Question: Sonika deposited Rs.7000 which amounted to Rs.9200 after 3 years at simple interest. Had the interest been 2% more. She would get how much?
(A) 9680
(B) 2277
(C) 9620
(D) 2774
(E) 1212
Rationale: (7000*3*2)/100 = 420
9200
--------
9620
Answer:C
Answer: (C) 9620
Question: An error 2%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) 4.04 %
(B) 2.02 %
(C) 4 %
(D) 2 %
(E) 2.40 %
Rationale: Explanation:
Error =2% while measuring the side of a square.
Let correct value of the side of the square =100
Then, measured value =100+2=102 (∵ 2 is 2%of 100)
Correct area of the square =100×100=10000
Calculated area of the square =102×102=10404
Error =10404−10000=404
Percentage error =error /actual value×100
=404/10000×100=4.04%
Answer: Option A
Answer: (A) 4.04 %
Question: What will come in place of the x in the following Number series? 12, 38, 116, 350, 1052, x
(A) 4300
(B) 4500
(C) 4000
(D) 4569
(E) 3158
Rationale: 12
12 × 3 + 2 = 38
38 × 3 + 2 = 116
116 × 3 + 2 = 350
350 × 3 + 2 = 1052
1052 × 3 + 2 = 3158
E
Answer: (E) 3158
Question: 2 men and 3 women are lined up in a row. What is the number of cases where they stand with each other in turn? (The number of cases in which men (or women) do not stand next to each other)
(A) 12
(B) 15
(C) 18
(D) 21
(E) 24
Rationale: First arrange 3 women. 3 women can be arranged in 3 places in 3! ways. Now
W Blank W BlankW
we have to fill the two blanks with 2 men. We can arrange 2 persons in 2 places in 2! ways.
3! * 2! = 12 ways.
A is the answer
Answer: (A) 12
Question: Lerry, Michael, and Doug have five donuts to share. If any one of the men can be given any whole number of donuts from 0 to 5, in how many different ways can the donuts be distributed?
(A)  21
(B)  42
(C)  120
(D)  504
(E)  5040
Rationale: Lerry, Michael, and Doug have five donuts to share to get the answer, see how can we get sum5with 3 numbers.
1) 0,0,5 = 3 combinations or 3! /2!
2) 0,1,4 = 6 combinations or 3!
similarly
3) 0,2,3 = 6 combinations
4) 1,1,3 = 3 combination
5) 2,2,1 = 3 combination
total =21=A
Answer: (A)  21
Question: A painting crew painted 80 houses. They painted the first y houses at a rate of x houses per week. Then more painters arrived and everyone worked together to paint the remaining houses at a rate of 4.25x houses per week. How many weeks did it take to paint all 80 houses, in terms of x and y?
(A) (320 - y)/(5x)
(B) (y +210)/(5x)
(C) 5(80 - y)/(4x)
(D) (y + 400)/(4x)
(E) (4y + 320)/(5x)
Rationale: Ans B
Plug some numbers
Let y = 40 houses and x = 20
then they painted 20 houses per week
as painters were added to the group , the rate of the group increased to 4.25 x => 4.25 * 20 = 85 houses per week
total time they took = (40/20) + (40/85) = 2.5 weeks
Putting the values of x and y in equation B
(y +210)/(5x) = (40+210)/5*20 = 250/100 = 2.5
Answer: (B) (y +210)/(5x)
Question: A man goes from A to B at a speed of 20 kmph and comes back to A at a speed of 30 kmph. Find his average speed for the entire journey?
(A) 76 kmph
(B) 24 kmph
(C) 54 kmph
(D) 56 kmph
(E) 76 kmph
Rationale: Distance from A and B be 'd'
Average Speed
= total distance/total time
Average Speed
= (2d)/[(d/20) + (d/30)]
= (2d)/[5d/60)
=> 24 kmph.
Answer: B
Answer: (B) 24 kmph
Question: A box contains 100 balls, numbered from 1 to 100. If 3 balls are selected at random and with replacement from the box. If the 3 numbers on the balls selected contain two odd and one even. What is the probability Z that the first ball picked up is odd numbered?
