mathewhe/aqua_rat huggingface dataset:
Question: Thirty five percent of the portfolios managed by the Crocodile Brokers company (C.B.C.) hold Hatsopoulos stocks. Forty percent of the portfolios managed by C.B.C. hold McQuarrie stocks and do not hold Hatsopoulos stocks. Fifteen percent of the portfolios managed by C.B.C. hold Hatsopoulos stocks and do not hold McQuarrie stocks. What percent of the portfolios managed by C.B.C. do NOT hold McQuarrie stocks?
(A) 20
(B) 25
(C) 40
(D) 60
(E) 65
Rationale: H represent those portfolios holding Hatsopoulos stocks
M represent those portfolios holding McQuarrie stocks
35% hold H => z+x=35z+x=35
40% hold M and do not hold H => y = 40
15% hold H and not M => z = 15
We have , x = 20
x+y+z=20+40+15=75 x+y+z=20+40+15=75
There are 25% portfolios holding neither H nor M.
Portfolios that do not hold M = z+(neither H nor M)z+(neither H nor M)
= 15+25
=40
ANSWER:C
Answer: (C) 40
Question: The population of a town increased from 1,75,000 to 2,45,000 in a decade. The average percent increase of population per year is
(A) 4%
(B) 5%
(C) 6%
(D) 8.75%
(E) None
Rationale: Solution
Increase in 10 years	= (245000 - 175000)
= 87500.
Increase%	= (70000/175000Ã—100)%
= 40%.
Required average	= (40/10)%
= 4%.
Answer A
Answer: (A) 4%
Question: Find the value of x from the below equation? : 3x^2+5x+2 = 0
(A) -1
(B) -2
(C) 1
(D) 2
(E) 3
Rationale: a = 3, b = 5, c = 2
x1,2 = (-5 ± √(52 - 4×3×2)) / (2×3) = (-5 ± √(25-24)) / 6 = (-5 ± 1) / 6
x1 = (-5 + 1)/6 = -4/6 = -2/3
x2 = (-5 - 1)/6 = -6/6 = -1
A
Answer: (A) -1
Question: 3 candidates in an election and received 3000, 5000 and 20000 votes respectively. What % of the total votes did the winningcandidate got in that election?
(A) 45.12%
(B) 50%
(C) 57%
(D) 71.42%
(E) 65%
Rationale: Total number of votes polled = (3000 + 5000 + 20000) = 28000
So, Required percentage = 11628/20400 * 100 = 71.42%
D
Answer: (D) 71.42%
Question: C and D started a business by investing Rs.1000/- and Rs.1500/- respectively. Find the D’s share out of a total profit of Rs.500:
(A) 400
(B) 300
(C) 200
(D) 100
(E) 150
Rationale: C = Rs.1000/-
D = Rs.1500/-
C share 2 parts & D share 3 parts
Total 5 parts -----> Rs.500/-
----> 1 part -------> Rs.100/-
D share = 3 parts -----> Rs.300/-
D
Answer: (D) 100
Question: x varies inversely as square of y. Given that y=3 for x=1. The value of x for y = 7 will be equal to:
(A) 3
(B) 6
(C) 1/9
(D) 1/3
(E) 9/49
Rationale: Explanation :
Solution: Given x = k/y^2, where k is constant. Now, y=3 and x =1 gives k = 9.
.'. x = 9/y^2
=> x =9 /7^2 = 9/49
Answer : E
Answer: (E) 9/49
Question: Ayesha’s father was 38 years of age when she was born while her mother was 36 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?
(A) 2 years
(B) 4 years
(C) 6 years
(D) 8 years
(E) None
Rationale: EXPLANATION
Mother’s age when Ayesha’s brother was born = 36 years.
Father’s age when Ayesha’s brother was born = (38 + 4) years = 42 years.
Required difference = (42 – 36) years = 6 years.
Answer C
Answer: (C) 6 years
Question: If x,y and z are positive integers, and 30x=35y=42z, then which of the following must be divisible by 3?
