mathewhe/aqua_rat huggingface dataset:
Question: The percentage profit earned by selling an article for Rs. 1920 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make 25% profit?
(A) Rs. 500
(B) Rs.2000
(C) Rs.1000
(D) Rs.693
(E) Rs.248
Rationale: Explanation:
Let C.P. be Rs. x.
Then,1920-x/x*100=(x-1280/x)*100
1920 - x = x - 1280
2x = 3200
x = 1600
Required S.P. = 125% of Rs. 1600 = Rs(125/100*1600)=Rs.2000.
Answer:B
Answer: (B) Rs.2000
Question: A marketing survey of Anytown found that the ratio of trucks to sedans to motorcycles was 3:7:2, respectively. Given that there are 9,800 sedans in Anytown, how many motorcycles are there?
(A) 2800
(B) 2100
(C) 3600
(D) 4200
(E) 5200
Rationale: Let the total number of trucks = 3x
total number of sedans = 7x
total number of motorcycles = 2x
total number of sedans = 9800
=> 7x = 9800
=> x = 1400
total number of motorcycles =2x = 2*1400
=2800
Answer A
Answer: (A) 2800
Question: 1,3,3,9,27,243,?
(A) 6565
(B) 6661
(C) 6861
(D) 6561
(E) 6531
Rationale: Each number is the product of the previous two numbers, ie 27*243 = 6561.
Answer : D
Answer: (D) 6561
Question: Two quarts containing 4⁄5 water and 2⁄5 formula are mixed with three quarts containing 7⁄10 water and 2⁄10 formula. Approximately what percent of the combined five-quart mixture is water?
(A) 50%
(B) 58%
(C) 54%
(D) 53%
(E) 52%
Rationale: 4/5 of 2 quarts = 4/5 quarts of water
7/10of 3 quarts = 21/10 quarts of water
4/5 = 0.8
21/10 = 2.1
Total water = 0.8 + 2.1= 2.9
Total quarts = 5
2.9/5 = 58%
Answer : B
Answer: (B) 58%
Question: A certain sum is invested at simple interest at 18% p.a. for two years instead of investing at 12% p.a. for the same time period. Therefore the interest received is more by Rs. 840. Find the sum?
(A) 7000
(B) 2787
(C) 2799
(D) 2699
(E) 2790
Rationale: Let the sum be Rs. x.
(x * 18 * 2)/100 - (x * 12 * 2)/100 = 840 => 36x/100 - 24x/100 =840
=> 12x/100 = 840 => x = 7000.Answer:A
Answer: (A) 7000
Question: How many of the positive factors of 42 are not factors of 56?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Factors of 42 - 1,2,3,6,7,14,42
factors of 56 - 1,2,4,7,8,14,28,56
Comparing both, we have three factors of 42 which are not factors of 56 - 3,6,42 .
The answer is 3. Pls check your options again - D $ E are same.
ANSWER:C
Answer: (C) 3
Question: A rectangular floor measures 2 by 3 meters. There are 5 white, 5 black, and 5 red parquet blocks available. Each block measures 1 by 1 meter. In how many different t colors patterns can be floor be parqueted?
(A)  104
(B)  213
(C)  3^5
(D)  705
(E)  726
Rationale: Total number of squares we need to fill = 6
Number of colors we have t = 3
Therefore, total number of patterns = 3*3*3*3*3*3 = 729
However, this is considering that we can have a case in which all tiles are the same color. Since we are given that the quantity of each tile is 5 and the number of tiles required is 6, we know that this case cannot be possible. Therefore we must subtract the cases in which all tiles will be of the same color (3 cases since there are 3 colors).
Thus our answer should be :729 - 3 = 726
Answer : E
Answer: (E)  726
Question: The ratio between the speeds of two trains is 7 : 8. If the second train runs 400 kms in 4 hours, then the speed of the first train is:
(A) 70 km/hr
(B) 75 km/hr
(C) 84 km/hr
(D) 87.5 km/hr
(E) 88.5 km/hr
Rationale: Let the speed of two trains be 7x and 8x km/hr.
Then, 8x = 400/4 = 100
Let the speed of two trains be 7x and 8x km/hr.