(A) 	0
(B) 	1/3
(C) 	1/2
(D) 	2/3
(E) 	1
Rationale: Answer-D
Selecting the balls either Even or Odd is having probability 50/100=1/2
We have already selected 3 balls with 2 odd numbers and 1 even number.
So we have 3 combinations OOE, OEO, EOO. We have 3 outcomes and 2 are favourable as in 2 cases 1st number is odd. So probability Z is 2/3.D
Answer: (D) 	2/3
Question: Two trains T1 and T2 start simultaneously from two stations X and Y respectively towards each other. If
they are 60 km apart both 3 and 6 hours after start, then find the distance between the two stations.
(A) 240 km
(B) 200 km
(C) 220km
(D) 180km
(E) 210km
Rationale: In first 3 hours T1 travels R km and T2 travels S km.
After 6 hours they traveled R+S+60+ 60
2(R+S ) = R+S +120
R+S = 120
Hence distance between XY is R+S+ 60 = 120 +60 =200
Answer : B
Answer: (B) 200 km
Question: A boat can travel with a speed of 25km/hr in still water. If the speed of the stream is 5km/hr, find the time taken by the boat to go 90km downstream.
(A) 1 hr
(B) 2 hrs
(C) 3 hrs
(D) 4 hrs
(E) 5 hrs
Rationale: Speed downstream = (25 + 5) km/hr = 30 km/hr.
Time taken to travel 90 km downstream = 90/30 hrs = 3 hrs.
Answer : C
Answer: (C) 3 hrs
Question: An incredible punch is composed of mango, orange juice, and milk. How many pints of orange juice are required to make 9 gallons of punch containing twice as much mango as orange juice and three times as much orange juice as milk? (1 Gallon = 8 Pints )
(A) 13 pints
(B) 7.2 pints
(C) 5 pints
(D) 12 pints
(E) 6.5 pints
Rationale: 1 gallon=8 pints
9 gallons=72
mango=2 orange
orange=3 milk
mango+orange+milk=72
2 orange+orange+1/3 orange=72
10 orange=72
orange=7.2pints
Answer B
Answer: (B) 7.2 pints
Question: If a man can cover 12 metres in 0ne second, how many kilometres can he cover in 3 hours 45 minutes?
(A) 132 km
(B) 167 km
(C) 143 km
(D) 162 kilometres
(E) 245 km
Rationale: D
12 m/s = 12 * 18/5 kmph
3 hours 45 minutes = 3 3/4 hours = 15/4 hours
Distance = speed * time = 12 * 18/5 * 15/4 km = 162 km.
Answer: (D) 162 kilometres
Question: John has on his shelf four books of poetry, two novels, and two reference works. Suppose from these ten books, we were to pick two books at random. What is the probability that we pick one novel and one reference work?
(A) 1/2
(B) 2/5
(C) 4/45
(D) 7/20
(E) 8/45
Rationale: When we are picking two books, one novel and one reference work, we could either pick a novel first and then a reference book or pick a reference book and then a novel. Therefore the answer is 2/10*2/9 + 2/10*2/9 = 4/45.
Answer: C
Answer: (C) 4/45
Question: Ajay can ride 50km in 1 hour. In how many hours he can ride 900km?
(A) 10hrs
(B) 15hrs
(C) 20hrs
(D) 25hrs
(E) 18hrs
Rationale: 1 hour he ride 50km
he ride 900km in = 900/50 * 1 = 18hours
Answer is E
Answer: (E) 18hrs
Question: A window 2 inches wide is placed on the back of a rectangular painted area with dimensions 8 inches by 12 inches. What is the area of the window, in square inches?
(A) 44
(B) 96
(C) 128
(D) 144
(E) 168
Rationale: This question is an example of a 'punch out' question - we have to find the area of EVERYTHING, then 'punch out' the part that we don't want.
We're told that a window 2 inches wide is placed around a rectangular painted area with dimensions 8 inches by 12 inches. We're asked for the area of the window, in square inches.
