mathewhe/aqua_rat huggingface dataset:
Question: An art gallery owner is hanging paintings for a new show. Of the seven paintings she has to choose from, she can only hang three on the main wall of the gallery. Assuming that she hangs as many as possible on that wall, in how many ways can she arrange the paintings?
(A) 18
(B) 30
(C) 64
(D) 120
(E) 210
Rationale: Arrangment means permutations questions..
7P3 = 7!/3! = 210.
IMO option E is correct answer..
Answer: (E) 210
Question: If a2 - b2 = 10 and a*b = 5, find a4 + b4.
(A) 50
(B) 100
(C) 150
(D) 92
(E) 25
Rationale: a2 - b2 = 10 : given
a4 + b4 - 2a2b2 = 102 : square both sides and expand.
a*b = 5 : given
a2b2 = 52 : square both sides.
a4 + b4 - 2(25) = 100 : substitute
a4 + b4 = 150
correct answer C
Answer: (C) 150
Question: A numberais squared and then multiplied by negative 3. The result of this operation T is equal to three times the sum of three timesaand two. What is one possible value ofa?
(A) -3
(B) -2
(C) 1
(D) 2
(E) 3
Rationale: T=-3*a^2=3(3a+2)
a= -2 or -1
a=-2=B
Answer: (B) -2
Question: Ramu rides his bike at an average speed of 45 km/hr and reaches his desitination in four hours. Somu covers the same distance in six hours. If Ramu covered his journey at an average speed which was 9 km/hr less and Somu covered his journey at an average speed which was 10 km/hr more, then the difference in their times taken to reach the destination would be (in minutes).
(A) 22 min
(B) 30 min
(C) 87 min
(D) 26 min
(E) 11 min
Rationale: Explanation:
Distance travelled by Ramu = 45 x 4 = 180 km
Somu travelled the same distance in 6 hours.
His speed = 180/6 = 30 km/hr
Hence in the conditional case, Ramu's speed = 45 - 9 = 36 km/hr and Somu's speed = 30 + 10 = 40km/hr.
Therefore travel time of Ramu and Somu would be 5 hours and 4.5 hours respectively.
Hence difference in the time taken = 0.5 hours = 30 minutes.
Answer: B
Answer: (B) 30 min
Question: If 9a - b = 10b + 50 = -12b - 2a, what is the value of 11a + 11b?
(A) -4
(B) -2
(C) 0
(D) 2
(E) 4
Rationale: This implies 9a - b = 10b + 50, 9a -b = -12b -2a, 10b + 50 = -12b -2a
Manipulating the second equation gives us 9a - b = -12b - 2a ==> 11a + 11b = 0
Answer is C
Answer: (C) 0
Question: If 40 percent of the members of a certain organization are women and 4/8 of the members of the organization are married men, which of the following statements concerning the membership must be true?
I. The number of women in the organization is greater than the number of married men in the organization.
II. The number of women in the organization is greater than the number of unmarried men in the organization.
III. The number of married men in the organization is greater than the number of unmarried men in the organization.
(A) I,II
(B) III
(C) II,III
(D) II
(E) I
Rationale: 4/10 (40%) of the members are women and 4/8 of the members are married men. Let the total numbers of members is 80 (the LCM of 10 and 8). Then there are:
4/10*80 = 32 women;
80 - 32 = 48 men;
4/8*48 = 24 married men;
48 - 24 = 24 unmarried men.
So, option I,II is true.
Answer: A
Answer: (A) I,II
Question: What is the remainder when (71)(73) is divided by 9?
(A) 1
(B) 2
(C) 4
(D) 6
(E) 8
Rationale: (71)(73) = (72-1)(72+1) = 72^2 - 1 which is 1 less than a multiple of 9.
Then the remainder will be 8.
The answer is E.
Answer: (E) 8
Question: A boat having a length 3 m and breadth 2 m is floating on a lake. The boat sinks by 1 cm when a man gets on it. The mass of the man is:
(A) 40 kg
(B) 42kg
(C) 50kg
(D) 58kg
(E) 60 kg
Rationale: Volume of water displaced	= (3 x 2 x 0.01) m3
= 0.06 m3.
Mass of man
= Volume of water displaced x Density of water
= (0.06 x 1000) kg
= 60 kg.
answer : E
Answer: (E) 60 kg
Question: Look at this series: 70, 71, 76, 70, 81, __, 70, 91, ... What number should fill the blank?
(A) 70
(B) 86
(C) 82
(D) 77
(E) 52
Rationale: B
86
In this series, 5 is added to the previous number; the number 70 is inserted as every third number.