I. x
II. y
III. z
(A) I
(B) II
(C) III
(D) I & III
(E) I, II & III
Rationale: 30X=35y=42z
x=35y/30---now check whether x is divisible by 3--35y/30 is not divisible by 3
y=30X/35---divisible by 3
z=35y/42----not divisible by 3
hence y is only divisible by 3.
Answer:B
Answer: (B) II
Question: Two vessels P and Q contain 62.5% and 87.5% of alcohol respectively. If 2 litres from vessel P is mixed with 6 litres from vessel Q, the ratio of alcohol and water in the resulting mixture is?
(A) 13:1
(B) 13:3
(C) 13:8
(D) 13:5
(E) 13:2
Rationale: Quantity of alcohol in vessel P = 62.5/100 * 2 = 5/4 litres
Quantity of alcohol in vessel Q = 87.5/100 * 6 = 21/4 litres
Quantity of alcohol in the mixture formed = 5/4 + 21/4 = 13/2 = 6.5 litres
As 8 litres of mixture is formed, ratio of alcohol and water in the mixture formed
= 6.5 : 1.5 = 13:3.
Answer: B
Answer: (B) 13:3
Question: The dairy condensed milk has only 20% water while the cow milk has 90% water. How many litres of milk maid will be obtained from 72 litres of milk?
(A) 2
(B) 7
(C) 6
(D) 9
(E) 8
Rationale: Explanation:
In this question, Pure milk in condensed milk = Pure milk in cow milk
80% (x) = 10% (72)
Therefore, x = 9 Liters.
Answer:D
Answer: (D) 9
Question: The average salary of workers in an industry is Rs.200 the average salary of technicians being Rs.400 and that of non-technicians being Rs.125. What is the total number of workers?
(A) 399
(B) 665
(C) 998
(D) 2771
(E) 22
Rationale: 8 * 84 = 672 – 7
= 665
Answer:B
Answer: (B) 665
Question: A sock drawer contains seven socks, each one a different solid color. The colors of the socks are red, orange, yellow, green, white,blue, indigo, and violet. If a person reaches into the drawer and pulls out two socks, how many different color combinations are possible in the selected pair of socks?
(A) 12
(B) 15
(C) 21
(D) 36
(E) 28
Rationale: Since the order in which we select the socks does not matter (e.g., selecting a red sock and then a blue sock is the same outcome as selecting a blue sock and then a red sock), we can usecombinations.
We can select 2 socks from 8 socks in 8C2 ways.
8C2 = 28
Answer : E
Answer: (E) 28
Question: In a friendship gang Andrew has 8 gang, in how many ways can he invite one or more of the gang to his house?
(A) 234
(B) 255
(C) 278
(D) 289
(E) 290
Rationale: Andrew can select one or more than one of his 8 gang.
=> Required number of ways = 28 – 1= 255.
B
Answer: (B) 255
Question: 11 cubic centimetres of silver is drawn into a wire 1 mm in diameter. The length of the wire in metres will be :
(A) 84 m
(B) 88 m
(C) 14 m
(D) 137 m
(E) None
Rationale: Sol.
Let the length of the wire b h.
Radius = 1/2 mm = 1/20 cm. Then,
22/7 * 1/20 * 1/20 * h = 11 ⇔ = [11 * 20 * 20 * 7 / 22] = 1400cm = 14 m.
Answer C
Answer: (C) 14 m
Question: A solution of X pounds of water and sugar is boiled until 20% of the water content evaporates. Originally q% of sugar was present in the solution. After evaporation, what percentage of the solution is sugar?