--> x = 100/8 = 12.5
--> Speed of first train = (7 x 12.5) km/hr = 87.5 km/hr.
Answer : D.
Answer: (D) 87.5 km/hr
Question: A sum of money place at compound interest doubles itself in 4 years. In how many years will it amount to eight times itself?
(A) 15 years
(B) 11 years
(C) 12 years
(D) 18 years
(E) 19 years
Rationale: 100 ---- 200 ---- 4
400 ---- 4
800 ---- 4
------
12 years
Answer: C
Answer: (C) 12 years
Question: The speed of a car increases by 2 km after every hour. If the distance travelled in the first hour was 35 km, what was the total distance travelled in 12 hours?
(A) 522 km
(B) 456 km
(C) 556 km
(D) 482 km
(E) None of these
Rationale: This is the problem of arithmetic progression (AP) with the first term (a) = 35, common difference (d) = 2 and total no. of terms (n) = 12. The sum of this series will be total distance travelled.
Sum (Sn) = n⁄2{2a + (n - 1)d} = 12⁄2{70 + 11 × 2}
= 12×92/2=552km
Answer E
Answer: (E) None of these
Question: If f(x)= 5x^2- 2x+6 and g(y)= 3y-5, then g(f(x))
(A) 82x^2-9x+38
(B) 15x^2-6x+13
(C) 58x^2-4x+58
(D) 87x^2-5x+96
(E) 98x^2-7x+94
Rationale: g(f(x))=3(5x^2-2x+6)-5
=15x^2-6x+18-5
=15x^2-6x+13
the answer is B
Answer: (B) 15x^2-6x+13
Question: The average age of A, B and C is 27 years. If the average age of A and C is 29 years, what is the age of B in years ?
(A) 19
(B) 35
(C) 20
(D) 32
(E) 23
Rationale: Age of B = Age of (A + B + C) â€“ Age of (A + C) = 27 Ã— 3 â€“ 29 Ã— 2 = 81 â€“ 58 = 23 years
E
Answer: (E) 23
Question: Set #1 = {A, B}
Set #2 = {K, L, M, N, O, P}
There are these two sets of letters, and you are going to pick exactly one letter from each set. What is the probability of picking at least one vowel?
(A) 1/6
(B) 1/3
(C) 7/12
(D) 2/3
(E) 5/6
Rationale: So Not a vowel in Set-1 : 1/2
And not a vowel in Ser-2:5/6
Now,
1/2∗5/6=5/12
This is for not a vowel.
Then for at least one vowel will be = 1−5/12=7/12
Answer will be C.
Answer: (C) 7/12
Question: If the sides of a triangle are 39 cm, 36 cm and 15 cm, what is its area?
(A) 230 cm^2
(B) 240 cm^2
(C) 250 cm^2
(D) 260 cm^2
(E) 270 cm^2
Rationale: The triangle with sides 39 cm, 36 cm and 15 cm is right angled, where the hypotenuse is 39 cm.
Area of the triangle
= 1/2 * 36 * 15
= 270 cm^2
Answer: E
Answer: (E) 270 cm^2
Question: The profit earned by selling an article for Rs. 832 is equal to the loss incurred when the same article is sold for Rs. 448. What should be the sale price for making 30% profit?
(A) 220
(B) 230
(C) 960
(D) 832
(E) 400
Rationale: C.P. = Rs. x.
Then, 832 - x = x - 448
2x = 1280 => x = 640
Required S.P. = 130% of Rs. 640 = 130/100 * 640 = Rs. 832.
D
Answer: (D) 832
Question: If A:B = 2:3, B:C = 4:5 and C:D = 5:9 then A:D is equal to:
(A) 11:17
(B) 8:27
(C) 5:9
(D) 2:9
(E) none
Rationale: Solution:
A/D = (A/B)*(B*C)*(C/D)
= (2/3)*(4/5)*(5/9)
= (2*4*5)/(3*5*9)
= 8/27.
Answer: Option B
Answer: (B) 8:27
Question: Jim is able to sell a hand-carved statue for $670 which was a 35% profit over his cost. How much did the statue originally cost him?