Area of a rectangle = (length)(width)
So the area of the window is... (8)(12) = 96
The window 'adds' 2 inches to the top, bottom, left and right 'sides' of the painted area, so the area of EVERYTHING is...
(8+2+2)(12+2+2) = (12)(16) = 196
When we 'punch out' the area of the painted area, we'll be left with the area of the window:
192 - 96 = 96
Final Answer:
B
Answer: (B) 96
Question: Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 seconds. The length of each train is:
(A) 50 m
(B) 72 m
(C) 80 m
(D) 82 m
(E) 84 m
Rationale: Let the length of each train be x metres.
Then, distance covered = 2x metres.
Relative speed = (46 - 36) km/hr
(10 x (5/18) ) m/s = 25/9 m/s
2x/36 = 25/9
2x=100
x=50
ANSWER:A
Answer: (A) 50 m
Question: X and Y invest Rs.12500 and Rs.17500 respectively in a business. At the end of the year, they make a profit of Rs.26400. What is the share of X in the profit?
(A) Rs.14400
(B) Rs.26400
(C) Rs.11000
(D) Rs.12500
(E) Rs.13500
Rationale: Ratio of the investment=12000:17500=5:7
Share of X in the profit=(26400×5)/12=11000
ANSWER:C
Answer: (C) Rs.11000
Question: The sum of the first 50 positive even integers is 2550. What is the sum of the even integers from 302 to 400 inclusive?
(A) 11,550
(B) 14,550
(C) 17,550
(D) 20,550
(E) 23,550
Rationale: 2 + 4 + 6 + 8 +...+ 100 = 2550
302 + 304 + ... + 400 = 50(300) + (2+4+...+100) = 15,000 + 2550 = 17,550
The answer is C.
Answer: (C) 17,550
Question: If Janice was 24 years old z years ago and Lisa will be 22 years old in p years, what was the average (arithmetic mean) of their ages 6 years ago?
(A) (z + p)/2
(B) (z - p + 34)/4
(C) (z - p + 24)/4
(D) (z + p + 44)/2
(E) (z - p + 34)/2
Rationale: Today, J = z+24 and L = 22-p
6 years ago, J = z+18 and L = 16-p
The average of their ages was (z-p+34) / 2
The answer is E.
Answer: (E) (z - p + 34)/2
Question: A train 225 m long passes a man, running at 10km/hr in the same direction in which the train is going, in10 seconds. The speed of the train is:
(A) 81
(B) 90
(C) 91
(D) 85
(E) 96
Rationale: Speed of the train relative to man =225/10 m/sec
=45/2m/sec.
=45/2x18/5km/hr
= 81 km/hr.
Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr.
x - 10 = 81 =91km/hr.
Answer:C
Answer: (C) 91
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 4 different offices?
(A) 52
(B) 64
(C) 32
(D) 11
(E) 12
Rationale: Each of three employee can be assigned to either of offices, meaning that each has 2 choices --> 4*4*4=4^3=64.
Answer: B.
Answer: (B) 64
Question: If Janice was 22 years old z years ago and Lisa will be 20 years old in p years, what was the average (arithmetic mean) of their ages 7 years ago?
(A) (z + p)/2
(B) (z - p + 28)/4
(C) (z - p + 18)/4
(D) (z + p + 38)/2
(E) (z - p + 28)/2
Rationale: Today, J = z+22 and L = 20-p
7 years ago, J = z+15 and L = 13-p
The average of their ages was (z-p+28) / 2
The answer is E.
Answer: (E) (z - p + 28)/2
Question: It takes John exactly 30 minutes to rake a lawn and it takes his son Todd exactly 60 minutes to rake the same lawn. If John and Todd decide to rake the lawn together, and both work at the same rate that they did previously, how many minutes will it take them to rake the lawn
(A) 16
(B) 45
(C) 36
(D) 20
(E) 90
Rationale: 1)POE- John takes 30 min so if he takes help of someone else, it has to be less than 30 min..
only A and B are left..
if both do the work in 30 mis each, the combined time will be 15 mins, so 16 is slightly less when the other person does in 60 mins..
ans 20 D
Answer: (D) 20
Question: The price of a certain product increased by the same percent from 1960 to 1970 as from 1970 to 1980. If its price of $2.00 in 1970 was 150 percent of its price in 1960, what was its price in 1980?
