mathewhe/aqua_rat huggingface dataset:
Question: A bag contains 7 red balls, 5 green 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) 3/5
(C) 1/5
(D) 7/15
(E) 8/15
Rationale: Total number of balls = (7 + 5 + 6) = 18.
Therefore, n(S) = 18.
Let E1 = event of drawing a red ball.
and E2 = event of drawing a green ball.
Then, E1 n E2 = f.
P (E1 n E2) = P(E1) + P(E2) = (7/18 + 5/18) = 2/3.
ANSWER:A
Answer: (A) 2/3
Question: The average of five numbers is 9. The average of first two numbers is 7 and the average of last two numbers is 12. What is the middle number?
(A) 7
(B) 8
(C) 5
(D) 10
(E) 6
Rationale: The total of five numbers = 5x9 = 45
The total of first 2 and last 2 numbers is = 2 X 7+2 X 12 = 38
So, the middle number is (45 - 38 ) = 7
A
Answer: (A) 7
Question: A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of this son is
(A) 78 years
(B) 22 years
(C) 88 years
(D) 66 years
(E) 65 years
Rationale: Let's Son age is x, then Father age is x+24.
=> 2(x+2) = (x+24+2)
=> 2x+4 = x+26
=> x = 22 years
Answer: B
Answer: (B) 22 years
Question: What is the smallest 6 digit number exactly divisible by 111?
(A) 100010
(B) 100012
(C) 100011
(D) 100013
(E) 120012
Rationale: Smallest 6 digit number = 100000
100000/111 = 900, remainder = 100. Hence 11 more should be added to 100000
to get the smallest 6 digit number exactly divisible by 111
=> smallest 6 digit number exactly divisible by 111 = 100000 + 11 = 100011
Answer is C
Answer: (C) 100011
Question: The equation x/y - 2/5 = 0 is equivalent to each of the following EXCEPT
(A) (x - y)/y = -3/5
(B) (5x - 3y)/y = 21/5
(C) (x + 3y)/y = 17/5
(D) (x + y)/x = 7/2
(E) x/y + 1 = 7/5
Rationale: x/y - 2/5 = 0
5x=2y
x= 2/5 * y or y = 5/2 *x
plug in x or y depending on the equation. all expressions are true except for
B. (5x - 3y)/y = 21/5
where y=-21
B. (5x - 3y)/y = 21/5
ANSWER:B
Answer: (B) (5x - 3y)/y = 21/5
Question: A train travels from New York to Chicago, a distance of approximately 840 miles, at an average rate of 60 miles per hour and arrives in Chicago at 7:00 in evening, Chicago time. At what hour in the morning, New York time, did the train depart for Chicago? (Note : Chicago time is one hour earlier than New York time)
(A) 3:00
(B) 4:00
(C) 5:00
(D) 6:00
(E) 7:00
Rationale: 7:00 in evening in Chicago = 8:00 in evening in New York. So, the train was in Chicago 8:00 in the evening, New York time.
The trip took T=D/R=840/60=14 hours. Therefore, the train depart from New York at 8:00 - 14 hours = 6:00 in the morning, New York time.
Answer: D.
Answer: (D) 6:00
Question: A rectangular courtyard, the sides of which are in the ratio of 4:3, cost Rs.600 for paving at 50 p per m2; find the length of the diagonal of the courtyard?
(A) 87
(B) 92
(C) 12
(D) 10
(E) 11
Rationale: Explanation:
1 m2 ---- 1/2
? ----- 600 => 1200 m2
4x * 3x = 1200 => x = 10
Answer: Option D
Answer: (D) 10
Question: In how many ways the letters of the word RAIXBON be arranged?
(A) 4500
(B) 5479
(C) 6478
(D) 5040
(E) 7658
Rationale: Total ways of arranging the letters = 7! = 5040 ways.
D)
Answer: (D) 5040
Question: In Lulu company 60% of the employees earn less than $50,000 a year, 60% of the employees earn more than $40,000 a year, 11% of the employees earn $43,000 a year and 5% of the employees earn $49,000 a year. What is the median salary for the company?