(A) $496.30
(B) $512.40
(C) $555.40
(D) $574.90
(E) $588.20
Rationale: 670 is the final price that is the selling price. now suppose, x is the cost price.
therefore 670 = 1.35 * x
now while doing x = 670/1.35 calculation. I saw that the answer choices begin with 5.
So i did 135 * 5 = 675. As 670 is less than 675. Therefore the quotient will be less than 5.
Which is only in the answer A.
Answer: (A) $496.30
Question: A box contains nine light out of which 4 are defective. If four light are chosen at random, find the probability that all the four light are defective?
(A) 2/113
(B) 3/121
(C) 1/126
(D) 3/101
(E) None of these
Rationale: Out of nine light , five are good and four are defective.
Required probability = ⁴C₄/⁹C₄ = 1/126
C
Answer: (C) 1/126
Question: A person jogged 10 times along the perimeter of a rectangular field at the rate of 12 kilometers per hour for 30 minutes. If field has a length that is twice its width, find the area of the field in square meters.
(A) 60.0
(B) 50.0
(C) 40.0
(D) 30.0
(E) 20.0
Rationale: Let us first find the distance d jogged
distance = rate × time = (12 km / hr) × 30 minutes
= (12 km/hr) × 0.5 hr = 6 km
The distance of 6 km corresponds to 10 perimeters and therefore 1 perimeter is equal to
6 km / 10 = 0.6 km = 0.6 × 1000 meters = 600 meters
Let L and W be the length and width of the field. The length is twice the width. Hence
L = 2 W
The perimeter is 600 meters and is given by
2 (L + W) = 600
Substitute L by 2 W
2 (2 W + W) = 600
Simplify and solve for W
4 W + 2 W = 600
6 W = 600
W = 100
Find L
L = 2 W = 200
Find the area A of the rectangle
A = L * W = 200 * 100 = 20,000 square meters
correct answer is E)20.000
Answer: (E) 20.0
Question: Insert the missing number.
3, 5, 6,10 , 9, 15, 12, 20, 15, (....)
(A) 25
(B) 20
(C) 10
(D) 30
(E) 15
Rationale: Explanation:
There are two series, beginning respectively with 3 and 5. In one 3 is added and in another 5 is added.
The next number is 20 + 5 = 25.
Answer: A) 25
Answer: (A) 25
Question: If a fair 6-sided die is rolled three times, what is the probability that exactly one 2 is rolled?
(A) 25/216
(B) 50/216
(C) 25/72
(D) 25/36
(E) 5/6
Rationale: Total ways in which a 6-sided die can be rolled three times = 6*6*6 = 216
To get exactly one 2, there are three ways:
A 2 on the first roll and non 2 on other two rolls. This can be done in 1*5*5 = 25 ways.
The 2 could be on the second or third roll too. So total favorable cases = 25*3 = 75
Required Probability = 75/216 = 25/72
Answer (C)
Answer: (C) 25/72
Question: An equal number of desks and bookcases are to be placed along a library wall that is 15 meters long. Each desk is 2 meters long, and each bookshelf is 1.5 meters long. If the maximum possible number of desks and bookcases are to be placed along the wall, then the space along the wall that is left over will be how many G meters long?
(A) 0.5
(B) 1
(C) 1.5
(D) 2
(E) 3
Rationale: Let x be the number of desks and bookcases that are placed along the library wall.
2x + 1.5x < 15
3.5x < 15
Since x is a non negative integer, the largest number x can be is 4.
When x is 4, the desks and bookcases take up 3.5 * 4 = 14m, leaving 1m of empty space.
Thus, I believe the answer is B) 1
Answer: (B) 1
Question: Find the least which when divided y 16,18,20, and 25 leaves 4 as remainder in each case, but when divided by 7 leaves no remainder.
(A) 17004
(B) 18000
(C) 18002
(D) 18004
(E) 18005
Rationale: Solution
L.C.M. of 16,18,20,25 = 3600. required number is of the form 3600 k + 4.
Least value of k for which (3600 k + 4 ) is divisible by 7 is k = 5.
So, Required number = (3600 × 5 + 4) = 18004. Answer D
Answer: (D) 18004
Question: 53, 60, 56, 8, 54, 3, 8
Which of the following numbers is lower than the median but greater than the mean of the set of the numbers in the list?