(A) 100q/(1-q)
(B) 80q/(1-q)
(C) 75q/(1-q)
(D) 100q/(80-0.2q)
(E) 100q/(80+0.2q)
Rationale: We'll go for the ALTERNATIVE approach since there are variables in all the answers (which means that any number could work). Since the question deals with percents, the easiest number to use is X = 100. Now let's say that q = 10. Before the evaporation we had 10 pound of sugar and 90 pounds of water. Since only water evaporated, after the evaporation the 10 pounds of sugar remained the same, but the water reduced by 20% of 90 (18 pounds), so we have only 72 pounds of water. 10 out of 82 is the fraction of sugar, so if we multiply it by 100 we get the percents. The correct answer is E: 100q/(80+0.2q) >>> 100x10 / 82
Answer: (E) 100q/(80+0.2q)
Question: A man rows down stream 40 km and upstream 21 km taking 4 hrs each time. what is the velocity of current?
(A) 2.735 Kmph
(B) 2.375 kmph
(C) 2. 573 kmph
(D) 2 kmph
(E) None of these
Rationale: Explanation:
Man's rate downstream = 40/4 = 10 Kmph
Man's rate upstream = 21/4 = 5.25 Kmph
Velocity of current = 1/2( 10 - 5.25)
= 2.375 Kmph
Answer: Option B
Answer: (B) 2.375 kmph
Question: If eight numbers are randomly selected without replacement from set {1, 2, 3, 4, 5, 6, 7, 8}, what is the probability that the numbers are selected in ascending order?
(A) 1/25600
(B) 1/36240
(C) 1/48360
(D) 1/24120
(E) 1/40320
Rationale: The total number of ways to arrange 8 numbers is 8! = 40320.
There is only one way to arrange the numbers in ascending order.
P(ascending order) = 1/40320
The answer is E.
Answer: (E) 1/40320
Question: Valentine day 14 Feb. 2005 was celebrated by Anand and shilpa on friday. They were very happy. What day of the week would come on 14 Feb. 2010?
(A) monday
(B) tuesday
(C) sunday
(D) wednesday
(E) thursday
Rationale: feb 14 2005 - friday
feb 14 2006 - saturday
feb 14 2007 - sunday
feb 14 2008 - monday
feb 14 2009 - wednesday[since 2008 is leap year , 2 days ll go forward]
feb 14 2010 - thursday
ANSWER:E
Answer: (E) thursday
Question: Due to construction, the speed limit along an 10-mile section of highway is reduced from 55 miles per hour to 20 miles per hour. Approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
(A) A) 6.24
(B) B) 8
(C) C) 10
(D) D) 19.1
(E) E) 24
Rationale: Old time in minutes to cross 10 miles stretch = 10*60/55 = 10*12/11 = 10.9
New time in minutes to cross 10 miles stretch = 10*60/20 = 10*3 = 30
Time difference = 19.1
Ans:D
Answer: (D) D) 19.1
Question: In how many ways can 5 boys and 2girls be arranged at a table if 2girls are never together?
(A) 329
(B) 350
(C) 378
(D) 390
(E) 480
Rationale: Total ways of arranging 7 person in a circle = 6! = 720 ways
If we consider two women as one, then we have 5+1=6 persons. Arranging these six persons in circle will take = 5! = 120 ways
And two women can arrange themselves in 2! ways
Total ways in which two women sit together in circle = 5!*2! = 240 ways
Total ways in which two women doesn’t sit together in circle = 6! - 5!*2! = 720 - 240 = 480 ways
E
Answer: (E) 480
Question: A car covers a distance of 624 km in 3 hours. Find its speed?
(A) 104
(B) 277
(C) 298
(D) 269
(E) 208
Rationale: 624/3 = 208 kmph
Answer:E
Answer: (E) 208
Question: A and B can do a piece of work in 50 days and 50 days respectively. They work together for 10 days and B leaves. In how many days the whole work is completed?
(A) 30days
(B) 35days
(C) 40days
(D) 44days
(E) 45days
Rationale: Explanation:
(A+B)’s 10 days work = 10[1/50+1/50]=10[1+1/50]= 2/5
A complete remaining work in 2/5*50 = 20
Total work = 10+20= 30days
Answer: Option A
Answer: (A) 30days
Question: Three boys, two girls, and two women are to be seated on a bench. If one specific boy must be seated on one of the end seats, and one specific girl must me seated exactly in the middle, find the number of possible arrangements E.