(A) 43.0
(B) 45.5
(C) 46.0
(D) 49.0
(E) 50.0
Rationale: In Lulu company 60% of the employees earn less than $50,000 a year, 60% of the employees earn more than $40,000 a year 50 and 51 employee will be each 43K. hence median = (43K+43k)/2=A
Answer: (A) 43.0
Question: The average age 6 members of a committee are the same as it was 2 years ago, because an old number has been replaced by a younger number. Find how much younger is the new member than the old number?
(A) 14 years
(B) 17 years
(C) 18 years
(D) 12 years
(E) 11 years
Rationale: 6 * 2
= 12
Answer:D
Answer: (D) 12 years
Question: How many 3-digit positive integers are there, where each digit is positive, and no two adjacent digits are same?
(A) 576
(B) 3024
(C) 4096
(D) 4608
(E) 6561
Rationale: First digit.. 9 posibilities
Second digit, 8 possibilities
third digit, 8 possibilities
9*8*8 = 576.
A
Answer: (A) 576
Question: 15.06 * 0.001 = ?
(A) 15060000
(B) 0.001506
(C) 0.01506
(D) 0.1506
(E) None of these
Rationale: Explanation:
Clearly after decimal 5 digits should be there.
Option C
Answer: (C) 0.01506
Question: A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 180 m in 18 sec. then find the length of the train?
(A) 877m
(B) 180m
(C) 786m
(D) 165m
(E) 456m
Rationale: Length of the train be ‘X’
X + 120/15 = X + 180/18
6X + 720 = 5X + 900
X = 180m
Answer: B
Answer: (B) 180m
Question: In the xy-plane the point (-2 -3) is the centre of a circle, the point (-2, 2) lies inside the circle and the point (5, -3) lies outside the circle. If the radius r of the circle r is an integer then r=
(A) 6
(B) 5
(C) 4
(D) 3
(E) 2
Rationale: Can be solved without much calculations.
You are given that (-2,-3) is the center of the circle. Point (5,-3) lies inside the circle ---> the radius is lesser than distance of (-2,-3) from (5,-3) ---> lesser than 7 units but the radius will also be greater than the distance of (-2,-3) from (-2,2) ----> greater than 5 units.
Thus the radius is >5 but <7and as it is an integer, the only possible value of radius = 6 units.
A is the correct answer.
Answer: (A) 6
Question: Mark and Cody invest in a business and each put in $12000. After 3 months, Cody withdraws half of his capital. How should they share the profits after 12 months?
(A) 10:7
(B) 3:2
(C) 8:5
(D) 4:3
(E) 11:8
Rationale: Mark invests $12000 for 12 months, but Cody invests $12000 for the first 3 months and then withdraws $6000. So, the investment of Cody for remaining 9 months is $6000 only.
Mark:Cody
12000*12 : (12000*3) + (6000*9)
144000 : 90000
Mark:Cody = 8:5
Answer: C
Answer: (C) 8:5
Question: Sum of two numbers is 63. Their difference is 1/8 of their sum. their L.C.M is
(A) 231
(B) 153
(C) 351
(D) 345
(E) 355
Rationale: Explanation:
Let the numbers be x and y
According to the problem
X + y = 63
x - y = 1/8 ( x+y)
x-y = 1/8 * 63, x-y = 9
2x = 72, x= 36 and y = 27
L.C.M of 36 and 27 is 351
Answer: Option C
Answer: (C) 351
Question: If x,p,q, and r are positive integers and (p)×(q)×(r)=x^2, which of the following could be the values of p,q, and r?
(A) 3, 16, 25
(B) 9, 25, 24
(C) 2,16, 32
(D) 2, 9, 16
(E) 8, 16, 36
Rationale: This is one of those questions where using the given options is fastest way to get the solution. We need to find a set where 3 numbers can be paired into 2 pairs of some numbers because we need a product which is a square number.