(A) 18
(B) 29
(C) 46
(D) 53
(E) 55
Rationale: Yes, it can be solved with observation even without approximation in 30 sec.
Just observe given numbers: 3, 8, 8, 53, 54, 56, 60
Median is very easy to tell - its 53. Now we want a number lower than 55 and greater than mean. How many numbers are lower than 53? DE are already out.
Now, we have 18, 29 and 46 and we want a number among these which is greater than mean. logically whatever be the mean, if one value out of these 5 has to be greater than mean it has to be 46. (Notice, if 18 is more than mean then 46 is also. If 28 is more than mean, 46 is also. )
Hence C it is!
Answer: (C) 46
Question: Double of Quarter of 4 percent written as a decimal is :
(A) 0.003
(B) 0.0005
(C) 0.25
(D) 0.02
(E) None of these
Rationale: Explanation :
Solution: (2)*(1/4)*4% = 2*(1/4 * 1/100)= 0.02.
Answer : D
Answer: (D) 0.02
Question: There are 10 points on a circle. A hexagon can be formed by linking 5 of the 10 points. How many such hexagons are possible?
(A) 60
(B) 120
(C) 200
(D) 252
(E) 600
Rationale: 5 points can be selected out of 10 points in 10C5 ways
=10 !/5!*5!=252
Ans D
Answer: (D) 252
Question: 20 throws of a die produces following results
SCORE -- NUMBER OF OCCURRENCES
---1-------------------4
---2-------------------3
---3-------------------5
---4-------------------2
---5-------------------2
---6-------------------4
What is the probability L that one more throw to this series will increase the mean score?
(A) 1/6
(B) 1/3
(C) 1/2
(D) 2/3
(E) 5/6
Rationale: I get the mean as 67/20 --> 3.35. Thus in order to raise this mean we would need a 4,5,or 6.
Thus probability L is 1/2.C
Answer: (C) 1/2
Question: A fort had provision of food for 150 men for 45 days. After 10 days, 25 men left the fort. The number of days for which the remaining food will last, is:
(A) 29 1/5
(B) 37 1/4
(C) 42
(D) 54
(E) 48
Rationale: After 10 days : 150 men had food for 35 days.
Suppose 125 men had food for x days.
Now, Less men, More days (Indirect Proportion)
Therefore 125 : 150 :: 35 : x <=> 125 x x = 150 x 35
=> x =150 x 35/125
=> x = 42.
Correct answer is C
Answer: (C) 42
Question: If it is true that x< 8 and 2x> -4, which of the following must be true?
(A)  -8 < x< 4
(B)  x> 2
(C)  x> -8
(D)  x< 4
(E)  None of the above
Rationale: Two points:
1) x< 8
2) 2x> -4 or x> -2
From 1 and 2: -2 < x< 8
(A) is not true because x could be > 4.
(B) is not true because x could be < 2.
(C) is true because x value is always > -8.
(D) is not true because x could be >4.
(E) is not true because C is true.
Answer: (C)  x> -8
Question: If $ 5,000 is invested in an account that earns 10% interest compounded semi-annually, then the interest earned after one year would be how much greater than if the $ 5,000 had been invested at 8% simple yearly interest?
(A) $ 4
(B) $ 8
(C) $ 12
(D) $ 16
(E) $ 10
Rationale: Solution
Amount (CI) = P+(1+r/n)^nt = 5000+(1+0.10/2)^2= 5410
Amount (SI) = P+PTR/100 = 5000+(5000*1*10/100)=5400
Difference = 5410-5400=10 $
E
Answer: (E) $ 10
Question: A train sets off at 2 p.m. at the speed of 70 kmph. Another train starts at 3:30 p.m. in the same direction at the rate of 85 kmph. At what time the trains will meet?
(A) 10.39
(B) 10.37
(C) 10.3
(D) 10.31
(E) 10.32
Rationale: D = 70 * 1 ½ = 105 km
RS = 85 – 70 = 15
T = 105/15 = 7 h
3.30 + 7 h = 10.30 p.m.Answer:C
Answer: (C) 10.3
Question: John found that the average of 15 numbers is 40. If 14 is added to each number then the mean of number is?