(A) a) E=48
(B) b) E=144
(C) c) E=240
(D) d) 288
(E) e) 120
Rationale: One specific boy is seated to either of end seat, lets call him b1
One specific girl is seated in the middle, lets call her g1
Note the question says *specific girl* and *specific boy*, so we do not consider for example the other girl , g2, being seated on seat #4. Same goes with the specific boy, b1.
b1 can be seated 2 different seats : 2!
g1 is seated on the seat #4, fixed (no other alternative) : 1
the remaining 5 seats can be filled with the remaining people b2,b3,g2,w1,w2: 5!
2! x 1 x 5! = 240
Answer C
Answer: (C) c) E=240
Question: An aeroplane covers a certain distance at a speed of 240 kmph in 5 hours. To cover the same distance in 1 2/3 hours, it must travel at a speed of?
(A) 600km/hr
(B) 720km/hr
(C) 710km/hr
(D) 510km/hr
(E) 480km/hr
Rationale: Distance = 240*5 = 1200 km
Required speed = 1200 * 3/5 = 720km/hr
Answer is B
Answer: (B) 720km/hr
Question: If a no. when divided by 44, gives 432 as quotient and 0 as remainder. What will be the remainder when dividing the same no. by 30
(A) 11
(B) 13
(C) 15
(D) 17
(E) 18
Rationale: P Ã· 44 = 432
=> P = 432 * 44 = 19008
P / 30 = 19008 / 30 = 633, remainder = 18
E
Answer: (E) 18
Question: 10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 8 women and 12 children take to complete the work?
(A) 4
(B) 5
(C) 7
(D) 8
(E) 2
Rationale: 1 women's 1 day work = 1/70
1 child's 1 day work = 1/140
(8 women + 12 children)'s 1 day work
= (8/70 + 12/140) = 1/5
8 women and 4 children will complete the work in 5 days.
B
Answer: (B) 5
Question: In a kilometer race, A beats B by 40 meters or 10 seconds. What time does A take to complete the race?
(A) 180 sec
(B) 190 sec
(C) 290 sec
(D) 490 sec
(E) 240 sec
Rationale: Time taken by B run 1000 meters = (1000 * 10)/40
= 250 sec.
Time taken by A = 250 - 10
= 240 sec.
Answer:E
Answer: (E) 240 sec
Question: If d is the standard deviation x, y, and z, what is the standard deviation of x +3, y + 3, z + 3 ?
(A) 3d
(B) 3d+3
(C) d
(D) 3d+9
(E) 3d-3
Rationale: CONCEPT: Standard Deviation is Defined as Average Deviation of Terms in the set from the Mean value of the set. i.e.
1) It depends on the separation between the successive terms of the set
2) If a Constant Value is Added/Subtracted in every terms of set then the Separation between successive terms does NOT change Hence S.D. remains Constant
e.g.{1, 2, 3, 4, 5} will have same standard Deviation as {1+10, 2+10, 3+10, 4+10, 5+10}
3) If a Constant Value is Multiplied in every terms then the Separation between succesive terms gets multiplied by the constant Hence S.D. remains gets multiplied by same Number
e.g. {0.7, 1.4, 2.1, 2.8, 3.5} will have Standard Deviation = 0.7* Standard deviation of set {1, 2, 3, 4, 5}
When 3 is added in each term of set {x, y, z} then the new set {x+3, y+3, z+3} will remain same as the previous standard deviation i.e. d
Answer: C
Answer: (C) d
Question: Right now, the ratio between the ages of Sandy and Molly is 4:3. After 6 years, Sandy’s age will be 30 years. What is Molly's age right now?
(A) 12
(B) 14
(C) 16
(D) 18
(E) 20
Rationale: Now, Sandy is 30 - 6 = 24
Molly's age is (3/4) * 24 = 18
The answer is D.
Answer: (D) 18
Question: A person lent a certain sum of money at 6% per annum at simple interest and in 8 years the interest amounted to $572 less than the sum lent. What was the sum lent?