C fits the bill. 2*16*32 = 2*4*4*8*4 =4*4*8*8
ans C
Answer: (C) 2,16, 32
Question: Circular gears P and Q start rotating at the same time at constant speeds. Gear P makes 10 revolutions per minute and Gear Q makes 40 revolutions per minute. How many seconds after the gears start rotating will gear Q have made exactly 10 more revolutions than gear P?
(A) 10
(B) 12
(C) 15
(D) 20
(E) 25
Rationale: Gear Q makes 30 more revolutions each 60 seconds.
The time to make 10 = 30/3 more revolutions is 60/3 = 20 seconds.
The answer is D.
Answer: (D) 20
Question: The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. What is the present age of the husband?
(A) 30
(B) 40
(C) 20
(D) 50
(E) 25
Rationale: Let the present age of the husband = h
Present age of the wife = w
Present age of the child = c
3 years ago, average age of husband, wife and their child = 27
=> Sum of age of husband, wife and their child before 3 years = 3 × 27 = 81
=> (h-3) + (w-3) + (c-3) = 81
=> h + w + c = 81 + 9 = 90 --- equation(1)
5 years ago, average age of wife and child = 20
=> Sum of age of wife and child before 5 years = 2 × 20 = 40
=> (w-5) + (c-5) = 40
=> w + c = 40 + 10 = 50 --- equation(2)
Substituting equation(2) in equation(1)
=> h + 50 = 90
=> h = 90 - 50 = 40
i.e., Present age of the husband = 40
Answer is B.
Answer: (B) 40
Question: Factor: x4y3 â€“ 16y3
(A) A) 3y3(x2 + 4)(x + 2)(x -2)
(B) B) y3(x2 + 4)(x + 2)(x -2)
(C) C) 3y3(x2 + 4)(x + 2)(x -3)
(D) D) 3y3(x2 + 4)(x + 3)(x -2)
(E) E) 3y3(x2 + 4)(x + 2)(x -4)
Rationale: x4y3â€“ 16y3.
= y3(x4 â€“ 16).
= y3[(x2)2 - 42].
= y3(x2 + 4)(x2 - 4).
= y3(x2 + 4)(x2 - 22).
= y3(x2 + 4)(x + 2)(x -2).
Answer: (B) y3(x2 + 4)(x + 2)(x -2)
Answer: (B) B) y3(x2 + 4)(x + 2)(x -2)
Question: A can do a piece of work in 12 days. When he had worked for 2 days B joins him. If the complete work was finished in 8 days. In how many days B alone can finish the work?
(A) 18 days
(B) 11 days
(C) 77 days
(D) 188 days
(E) 66 days
Rationale: 8/12 + 6/x = 1
X = 18 days
Answer: A
Answer: (A) 18 days
Question: A man buys a truck for Rs. 2,50,000. The annual repair cost comes to 2% of the price of purchase. Besides, he has to pay an annual tax of Rs. 2000. At what monthly rent must he rent out the truck to get a return of 15% on his net invests of the first year?
(A) Rs. 3359
(B) Rs. 2500
(C) Rs. 4000
(D) Rs. 3212.5
(E) None
Rationale: Solution: The total cost for the year = 250000+2% of 2500000+2000 = Rs. 257000.
For getting return of 15% he must earn = 257000*15/100 = Rs. 38550 per year.
Then, monthly rent = 38550/12 = Rs. 3212.5.
Answer: Option D
Answer: (D) Rs. 3212.5
Question: The average of 13 numbers is 14.8. If the average of the first seven numbers is 14.6 and that of the last seven numbers is 14.4,then the middle number is?
(A) 11.6
(B) 12.6
(C) 10.6
(D) 9.6
(E) 8.6
Rationale: Middle number = 14.6*7 + 14.4*7- 14.8*13 = 102.2+100.8-192.4=10.6
Answer is C
Answer: (C) 10.6
Question: Of the 440 members at a health club, 260 use the weight room and 300 use the pool. If at least 60 of the members do not use either, then the number of members using both the weight room and the pool must be between:
(A) 240 to 280
(B) 230 to 260
(C) 240 to 260
(D) 200 to 260
(E) 180 to 260
Rationale: W=260
P=300
ALL=440
N(NEITHER)=AT LEAST 60
BOTH=?