(A) 54
(B) 45
(C) 65
(D) 78
(E) 64
Rationale: (x+x1+...x14)/15 = 40
54
Option A
Answer: (A) 54
Question: Given a spinner with four sections of equal size labeled R, B, C, and D, what is the probability of NOT getting an R 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 R 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: On a 26 question test, five points were deducted for each wrong answer and eight points were added for each correct answer. If all the questions were answered, how many were correct, if the score was zero ?
(A) 10
(B) 12
(C) 11
(D) 13
(E) 16
Rationale: Explanation :
Let the correct answer be : x
Therefore wrong answers = (26 - x)
Total socre = 8x - 5(26-x) = 0
or, 13x = 130
Therefore x = 10
Answer : A
Answer: (A) 10
Question: Ramu bought an old car for Rs. 36000. He spent Rs. 15000 on repairs and sold it for Rs. 62900. What is his profit percent?
(A) 16%
(B) 17%
(C) 18%
(D) 58%
(E) 23%
Rationale: Total CP = Rs. 36000 + Rs. 15000
= Rs. 51000 and SP = Rs. 62900
Profit(%)
= (62900 - 51000)/51000 * 100
= 23%
Answer: E
Answer: (E) 23%
Question: A thief is noticed by a policeman from a distance of 450 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km and 11 km per hour respectively. What is the distance between them after 6 minutes?
(A) 150 m
(B) 200 m
(C) 170 m
(D) 100 m
(E) 350 m
Rationale: Relative speed of the thief and policeman = 11 - 10 = 1 km/hr.
Distance covered in 6 minutes = 1/60 * 6 = 1/10 km = 100 m.
Distance between the thief and policeman = 450 - 100 = 350 m
E
Answer: (E) 350 m
Question: Dan’s car gets 32 miles per gallon. If gas costs $4/gallon, then how many miles can Dan’s car go on $46 of gas?
(A) 124
(B) 256
(C) 368
(D) 424
(E) 512
Rationale: 46/4 = 11.5 gallons
11.5*32 = 368 miles
The answer is C.
Answer: (C) 368
Question: R is the set of positive even integers less than 101, and S is the set of the squares of the integers in R. How many elements does the intersection of R and S contain ?
(A)  None
(B)  Two
(C)  Four
(D)  Five
(E)  Seven
Rationale: R is the set of positive even integers less than 101, and S is the set of the squares of the integers in R.
How many elements does the intersection of R and S contain?
R=2,4,6,8,10,12...
S=4,16,36,64...
Numbers: 4, 16, 36, 64, and 100 are even integers (less than 101) that are in both sets.
Solution: Five
Answer: D
Answer: (D)  Five
Question: If Z is a positive integer greater than 1, what is the sum of the multiples of Z from Z to Z^2, inclusive?
(A)  Z(Z + 1)(Z-1)
(B)  Z^2(Z + 1)/2
(C)  Z^2(Z-1)
(D)  (x^3 + 2x)/2
(E)  x(x-1)^2
Rationale: Ans :- B=Z^2(Z + 1)/2
I substituted 3 in all answer choices.
Option B and C were both satisfying the condition.
So i substituted 4 instead of 3 in all answer choices,
Only B option satisfied.
Answer: (B)  Z^2(Z + 1)/2
Question: Out of eight crew members three particular members can sit only on the left side. Another two particular members can sit only on the right side. Find the number of ways in which the crew can be arranged so that four men can sit on each side.
(A) 864
(B) 863
(C) 865
(D) 1728
(E) None
Rationale: Solution:
Required number of ways, = 3C2 *4! *4! = 1728.
Answer: Option D
Answer: (D) 1728
Question: A 14% stock yields 8%.The market value of the stock is :
(A) Rs. 175
(B) Rs. 92
(C) Rs. 112.50
(D) Rs. 116.50
(E) None of these
Rationale: solution
To obtain Rs. 8, investment = Rs. 100.
To obtain Rs. 14, investment = Rs.(100/8X14)= Rs. 175
∴ Market value of Rs. 100 stock = Rs.175
Answer A
Answer: (A) Rs. 175
Question: If the digits 27 in the decimal 0.00027 repeat indefinitely, what is the value of (10^5-10^3)(0.00027)?