(A) a) $ 1.80
(B) b) $ 2.00
(C) c) $ 2.40
(D) d) $ 2.70
(E) e) $ 3.00
Rationale: The price in 1970 was 150 percent of its price in 1960, means that the percent increase was 50% from 1960 to 1970 (and from 1970 to 1980).
Therefore the price in 1980 = $2.0*1.5 = $3.00.
Answer: E.
Answer: (E) e) $ 3.00
Question: What will come in place of the x in the following Number series? 12, 38, 116, 350, x
(A) 1052
(B) 5464
(C) 3456
(D) 7554
(E) 3158
Rationale: 12
12 Ã— 3 + 2 = 38
38 Ã— 3 + 2 = 116
116 Ã— 3 + 2 = 350
350 Ã— 3 + 2 = 1052
A
Answer: (A) 1052
Question: Machine A and machine G are each used to manufacture 660 sprockets. It takes machine A 10 hours longer to produce 660 sprockets than machine G. Machine G produces 10 percent more sprockets per hour than machine A. How many sprockets per hour does machine A produces?
(A) 6
(B) 6.6
(C) 60
(D) 100
(E) 110
Rationale: [Reveal]Spoiler:
TimeG: 660/x
TimeA: [660/x+10]
660/x = [660/x+10] *110/100
660/x =66*11/x+10
660x+10= 66*11*x
660x +6600 = 66*11*x
x= 100
plug in back to timeA
660/100+10 => 660/110 = 6
Answer: (A) 6
Question: 350 is increased by 50%. Find the final number.
(A) 725
(B) 625
(C) 225
(D) 525
(E) 425
Rationale: ExplanationFinal number = Initial number + 50%(original number) = 350 + 50%(350) = 350 + 175 = 525.Answer D
Answer: (D) 525
Question: If f(x) = 12 - x^2/2 and f(2k) = 5k, what is one possible value for k?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 8
Rationale: First of all, see thisGMAT blog postand check the related lesson linked below for some background on function notation.
We can plug anything in for x and get a result. You can find f(1), for example, by plugging in 1 where x is, and you would get 12 - 1/2 = 11.5. Or we could find f(2), which would be 12 - 4/2 = 10.
So the notation f(2k) means that we are going to plug a 2k in for x everywhere in the formula for f(x). That would be:
f(2k) = 12 - (2k)^2/2 = 12 - 2k^2.
Remember that we have to square both the 2 and the k, to get 4k2. Now, this expression, the output, we will set equal to 2k.
12 - 2k^2 = 2k --> k = -3 or k =5.
All the answers are positive, so we choose k = 5.
Answer =D
Answer: (D) 5
Question: A card is drawn from a pack of 52 cards the probability of getting queen of club or aking of a heart?
(A) 8/58
(B) 9/25
(C) 1/26
(D) 6/25
(E) 8/45
Rationale: here n(s)=52
let E be the event of getting queen of the club or king of kings
n(E)=2
p(E)=n(E)/n(S)=2/52=1/26
Answer(C)
Answer: (C) 1/26
Question: A reduction of 40% in the price of oil enables a house wife to obtain 8 kgs more for Rs.2400, what is the reduced price for kg?
(A) Rs.120
(B) Rs.125
(C) Rs.130
(D) Rs.135
(E) Rs.140
Rationale: Explanation:
2400*(40/100) = 960 ---- 8
? ---- 1 => Rs.120
Answer: A
Answer: (A) Rs.120
Question: Eleven bags are bought for Rs.1000 and sold at 10 for Rs.1200. What is the gain or loss in percentage?
(A) 10%
(B) 22%
(C) 25%
(D) 20%
(E) None of these
Rationale: Explanation:
As selling price is Rs.1200 for 10 bags, each bag is sold at Rs.120.