(A) 1000
(B) 1100
(C) 1200
(D) 1300
(E) 1400
Rationale: P - 572 = (P*6*8)/100
P = 1100
The answer is B.
Answer: (B) 1100
Question: The ratio between the speeds of two trains is 7 : 8. If the second train runs 400 km in 4 hours, What is the the speed of the first train?
(A) 87.0
(B) 87.5
(C) 87.2
(D) 87.1
(E) 87.4
Rationale: Speed and time are inversely proportional (when distance is constant) ⇒Speed ∝ 1Time (when distance is constant)
Here distance is constant and hence speed and time are inversely proportionalSpeed ∝ 1Time⇒Speed1Speed2=Time2Time1⇒78=4Time1⇒Time1 = 4×87 hr⇒Speed of the first train = DistanceTime1=400(4×87)=100×78=12.5×7=87.5 km/hr
Answer :B
Answer: (B) 87.5
Question: The diameter of the driving wheel of a bus in 140 cm. How many revolutions per minute must the wheel make in order to keep a speed of 20 kmph?
(A) 21.21
(B) 20.25
(C) 32.25
(D) 75.75
(E) 62.61
Rationale: distance covered in 1 min=(20*1000)/60=333.33m
circumference of the wheel=(2*(22/7)*.70)=4.4m
no of revolution per min=333.33/4.4=75.75
ANSWER:D
Answer: (D) 75.75
Question: 6, 11, 21, 36, 56, ?
(A) 51
(B) 71
(C) 81
(D) 61
(E) 91
Rationale: The pattern is + 5, + 10, + 15, + 20,....
Answer : C.
Answer: (C) 81
Question: Salaries of A, B and C were in the ratio 3 : 5 : 7 respectively. If their salaries were increased by 50 per cent, 60 per cent and 50 per cent respectively, what will be the new ratio of their respective salaries?
(A) 4 : 5 : 7
(B) 3 : 6 : 7
(C) 4 : 15 : 18
(D) 9 : 16 : 21
(E) 8 : 16 : 21
Rationale: New ratio will be 3 x (150/100) : 5 x (160/100) : 7 x (150/100) = (9/2) : 8 : (21/2)
= 9 : 16 : 21
ANSWER:D
Answer: (D) 9 : 16 : 21
Question: How many terms are there in 2, 4, 8, 16,..., 2048?
(A) 14
(B) 11
(C) 12
(D) 10
(E) 8
Rationale: 2, 4, 8, 16, ...,2048 is a G.P with a =2
and r =4/2 =2
Let the number of terms be n. Then
2 x 2 ^n-1 = 2048
or 2^n-1 = 1024= 2^10
Thus n - 1 =10
n= 11
ANSWER:B
Answer: (B) 11
Question: Which of the following is the product of two integers whose sum is 12?
(A)  -42
(B)  -28
(C)  12
(D)  26
(E)  32
Rationale: I solved this Question like this,
Let the two integers are x,y
x+y=12 (Given)
xy=? (Needed)
instead of solving this algebraically, Test the Answer choices
B. -28
Do the factorization : (-1,28)----> There sum is not 12--eliminate
(-2,14)---->There sum is 12 Bingo!!!!
So, my answer is B...
As the answer is in B, it took me very less time to answer the question. but i think this method is be simple and efficient.
Answer: (B)  -28
Question: In the formula V = 1/(2r)^2, if r is halved, then V is multiplied by?
(A) 4
(B) 8
(C) 1
(D) 1/8
(E) 1/64
Rationale: Say r=2 => V1 = 1/16
when r=1; V2 = 1/4
V2 = 4*V1.
Answer : A
Answer: (A) 4
Question: Mrs. Napier has 38 stickers to give to 5 students for a reward. How many
stickers will each student get? Will there be any stickers left over?