(A) 0.27
(B) 0.027
(C) 27
(D) 0.0027
(E) 2.7e-06
Rationale: 99*0.27=26.73 approx. 27
Answer : C
Answer: (C) 27
Question: What is the remainder when 7^74 - 5^74 is divided by 2?
(A) 5
(B) 1
(C) 2
(D) 3
(E) None of these
Rationale: easiest way for me: 7^74 - 5^74 = (49)^37-25^37 = (24*2+1)^37 - (24+1)^37 -> remainder is 1^37 - 1^37 = 0
Ans :E
Answer: (E) None of these
Question: In a 1000 m race, A beats B by 50 m and B beats C by 100 m. In the same race, by how many meters does A beat C?
(A) 145 m
(B) 176 m
(C) 268 m
(D) 129 m
(E) 218 m
Rationale: By the time A covers 1000 m, B covers (1000 - 50) = 950 m.
By the time B covers 1000 m, C covers (1000 - 100) = 900 m.
So, the ratio of speeds of A and C =
1000/950 * 1000/900 = 1000/855 So, by the time A covers 1000 m, C covers 855 m.
So in 1000 m race A beats C by 1000 - 855 = 145 m.
Answer:A
Answer: (A) 145 m
Question: If a 4-member subcommittee is to be formed from a certain 6-member committee, how many different such subcommittee are possible?
(A) 6
(B) 15
(C) 20
(D) 60
(E) 216
Rationale: Another way:
1st member can be selected in 6 ways
2nd can be selected in 5 ways
3rd can be selected in 4 ways
4th can be selected in 3 ways
So total ways : 360
But to avoid the similar scenarios 360/4!=15
B
Answer: (B) 15
Question: In a function they are distributing noble prize. In how many ways can 4 prizes be distributed among 5 boys when a boy gets any no. of prizes?
(A) 48
(B) 50
(C) 625
(D) 602
(E) 525
Rationale: Ans.(C)
Sol. In this case, repetitions are allowed, so all the four prizes can be given in 5 ways, i.e. (5*5*5*5) ways = 54 ways = 625 ways Or nr ways = 54 ways = 625 ways
Answer: (C) 625
Question: If an object travels 90 feet in 3 seconds, what is the object’s approximate speed in miles per hour? (Note: 1 mile = 5280 feet)
(A) 17.36
(B) 20.45
(C) 23.87
(D) 26.92
(E) 29.56
Rationale: 90 feet/3 seconds = 30 feet/second
(30 feet/second)*(3600 seconds/hour)*(1 mile/5280 feet) = 20.45 miles/hour (approximately)
The answer is B.
Answer: (B) 20.45
Question: Rs.8000 become Rs.8652.8 in a certain interval of time at the rate of 4% per annum of C.I. Find the time?
(A) 6 years
(B) 8 years
(C) 9 years
(D) 3 years
(E) 2 years
Rationale: 8652.8 = 8000(26/25)N
(26/25)^2 = (26/25)N => N = 2
At the end of two years what will be the comp.Answer: E
Answer: (E) 2 years
Question: The mean of 50 observations was 36. It was found later that an observation 34 was wrongly taken as 23. The corrected new mean is :
(A) 36.0
(B) 36.5
(C) 36.24
(D) 36.12
(E) 36.22
Rationale: Explanation:
Correct Sum = (36 * 50 + 434 - 23) = 1825.
Correct mean = = 1811/50 = 36.5
Answer: E) 36.22
Answer: (E) 36.22
Question: On a ranch, a rancher can place a loop of rope, called a lasso, once in every 3 throws around a cow’s neck. What is the probability that the rancher will be able to place a lasso around a cow’s neck at least once in 3 attempts?
(A) 1/3
(B) 5/9
(C) 7/9
(D) 19/27
(E) 23/27
Rationale: P(missing all 3)=(2/3)^3=8/27
P(success on at least one attempt)=1-8/27=19/27
The answer is D.
Answer: (D) 19/27
Question: Find the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 10 cm?