W+P-BOTH+N=ALL
260+300-BOTH+60=440
BOTH=180
now pay attention to the fact, that both at most can be 260, since W=260
E
Answer: (E) 180 to 260
Question: 3/7 of a congregation are men while 11/21are women. What is the increase in percentage from ratio of men to ratio of women in the congregation?
(A) A) 69%
(B) B) 54%
(C) C) 18.81%
(D) D) 16%
(E) E) 81.82%
Rationale: Ratio of men: 3/7
Ratio of women: 11/21
percentage increase is (difference/initial quantity)*100
(3/7)/(11/21 )* 100= 81.82%
Correct options is E
Answer: (E) E) 81.82%
Question: If x is 20 percent more than y and y is 70 percent less than z, then x is what percent of z?
(A) 500%
(B) 250%
(C) 500/3%
(D) 36%
(E) 60%
Rationale: Z = 100 ; Y = 30 so X = 36
X as % of Z = 36/100 * 100 => 36%
Answer will be (D)
Answer: (D) 36%
Question: The average monthly salary of 20 employees in an organisation is Rs. 1500. If the manager's salary is added, then the average salary increases by Rs. 100. What is the manager's monthly salary?
(A) Rs.3601
(B) Rs.3618
(C) Rs.3600
(D) Rs.3619
(E) Rs.3610
Rationale: Manager's monthly salary
= Rs. (1600 * 21 - 1500 * 20)
= Answer:C
Answer: (C) Rs.3600
Question: 1/6 = 4/5 . which method did you use to determine whether this proportion is true or false?
(A) true
(B) neutral
(C) false
(D) not sure
(E) none
Rationale: 1/6= 3/18. cross multiplication: 1 * 18 = 18, 3 * 6= 18,
we see that 18 are not equal to 18. so there is proportion. corrcet answer: (A)
Answer: (A) true
Question: During a certain season, a team won 70 percent of its first 100 games and 50 percent of its remaining games. If the team won 70 percent of its games for the entire season, what was the total number of games that the team played?
(A) 180
(B) 170
(C) 156
(D) 150
(E) 100
Rationale: We are first given that a team won 70 percent of its first 100 games. This means the team won 0.7 x 100 = 70 games out of its first 100 games.
We are next given that the team won 50 percent of its remaining games. If we use variable T to represent the total number of games in the season, then we can say T – 100 equals the number of remaining games in the season. Thus we can say:
0.5(T – 100) = number of wins for remaining games
0.5T – 50 = number of wins for remaining games
Lastly, we are given that team won 70 percent of all games played in the season. That is, they won 0.7T games in the entire season. With this we can set up the equation:
Number of first 100 games won + Number of games won for remaining games = Total Number of games won in the entire season
70 + 0.5T – 50 = 0.7T
20 = 0.2T
200 = 2T
100 = T
Answer is E.
Answer: (E) 100
Question: You have been given the task of transporting 3,000 apples 1,000 miles from Appleland to Bananaville. Your truck can carry 1,000 apples at a time. Every time you travel a mile towards Bananaville you must pay a tax of 1 apple but you pay nothing when going in the other direction (towards Appleland).
What is highest number of apples you can get to Bananaville?
(A) 767
(B) 833
(C) 916
(D) 1123
(E) 907
Rationale: Step one: First you want to make 3 trips of 1,000 apples 333 miles. You will be left with 2,001 apples and 667 miles to go.
Step two: Next you want to take 2 trips of 1,000 apples 500 miles. You will be left with 1,000 apples and 167 miles to go (you have to leave an apple behind).
Step three: Finally, you travel the last 167 miles with one load of 1,000 apples and are left with 833 apples in Bananaville.