Answer: (B) 86
Question: The average age of students of a class is 15.8 years. The average age of boys in the class is 16.4 years and that of the girls is 15.4 years. The ration of the number of boys to the number of girls in the class is?
(A) 2:7
(B) 2:3
(C) 2:1
(D) 2:9
(E) 2:2
Rationale: Let the ratio be k : 1. Then,
k * 16.4 + 1 * 15.4 = (k + 1) * 15.8
= (16.4 - 15.8)k = (15.8 - 15.4)
= k = 0.4/0.6 = 2/3
Required ratio = 2/3 : 1 = 2:3.
Answer: Option B
Explanation:
Let the ratio be k : 1. Then,
k * 16.4 + 1 * 15.4 = (k + 1) * 15.8
= (16.4 - 15.8)k = (15.8 - 15.4)
= k = 0.4/0.6 = 2/3
Required ratio = 2/3 : 1 = 2:3.
Answer: B
Answer: (B) 2:3
Question: What is the smallest positive integer X such that (X+1)^2 is divisible by 28, 98, 242, and 308?
(A) 153
(B) 308
(C) 121
(D) 96
(E) 511
Rationale: 28 = 2 * 2 * 7
98 = 2 * 7 * 7
242 = 2 * 11 * 11
308 = 2 * 2 * 7 * 11
So (X+1)^2 = 2 * 2 * 7 * 7 * 11 * 11, which means (X+1) = 2 * 7 * 11 = 154, which means X = 153, which is option A
Answer: (A) 153
Question: The area of a right-angled triangle is two-thirds of the area of a rectangle. The base of the triangle is 80 percent of the breadth of the rectangle. If the perimeter of the rectangle is 200 cm, what is the height of the triangle?
(A) 20 cm
(B) 30 cm
(C) 15 cm
(D) Data inadequate
(E) None of these
Rationale: Let the base and height of triangle, and length and breadth of rectangle be L and h, and L1 and b1 respectively.
Then 1⁄2 × L × h = 2⁄3 × L1 × b1 .....(i)
L = 4⁄5b1 .....(ii)
and L1 + b1 = 100 .....(iii)
In the above we have three equations and four unknowns. Hence the value of ‘h’ can’t be determined.
Answer D
Answer: (D) Data inadequate
Question: If t and g are distinct prime numbers less than 10, which of the following cannot be the product of t and g?
(A) 6
(B) 9
(C) 10
(D) 14
(E) 15
Rationale: If t and g are distinct prime numbers less than 10 prime numbers less than 10 are 2, 3, 5, 7
all except 9 is product of any two numbers picked from above set.
Ans: B
Answer: (B) 9
Question: A rectangular cube has a volume of 10 cubic feet. If a similar cube is twice as long, twice as wide, and twice as high, then the volume, in cubic feet of such cube is?
Choices
(A) 24
(B) 48
(C) 64
(D) 80
(E) 100
Rationale: Lets say the sides of the rectangular cube are x, y and z. Problem states volume is 10.
i.e,
x*y*z = 10 .
If every side is increased twice as before. then new volume is
2x*2y*2z = 8*(x*y*z) = 8*10 = 80.
Answer is D
Answer: (D) 80
Question: In 2008, a certain factory produced 40% more widgets than it did in 2007, and its production in 2009 was 120% of its production in 2008. By approximately what percent would its production need to decrease the following year for the factory to produce the same number of widgets it did in 2007?
(A) 25.5%
(B) 30.5%
(C) 36.5%
(D) 40.5%
(E) 48.5%
Rationale: Let P be the original level of production in 2007.
Let x be the rate of production in 2010 compared to 2009.
x*1.2*1.4*P = P
x = 1/1.68 = 0.595 which is a decrease of 40.5%.
The answer is D.
Answer: (D) 40.5%
Question: Find the first term of an AP whose 8th and 12th terms are respectively 39 and 59.
(A) 5
(B) 6
(C) 4
(D) 3
(E) 7
Rationale: Solution: 1st Method:
8th term = a+7d = 39 ........... (i)
12th term = a+11d = 59 ........... (ii)
(i)-(ii);
Or, a+7d-a-11d = 39-59; Or, 4d = 20;
Or, d = 5;
Hence, a+7*5 = 39;
Thus, a = 39-35 = 4.
2nd Method (Thought Process):
8th term = 39;
And, 12th term = 59;
Here, we see that 20 is added to 8th term 39 to get 12th term 59 i.e. 4 times the common difference is added to 39.
So, CD = 20/4 = 5.
Hence, 7 times CD is added to 1st term to get 39. That means 4 is the 1st term of the AP.
Answer: Option C
Answer: (C) 4
Question: If x, 2, 3, 4 are there and the range and median of them are the same, what is the value of x?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: Try taking the values of x as you suggested and then see if the median and the range are equal.