(A) 827 cm2
(B) 216 cm2
(C) 285 cm2
(D) 178 cm2
(E) 190 cm2
Rationale: Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them)
= 1/2 (20 + 18) * (10)
= 190cm2
Answer:E
Answer: (E) 190 cm2
Question: A committee is reviewing a total of 20x black-and-white films and 6y color films for a festival. If the committee selects y/x% of the black-and-white films and all of the color films, what fraction Q of the selected films are in color?
(A) 1/130
(B) 1/5
(C) 3/13
(D) 10/13
(E) 30/31
Rationale: It's y/xpercentnot y/x.
If x=20 and y=10. Then:
20x=400 black-and-white films;
6y=60 color films.
y/x%=10/20%=0.5% of the black-and-white films, so 2 black-and-white films and all 60 color films, thus total of 62 films were selected.
Color films thus compose Q=60/62=30/31 of the selected films.
Answer: E.
Answer: (E) 30/31
Question: If the price has fallen by 14% what percent of its consumption be: increased so that the expenditure may be the same as before?
(A) 11 1/8%
(B) 11 1/5%
(C) 16 12/43%
(D) 17 7/9%
(E) 21 1/9%
Rationale: 100 â€“ 14 = 86
86------14
100------? => 16 12/43%
Answer: C
Answer: (C) 16 12/43%
Question: If the ratio of boys to girls in a class is B and the ratio of girls to boys is G; then 10(B + G) is ?
(A) Equal to 3
(B) Less than 3
(C) More than 10
(D) Less than 10
(E) none of these
Rationale: Let number of boys = x
Let number of girls = y
Therefore x/y = B and y/x = G
10(B + G) = 10[(x/y) + (y/x)] = 10[(x2 + y2)/xy] > 10
ANSWER:C
Answer: (C) More than 10
Question: A train 345 m long passed a pole in 15 sec. How long will it take to pass a platform 760 m long?
(A) 76 sec
(B) 43 sec
(C) 45 sec
(D) 15 sec
(E) 16 sec
Rationale: Speed = 345/15 = 23 m/sec.
Required time = (345 + 760)/23
= 48 sec.
Answer:B
Answer: (B) 43 sec
Question: In a series of four football matches between Germany and Argentina , the probability of Germany winning a match is 1/3 and the probability that the match ends in a draw is 1/4. If a win gets the team 2 points, a draw 1 point and a loss 0 Points, What is the probability that Germany will end up in 4 draws in the series?
(A) 24/576
(B) 125/864
(C) 1/25
(D) 1/256
(E) 1/5
Rationale: Since the probability of a draw is 1/4, then the probability of 4 draws in 4 matches is (1/4)^4=1/256.
Answer: D.
Answer: (D) 1/256
Question: A flight takes off at 2.00 a.m. from a place at 18N 10E and landed 10 hours later at a place with co-ordinates 36N 70W. What is the local time when the plane landed?
(A) 6.00 a.m.
(B) 6.40 a.m.
(C) 7.00 a.m.
(D) 7.40 a.m.
(E) 8.00 a.m.
Rationale: Time difference between places will be 4*(70+10) minutes = 320 min =
5 hrs 20 min
as change of 1 degree in longitude cause change of 4 minutes in time.
and that change is 80 degrees here.
so when plane land. time will be = 2.00 + 10.00 -5.20 = 6.40 a.m.
ANSWER:B
Answer: (B) 6.40 a.m.
Question: If log 27 = 1.401, then the value of log 9 is:
(A) 0.934
(B) 0.945
(C) 0.954
(D) 0.958
(E) 0.998
Rationale: log 27 = 1.401
log (3cube ) = 1.401
3 log 3 = 1.401
log 3 = 0.467
log 9 = log(3square ) = 2 log 3 = (2 x 0.467) = 0.934.
Answer: Option A
Answer: (A) 0.934
Question: 95 80 85 65 50 85 35 ? ?
(A) 25 15
(B) 25 85
(C) 20 85
(D) 85 35
(E) 25 75
Rationale: 95-15=80
again 85
80-15=65
65-15=50
again 85
50-15=35
35-15=20
again 85
then answer is 20 ,85
ANSWER:C
Answer: (C) 20 85