Answer: (B) 833
Question: In how many different ways can 5 girls and 6 boys form a circle such that the boys and the girls alternate?
(A) 28800
(B) 14000
(C) 12000
(D) 14400
(E) None of these
Rationale: Explanation :
In a circle, 6 boys can be arranged in 5! ways
Given that the boys and the girls alternate.
Hence there are 5 places for girls which can be arranged in 5! ways
Total number of ways = 5! x 5! = 24 x 120 = 14400. Answer : Option D
Answer: (D) 14400
Question: When a Bike is sold for Rs. 63,000, the owner loses 10%. At what price must that Bike be sold in order to gain 10%?
(A) 74000
(B) 75000
(C) 76000
(D) 77000
(E) 78000
Rationale: 90 : 63000 = 110 : x
x = (63000 x 110)/90 = 77,000.
Hence, S.P. = Rs. 77,000.
Answer: Option D
Answer: (D) 77000
Question: A rectangular farm has to be fenced one long side, one short side and the diagonal. If the cost of fencing is Rs.10 per meter. The area of farm is 1200 m2 and the short side is 30 m long. How much would the job cost?
(A) 1278
(B) 1200
(C) 2887
(D) 1688
(E) 2768
Rationale: l * 30 = 1200 è l = 40
40 + 30 + 50 = 120
120 * 10 = 1200
Answer: B
Answer: (B) 1200
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are drawn at random, what is the probability that at least one is green?
(A) 23/35
(B) 23/38
(C) 23/15
(D) 22/35
(E) 21/35
Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.
Probability that at least one green marble can be picked in the random draw of two marbles = Probability that one is green + Probability that both are green
= (6C1 * 9C1)/15C2 + 6C2/15C2
= (6 * 9 * 2)/(15 * 14) + (6 * 5)/(15 * 14) = 36/70 + 1/7
= 46/70 = 23/35
Answer: A
Answer: (A) 23/35
Question: In a bag, there are six 6-sided dice (numbered 1 to 6), three 12-sided dice (numbered 1 to 12), and two 20-sided dice (numbered 1 to 20). If four of these dice are selected at random from the bag, and then the four are rolled and we find the sum of numbers showing on the four dice, how many different possible totals are there for this sum?
(A) 42
(B) 60
(C) 61
(D) 84
(E) 960
Rationale: As 'complex-looking' as this question might appear, it's actually rather simple. Pay careful attention to what the specific questions asks for - the number of DIFFERENT possible SUMS from 4 dice. Since we're dealing with some 'special' dice (some 12-sided and 20-sided dice), we have to adjust out math accordingly, but the possibilities are rather limited:
1) The minimum number on any given die is 1
2) The maximum possible sum would only occur if we took the 4 biggest possible dice and rolled the highest possible number on each.
With 4 dice, we could end up with any SUM between:
4 (if we rolled 1s on all 4 dice)
to
64 (if we rolled two 20s on the 20-sided dice and two 12s on the 12-sided dice).
Thus, there are only 61 possible sums.
C
Answer: (C) 61
Question: Sandy is younger than Molly by 14 years. If their ages are in the respective ratio of 7:9, how old is Molly?
(A) 36
(B) 45
(C) 54
(D) 63
(E) 72
Rationale: S = M - 14
S / M = 7/9
9S = 7M
9(M-14) = 7M
M = 63
The answer is D.
Answer: (D) 63
Question: A cyclist rides a bicycle 7 km at an average speed of 10 km/hr and again travels 10 km at an average speed of 7 km/hr. What is the average speed for the entire trip?
(A) 7.59
(B) 7.79
(C) 7.99
(D) 8.19
(E) 8.39
Rationale: distance = 17 km
time = 7/10 + 10/7 = (49 + 100) / 70 = 149 / 70 hours
average speed = (17 * 70) / 149 = 7.99 km/h
The answer is C.