Once you do that, you will get the answer yourself.
Tried substituting values starting with 2, 3, 4...
only x = 3 satisfies the condition.
D
Answer: (D) 3
Question: A shopkeeper has 280 kg of apples. He sells 30% of these at 20% profit and remaining 60% at 30% profit. Find his % profit on total.
(A) 24%
(B) 25%
(C) 26%
(D) 28%
(E) 35%
Rationale: If the total quantity was 100
Then 30X 20% + 60 X30%= 24
This profit will remain same for any total quantity unless the % of products remains the same. Hence 'A' is the answer
Answer: (A) 24%
Question: A man standing at a point P is watching the top of a tower, which makes an angle of elevation of 30º with the man's eye. The man walks some distance towards the tower to watch its top and the angle of the elevation becomes 60º. What is the distance between the base of the tower and the point P?
(A) 43 units
(B) 8 units
(C) 12 units
(D) Data inadequate
(E) None of these
Rationale: One of AB, AD and CD must have given.
So, the data is inadequate.
ANSWER:D
Answer: (D) Data inadequate
Question: David and Rachel are getting married. The extended family wants to have its picture taken, but David's father is unwilling to stand next to Rachel's mother. How many options does the photographer have to arrange the 10 family members in a row for the picture?
(A) 9!
(B) 9×8!
(C) 8×9!
(D) 10!/2!
(E) 10!
Rationale: Total - Restriction =
= 10! - 9!*2! =
= 9!(10 - 2!) =
= 8*9!.
Answer: C
Answer: (C) 8×9!
Question: The difference of 2 digit no. & the no. obtained by interchanging the digits is 36. What is the difference the sum and the number if the ratio between the digits of the number is 1:2 ?
(A) 6
(B) 8
(C) 10
(D) 12
(E) 13
Rationale: Let the number be xy.
Given xy – yx = 36.
This means the number is greater is than the number got on reversing the digits.
This shows that the ten’s digit x > unit digit y.
Also given ratio between digits is 1 : 2 => x = 2y
(10x + y) – (10y +x) = 36 => x – y = 4 => 2y – y =4.
Hence, (x + y) – (x – y) = 3y – y = 2y = 8
B
Answer: (B) 8
Question: Two years ago, Arthur gave each of his five children 20 percent of his fortune to invest in any way they saw Fit. In the first year, three of the children, Alice, Bob, and Carol, each earned a profit of 50 percent on their Investments, while two of the children, Dave and Errol, lost 40 percent on their investments. In the second Year, Alice and Bob each earned a 10 percent profit, Carol lost 60 percent, Dave earned 100 percent in profit, And Errol lost all the money he had remaining. What percentage of Arthur's fortune currently remains?
(A) 93%
(B) 97%
(C) 102%
(D) 107%
(E) 120%
Rationale: Say Arthur's fortune was $100. Then:
A = 20*1.5*1.1 = 33
B = 20*1.5*1.1 = 33
C = 20*1.5*0.4 = 12
D = 20*0.6*2.0 = 24
E = 0
Total 33 + 33 + 12 + 24 = 102.
Answer: C.
Answer: (C) 102%
Question: Four persons have to cross the bridge they are having one torch light. Four persons take 1,2,5,10 minutes respectively, when two persons are going the will take the time of the slowest person what is the time taken to cross all of them.
(A) 17 min
(B) 18 min
(C) 19 min
(D) 16 min
(E) 15 min
Rationale: Let A takes 1 min, B takes 2 min, C takes 5 min, D takes 10 min
First A & B goes=> 2 min
A returns=> 1 min
C & D goes=>10 min
B returns=>2 min
A & B goes=>2 min
Taotal time=2+1+10+2+2=17min
Therefore, 17 min is the minimum time
ANSWER:A
Answer: (A) 17 min
Question: A rectangular grass field is 75 m * 55 m, it has a path of 2.8 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.2 per sq m?
(A) s.1518.8
(B) s.1327
(C) s.1328
(D) s.1397
(E) s.1927
Rationale: Area = (l + b +2d) 2d
= (75 + 55 +2.8 * 2) 2*2.8 => 759.4
759.4 * 2 = Rs.1518.8
Answer: A
Answer: (A) s.1518.8
Question: 1.	How much more would Rs.12000 fetch, after two years, if it is put at 20% p.a. compound interest payable half yearly than if is put at 20% p.a. compound interest payable yearly?