Hence, the profit is Rs.100 after selling 10 bags plus the selling price of 1 bag = 100 + 120 = Rs.220.
%profit = 220/1000 *100
= 22%
ANSWER B
Answer: (B) 22%
Question: I. x + 2y + 3z = 2
II. x + y - z = 0
III. 2x + 2y - z = 1
What is the value of y in the system above?
(A)  -2
(B)  -1
(C)  0
(D)  1
(E)  2
Rationale: 1. from the given system of equations i can make equation II. to be x + y = z
2. now put that in III. :
2x + 2y - (x + y) = 1
= 2x + 2y - x - y = 1
= x + y = 1
that gives usz = 1!
3. put z = 1 in I. and solve:
x + 2y + 3 = 2; calculate minus 3
= x + 2y = -1; calculate minus x
=2y = -1 - x;
4. now put 2y = -1 - x in III. and solve:
2x + (-1 - x) - 1 = 1
= x - 2 = 1; calculate plus 2
that gives usx = 3
5. now solve for y with x = 3 and z = 1:
x + y = 1
= 3 + y = 1; calculate minus 3
that gives y = -2, and hence answer (A) -2
Answer: (A)  -2
Question: Steve gets on the elevator at the 11th floor of a building and rides up at a rate of 47 floors per minute. At the same time Joyce gets on an elevator on the 51st floor of the same building and rides down at a rate of 53 floors per minute. If they continue traveling at these rates, at which floor will their paths cross?
(A) 19
(B) 28
(C) 30
(D) 33
(E) 44
Rationale: Steve gets on the elevator at the 11th floor of a building and rides up at a rate of 47 floors per minute. At the same time Joyce gets on an elevator on the 51st floor of the same building and rides down at a rate of 53 floors per minute. If they continue traveling at these rates, at which floor will their paths cross?
40 floors/100 floors per minute=2/5 minutes
11+57/3=33
51-63/3=33
Answer : D
Answer: (D) 33
Question: A tap can fill the tank in 15 minutes and another can empty it in 8 minutes. If the tank is already half full and both the taps are opened together, the tank will be:
(A) filled in 12 min
(B) emptied in 12 min
(C) filled in 8 min
(D) will be empty in 8 min
(E) emptied in 10 min
Rationale: work done by both taps= 1/15+(-1/8)= -7/120 so tank will be emptied becoz of minus sign.
so time taken= 120/7
given the tank is already half filled
so another half will be emptied in 120/7*1/2
nearly 8 minutes
ANSWER:D
Answer: (D) will be empty in 8 min
Question: For my anniversary, I decided to surprise my wife. Since she is a voracious reader, I decided to collect a lot of books for her. On the first day of the month, I bought one book, on the second, I bought two and on the third, I bought three. This process went on till the anniversary and on the day, I had 231 books with me to gift her.
Can you calculate, on which day is our anniversary?
(A) 31
(B) 28
(C) 23
(D) 21
(E) 25
Rationale: D
21rd day
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20 + 21 = 231
Thus our anniversary falls on the 21rd day of the month.
You can apply other formulas to shorten the process but that is the simplest way to do it.
Answer: (D) 21
Question: After M students took a test, the average score was 56%. If the test has 50 questions, what is the least number of questions that the next student has to get right to bring the average score up to 60%?
(A) M + 30
(B) 0.56M + 30
(C) M + 28
(D) 2M + 28
(E) 2M + 30
Rationale: The total number of correct answers for M students is (0.56)*50*M=28*M
For an average of 75%: (total correct answers) / (M+1) = 0.6*50=30
Let x be the number of correct answers for the next student.
(x + 28M) / M+1 = 30
x + 28M= 30M+30
x = 2M + 30
The answer is E.
Answer: (E) 2M + 30
Question: A company has two models of computers, model X and model Y. Operating at a constant rate, a model X computer can complete a certain task in 72 minutes and a model Y computer can complete the same task in 36 minutes. If the company used the same number of each model of computer to complete the task in 1 minute, how many model X computers were used?