Answer: (C) 7.99
Question: Last year, for every 100 million vehicles that traveled on a certain highway, 80 vehicles were involved in accidents. If 4 billion vehicles traveled on the highway last year, how many of those vehicles were involved in accidents? (1 billion = 1,000,000,000)
(A) 1600
(B) 3200
(C) 800
(D) 400
(E) 200
Rationale: To solve we will set up a proportion. We know that “100 million vehicles is to 80 accidents as 4 billion vehicles is to x accidents”. To express everything in terms of “millions”, we can use 4,000 million rather than 4 billion. Creating a proportion we have:
100/80 = 4,000/x
Cross multiplying gives us:
100x = 4,000 * 80
x = 40 * 80 = 3200
Answer : B
Answer: (B) 3200
Question: In track last week, the boys ran sixteen laps. The girls ran four more
laps. Each lap is a quarter of a mile. How many miles did the girls run?
(A) 3 miles
(B) 2 miles
(C) 5 miles
(D) 9 miles
(E) 7 miles
Rationale: The girls ran 16 + 4 = 20 laps. 20 x ¼ = 20/4, which reduces to 5.
The girls ran 5 miles
correct answer C
Answer: (C) 5 miles
Question: Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?
(A) 10.7
(B) 10.9
(C) 10.2
(D) 10.8
(E) 18.8
Rationale: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other = 140 + 160 = 300 m.
Required time = 300 * 9/250 = 54/5
= 10.8 sec.
Answer:D
Answer: (D) 10.8
Question: The cross-section of a cannel is a trapezium in shape. If the cannel is 9 m wide at the top and 7 m wide at the bottom and the area of cross-section is 560 sq m, the depth of cannel is?
(A) 39
(B) 28
(C) 70
(D) 80
(E) 71
Rationale: 1/2 * d (9 + 7) = 560
d = 70
Answer: C
Answer: (C) 70
Question: The volume of the sphere QQ is (dfrac{37}{64}%)less than the volume of sphere PP and the volume of sphere RR is (dfrac{19}{27}%) less than that of sphere QQ. By what is the surface areaof sphere RR less than the surfacearea of sphere PP?
(A) 56%
(B) 68%
(C) 75%
(D) 85%
(E) 95%
Rationale: Let the volume of sphere PP be 64 parts.
Therefore volume of sphere QQ
=64−3764%=64−3764% of 6464
=64−37=27=64−37=27 parts.
The volume of RR
=27−1927×27=27−1927×27
=27−19=8=27−19=8 parts.
Volume ratio:
=P:Q:R=64:27:8=P:Q:R=64:27:8
Radius ratio:
=P:Q:R=4:3:2=P:Q:R=4:3:2
The surface area will be 16:9:516:9:5
Surface area of RR is less than the surface area of sphere PP
16k−4k=12k16k−4k=12k
Now,
=12k16k×100=12k16k×100
=75%=75%
Thus surface area of sphere RR is less than the surface area of sphere P by 75%
C
Answer: (C) 75%
Question: On January 1, 2076, Lake Loser contains x liters of water. By Dec 31 of that same year, 2/7 of the x liters have evaporated. This pattern continues such that by the end of each subsequent year the lake has lost 2/7 of the water that it contained at the beginning of that year. During which year will the water in the lake be reduced to less than 1/4 of the original x liters?
(A) 2077
(B) 2078
(C) 2079
(D) 2080
(E) 2081
Rationale: The answer is D
here is the long explanation
This fraction problem contains anunspecifiedtotal (the x liters of water in the lake). Pick an easysmartnumber to make this problem easier. Usually, the smart number is the lowest common denominator of all the fractions in the problem. However, if you pick 28, you will quickly see that this yields some unwieldy computation.
The easiest number to work with in this problem is the number 4. Let's say there are 4 liters of water originally in the lake. The question then becomes: During which year is the lake reduced to less than 1 liter of water?
At the end of 2076, there are 4 × (5/7) or 20/7 liters of water in the lake. This is not less than 1.