(A) 2-5
(B) 2-4
(C) 7-6
(D) 2-3
(E) 2-8
Rationale: 38/5 = 7 R 6 Mrs. Napier will give each student 7 stickers and there
will be 6 left over.
correct answer C
Answer: (C) 7-6
Question: If 3<x<6<y<8, then what is the greatest possible positive integer difference of x and y?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: 3 < x < 6 < y < 8;
3 < x
y < 8
3 + y < x + 8
y - x < 5.
Positive integer difference is 4 (for example y = 7.5 and x = 3.5)
Answer: B.
Answer: (B) 4
Question: Two Copiers are being used to produce 2400 copies of a 1-page document. One Copier runs at 150% of the speed of the other. How many copies should be made on the faster copier so that both copiers will finish the same time?
(A) 1240
(B) 1440
(C) 1340
(D) 1540
(E) 1640
Rationale: Let the speed of one copier be x
Speed of other copier 150x/100
Ratio of speed = 1:150/100 = 2:3
copies made on faster copier = 3/5 *2400
= 1440
ANSWER:B
Answer: (B) 1440
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 290 lbs, how much does substance x weigh?
(A) 48
(B) 36
(C) 24
(D) 52
(E) 60
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 = 290 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=290
k=5
Hence x=12(5)=60
Ans E
Answer: (E) 60
Question: When a random experiment is conducted, the probability that event A occurs is 1/5. If the random experiment is conducted 5 independent times, what is the probability that event A occurs exactly twice?
(A) 36/625
(B) 48/625
(C) 64/625
(D) 98/625
(E) 128/625
Rationale: One case is: 1/5*1/5*4/5*4/5*4/5=64/3125
The total number of possible cases is 5C2 = 10
P(event A occurs exactly twice) = 10*(64/3125) = 128/625
The answer is E.
Answer: (E) 128/625
Question: Two students appeared at an examination. One of them secured 9 marks more than the other and his
marks was 56% of the sum of their marks. The marks obtained by them are
(A) 42,30
(B) 42,31
(C) 42,32
(D) 42,33
(E) None of these
Rationale: Explanation:
Let their marks be (x+9) and x.
Then, x+9 = 56/100(x + 9 +x)
=> 25(x+9)
=> 14 (2x + 9)
=> 3x = 99
=> x = 33.
So, their marks are 42 and 33
Answer: Option D
Answer: (D) 42,33
Question: 12 men and 18 boys working 7.5 minutes an hour complete a particular piece of work in 60 hours. If a boy’s work is half as efficient as a man’s work, how many boys will be needed to help 21 men to achieve twice the work in 50 hours working 9 minutes in an hour.
(A) 28
(B) 77
(C) 42.
(D) 99
(E) 17
Rationale: Explanation:
1 man is equivalent to 2 boys in work capacity. 12 men + 18 boys = 12 x 2 + 18 = 42 boys.
Let the required number of boys be x. So Total number of people doing work = 21 men x 2 (according to work capacity) + x boys.
Taking respective ratios as required:
Given:
=> Hours 50:60
=> Minutes per hour 9: 15/2
=> Work 1:2
=> People: 42: 42 + x
=> 50 x 9 x 1 x (42+x) = 60 x 15/2 x 2 x 42
=> 42 +x = 84
x = 42
ANSWER:C
Answer: (C) 42.
Question: Find a sum for first 5 prime number's?
(A) 24
(B) 28
(C) 30
(D) 32
(E) 34
Rationale: Required sum = (2 + 3 + 5 + 7 + 11) = 28
Note: 1 is not a prime number
Option B
Answer: (B) 28
Question: The number of new words that can be formed by rearranging the letters of the word 'OF' is
(A) 5
(B) 8
(C) 1
(D) 3
(E) 4
Rationale: Explanation:
Number of words which can be formed = 2! - 1 = 2- 1 = 1.
Answer: C
Answer: (C) 1
Question: A student travels from his house to school at 10 km/hr and reaches school 2 hours late. The next day he travels 15 km/hr and reaches school 1 hour early. What is the distance between his house and the school?