(A) 22
(B) 23
(C) 24
(D) 25
(E) 26
Rationale: Let's say 1 work is processing 72 gb of data.
Model X : 1 gb per min
Model Y : 2 gb per min
Working together, 1 X and 1 Y = 3 gb per min
So, 24 times as many computers would work at 72 gb per min.
So no. of X =24
Answer is C
Answer: (C) 24
Question: Laura has a deck of standard playing cards with 13 of the 52 cards designated as a "heart." If Laura shuffles the deck thoroughly and then deals 10 cards off the top of the deck, what is the probability that the 10th card dealt is a heart?
(A) 1/4
(B) 1/5
(C) 5/26
(D) 12/42
(E) 13/42
Rationale: Desired outcomes= 13
Total outcomes= 52
Probability of getting any card as the heart card= 13/52= 1/4
And the same probability will be for 10th card as well.
A is the answer
Answer: (A) 1/4
Question: Find the area of the sector whose are is making an angle of 90° at the center of a circle of radius 3.2 Cm.
(A) 56.72 Sq.Cm
(B) 56.22 Sq.Cm
(C) 56.82 Sq.Cm
(D) 56.42 Sq.Cm
(E) 56.32 Sq.Cm
Rationale: Area of the sector = 90/360 × πr(power)2
= 90/360 × 22/7 × 3.2 × 3.2
= (11 × 10.24)/2 = 112.64/2 = 56.32 Sq.Cm
Answer is E.
Answer: (E) 56.32 Sq.Cm
Question: If P = Q-R, -1 < R < 0 and Q=0, which of the following is correct?
(A) P < -1.
(B) 0 < P <2
(C) P > 0
(D) 0 < P <4
(E) P < -20
Rationale: Q is 0 & R is -ve
For min. value max. numerator and minimize denominator
take Q=0 & R=-0.9
P=0-(-0.9)
P > 0
Ans C
Answer: (C) P > 0
Question: Approximately what percentage of the world’s forested area is represented by Finland given that Finland has 53.42 million hectares of forested land of the world’s 8.076 billion hectares of forested land.
(A) 0.0066%
(B) 0.066%
(C) 0.66PERCENT
(D) 6.6%
(E) 66%
Rationale: Approximation is a strategy that helps us arrive at less than an exact number and the inclusion in this problem of the word “approximately” is an obvious clue. First, 8.076 billion is 8,076 million. Next, 8,076 million rounds to 8,000 million and 53.42 million rounds to 53 million. Dividing 53 million by 8,000 million we arrive at 0.0066 (53M/8,000M). We convert this decimal figure to a percentage by multiplying by 100 (or moving the decimal point two places to the right) and adding a percent sign in order to obtain our answer of 0.66%. Note that the shortcut method involves comparing 53 million to 1% of 8,000 million or 80 million. Since 53 million is approximately two-thirds of 80 million then the answer is some two-thirds of 1% or 0.66%.
Answer: C.
Answer: (C) 0.66PERCENT
Question: Kim can walk 4 kilometers in one hour. How long does it take Kim to walk 18 kilometers?
(A) 7 hours and 30 minutes.
(B) 8 hours and 30 minutes.
(C) 9 hours and 30 minutes.
(D) 3 hours and 30 minutes.
(E) 4 hrs and 30 min
Rationale: The time it takes Kim to walk 18 kilometers is equal to
18 / 4 = 4.5 hours = 4 hours + 0.5 * 60 minutes
= 4 hours and 30 minutes.
correct answer E
Answer: (E) 4 hrs and 30 min
Question: If y = 2 + 2K and y≠0y≠0, then 2/y + 1/y + 1/y + 1/y = ?
(A) 1/(8+8k)
(B) 5/2(1+k)
(C) 1/(8+k)
(D) 4/(8+k)
(E) 4/(1+k)
Rationale: 2/Y + 1/Y + 1/Y + 1/Y
= 5/Y
= 5/(2 + 2K)
= 5/2(1 + K)
ANSWER:B
Answer: (B) 5/2(1+k)