At the end of 2077, there are (20/7) × (5/7) or 100/49 liters of water in the lake. This is not less than 1.
At the end of 2078, there are (100/49) × (5/7) or 500/343 liters of water in the lake. This is not less than 1.
At the end of 2079, there are (500/343) × (5/7) or 2500/2401 liters of water in the lake. This is not less than 1.
At the end of 2080, there are (2500/2401) × (5/7) or 12500/16807 liters of water in the lake. This is less than 1.
Notice that picking the number 4 is essential to minimizing the computation involved, since it is very easy to see when a fraction falls below 1 (when the numerator becomes less than the denominator.) The only moderately difficult computation involved is multiplying the denominator by 7 for each new year.
The correct answer is D.
Answer: (D) 2080
Question: In a group of 6 boys and 4 girls are to be selected. In how many different ways can they be selected such that at least one boy should be there ?
(A) 209
(B) 200
(C) 210
(D) 225
(E) 221
Rationale: No of boys = 6
No of girls = 4
Therefore,
No of ways at least 1 boy can be selected = 6C4 * 4C0 + 6C3* 4C1 + 6C2*4C2 + 6C1 * 4C3
= 15 + 80 +90 + 24
= 209
Ans - A
Answer: (A) 209
Question: A rope of which a calf is tied is increased from 12 m to 23 m, how much additional grassy ground shall it graze?
(A) 1120 m2
(B) 1250 m2
(C) 1210 m2
(D) 1200 m2
(E) 1300 m2
Rationale: π (232 – 122) = 1210
ANSWER:C
Answer: (C) 1210 m2
Question: How many 4-digit positive integers are there, where each digit is positive, and no 4 adjacent digits are same?
(A) 1236
(B) 3024
(C) 4096
(D) 4608
(E) 6561
Rationale: First digit.. 9 posibilities
Second digit, 8 possibilities
third digit, 7 possibilities
Fourth digit, 6 possibilities.
9*8*7*6 = 3024.
B
Answer: (B) 3024
Question: According to the directions on the can of frozen orange juice concentrate, 1 can of concentrate is to be mixed with 3 cans of water to make orange juice. How many 12 ounces cans of the concentrate are required to prepare 360 6 ounces servings of orange juice?
(A) a) 45
(B) b) 34
(C) c) 50
(D) d) 67
(E) e) 100
Rationale: Its A.
Total juice rquired = 360*6 = 2160 ounce
12 ounce concentate makes = 12 * 4 = 48 ounce juice
Total cans required = 2160/48 = 45.
Answer A
Answer: (A) a) 45
Question: Jack and Jill are marathon runners. Jack can finish a marathon (42 km) in 7 hours and Jill can run a marathon in 4.2 hours.What is the ratio of their average running speed? (Jack: Jill)
(A) 14/15
(B) 15/14
(C) 5/5
(D) 5/4
(E) Cannot be determined
Rationale: Average Speed of Jack =Distance/ Time
= 42 /7 = 6
Average Speed of Jill = 42/(4.2) = 10
Ratio of Average speed of Jack to Jill =6/10 = 3/5
Answer C
Answer: (C) 5/5
Question: If the sides of a square are multiplied by sqrt(5), the area of the original square is how many times as large as the area of the resultant square?
(A) 5%
(B) 20%
(C) 50%
(D) 100%
(E) 120%
Rationale: Let x be the original length of one side.
Then the original area is x^2.
The new square has sides of length sqrt(5)*x, so the area is 5x^2.
The area of the original square is 1/5 = 20% times the area of the new square.
The answer is B.
Answer: (B) 20%
Question: A sum of Rs. 12500 amounts to Rs. 16000 in 4 years at the rate of simple interest. What is the rate of interest?
(A) 7%
(B) 5%
(C) 6%
(D) 8%
(E) 14%
Rationale: S.I. = (16000 - 12500) = Rs. 3500/-
Rate = (100 * 3500) / (12500 * 4) = 7%
ANSWER:A
Answer: (A) 7%