(A) 60
(B) 70
(C) 80
(D) 90
(E) 100
Rationale: Let x be the distance from his house to the school.
x/10 = x/15 + 3
6x = 4x + 180
2x = 180
x = 90 km
The answer is D.
Answer: (D) 90
Question: How many positive integers less than 7,000 are there in which the sum of the digits equals 5?
(A) 52
(B) 54
(C) 56
(D) 58
(E) 60
Rationale: Basically, the question asks how many 4 digit numbers (including those in the form 0XXX, 00XX, and 000X) have digits which add up to 5. Think about the question this way: we know that there is a total of 5 to be spread among the 4 digits, we just have to determine the number of ways it can be spread.
Let X represent a sum of 1, and | represent a seperator between two digits. As a result, we will have 5 X's (digits add up to the 5), and 3 |'s (3 digit seperators).
So, for example:
XX|X|X|X = 2111
||XXX|XX = 0032
etc.
There are 8C3 ways to determine where to place the separators. Hence, the answer is 8C3 = 56.
C
Answer: (C) 56
Question: The value of a scooter depreciates in such a way that its value of the end of each year is 3/4 of its value of the beginning of the same year. If the initial value of the scooter is Rs.40,000, what is the value at the end of 1 year?
(A) 3277
(B) 2977
(C) 30000
(D) 6077
(E) 17112
Rationale: Explanation: 40,000*(3/4)^1
Answer:C
Answer: (C) 30000
Question: For integers x, y, and z, if (3^x) (4^y) (5^z) = 13,107,200,000 and x + y + z = 16, what is the value of xy/z?
(A) undefined
(B) 0
(C) 3
(D) 5
(E) 7
Rationale: The number 13,107,200,000 is not divisible by 3. (We can verify this by adding the digits of the number to see that the sum is not a multiple of 3.)
Thus x = 0 and xy/z = 0.
The answer is B.
Answer: (B) 0
Question: A does a work in 20 days and B does the same work in 30 days. In how many days they together will do the same work ?
(A) 5 days
(B) 6 days
(C) 9 days
(D) 12 days
(E) None of these
Rationale: Explanation:
Firstly we will find 1 day work of both A and B, then by adding we can get collective days for them,
So,
A's 1 day work = 1/20
B's 1 day work = 1/30
(A+B)'s 1 day work =
(1/20+1/30)=1/12
So together they can complete work in 12 days.
Answer: D
Answer: (D) 12 days
Question: A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
(A) 246
(B) 240
(C) 88
(D) 76
(E) 121
Rationale: Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/36 = 15 ==> x + 300 = 540 ==> x = 240 m.
Answer:B
Answer: (B) 240
Question: A rectangular grass field is 75 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.6 per sq m?
(A) 675, Rs.1350
(B) 575, Rs.1350
(C) 1350, Rs.675
(D) 1450, Rs.775
(E) 675, Rs.4050
Rationale: Area = (l + b +2d) 2d
= (75 + 55 +2.5 * 2) 2*2.5 => 675
675 * 6 = Rs.4050
ANSWER:E
Answer: (E) 675, Rs.4050
Question: If 4 (A's capital) = 8 (B's capital) = 10 (C's capital). Then the ratio of their capitals is?
(A) 10:5:5
(B) 10:5:8
(C) 10:5:2
(D) 10:5:4
(E) 10:5:1
Rationale: 4A = 8B = 10 C
A:B:C = 1/4:1/8:1/10
= 10:5:4
Answer: D
Answer: (D) 10:5:4
Question: Frank the Fencemaker needs to fence in a rectangular yard. He fences in the entire yard, except for one full side of the yard, which equals 40 feet. The yard has an area of 200 square feet. How many feet offence does Frank use?
(A) 14
(B) 47
(C) 50
(D) 180
(E) 240
Rationale: Area = Length x Breadth
200 = 40 x Breadth
So, Breadth = 5 Units
Fencing required is -
Breadth + Breadth + Length
5 + 5 + 40 => 50 feet
Answer must be (C) 50
Answer: (C) 50