(A) A)Rs.3,169.20
(B) B)Rs.3,170.20
(C) C)Rs.3,171.20
(D) D)Rs.3,172.20
(E) E)Rs.3,173.20
Rationale: 12000(11/10)4 - 12000(6/5)2 = 3,169.20
ANSWER:A
Answer: (A) A)Rs.3,169.20
Question: John and Jane went out for a dinner and they ordered the same dish. Both used a 10% discount coupon. John paid a 15% tip over the original price of the dish, while Jane paid the tip over the discounted price for the coupon. If John paid $1.26 more than Jane, what was the original price of the dish?
(A)  24
(B)  34.8
(C)  37.8
(D)  42
(E)  84
Rationale: The difference between the amounts John paid and Jane paid is the deference between 15% of p and 15% of 0.9p:
0.15p - 0.15*0.9p = 1.26 --> 15p - 13.5p = 126 --> p = 84.
Answer: E.
Answer: (E)  84
Question: Find the area of a parallelogram with base 24 cm and height 16 cm?
(A) 776
(B) 384
(C) 666
(D) 288
(E) 211
Rationale: Area of a parallelogram = base * height
= 24 * 16
= 384 cm2
Answer: B
Answer: (B) 384
Question: The total marks obtained by a student in Mathematics and Physics is 40 and his score in Chemistry is 20 marks more than that in Physics. Find the average marks scored in Mathamatics and Chemistry together.
(A) 40
(B) 30
(C) 25
(D) Data inadequate
(E) None of these.
Rationale: Let the marks obtained by the student in Mathematics, Physics and Chemistry be M, P and C respectively.
Given , M + C = 40 and C - P = 20 M + C / 2 = [(M + P) + (C - P)] / 2 = (40 + 20) / 2 = 30.
ANSWER:B
Answer: (B) 30
Question: A scuba diver descends at a rate of 60 feet per minute. a diver dive from a ship to search for a lost ship at the depth of 3600feet below the sea level..how long will he take to reach the ship?
(A) 60 minutes
(B) 72 minutes
(C) 75 minutes
(D) 76 minutes
(E) 77 minutes
Rationale: Time taken to reach = 3600/60= 60 minutes
ANSWER:A
Answer: (A) 60 minutes
Question: The ratio T , by volume of soap to alcohol to water in a 76 litre solution is 2: 50: 100 . The solution is then altered by adding more soap, alcohol and water.After this alteration the ratio, by volume of soap to water in the solution doubles whereas the ratio, by volume of soap to water remains the same as before. What COULD BE the resulting volume.
(A) 79 litres
(B) 78 litres
(C) 77 litres
(D) 152 liters
(E) 304 litres
Rationale: I guess it should be
the ratio T, by volume ofsoaptowaterin the solutiondoubleswhereas the ratio, by volume ofalocoholtowaterremains thesameas before
2:50: 100 => 1 : 25 : 50. If we add all the parts, we get 76 liters
So we have 1 liters of Soap, 25 liters of Alcohol and 50 liters of Water.
Now as per the Question, Soap : Water doubles but alcohol to water remains the same.
So Soap becomes 2 liters, Alcohol remains 25 liters and Water remains at 50 liters.
Hence 77 liters - Option C)
Answer: (C) 77 litres
Question: A rectangular swimming pool is 20 feet by 20 feet. A deck that has uniform width surrounds the pool. The total area of the pool and deck is 576 square feet. What is the width of the deck?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: Let the width =W
Total Area of the pool and deck= (2W+20)(2W+20)
We can Test the answer choices along with unit digit method
A) 2 feet ...........24*24 has unit digit 6..........hold
B) 2.5 feet.........25*25 has unit digit 5..........Eliminate
C) 3 feet............26*26 has unit digit 6...........elimate ( area is more than stipulated)
D) 4 feet............28*28 has unit digit 4...........Eliminate
E) 5 feet............30*30 has unit digit 0...........Eliminate
Answer: A
Answer: (A) 2
Question: There are n cities. What is the number of airlines that connected 6 different cities (airline from city A to city B is different with airline from city B to city A)?
(A) n(n-5)
(B) n(n+1)
(C) n(n-1)/2
(D) n(n+1)/2
(E) n2
Rationale: First of all, the possible number of airlines is n. Then, the possible number of airlines departing from one city to another becomes (n-5). Hence, the answer is n(n-5), which makes A an answer choice.
A
Answer: (A) n(n-5)
Question: How many 4-letter word with or without meaning can be formed out
of the letters of the word 'LOGARITHMS' if repetition of letters is
not allowed
(A) 200
(B) 100
(C) 5040
(D) 5000
(E) 500
Rationale: 'LOGARITHMS' contains 10 different letters
Required number of words
= Number of arrangements of 100 letters taking
4 at a time
= 10P4
= 10 * 9 * 8 * 7
= 5040
ANSWER C 5040
Answer: (C) 5040
Question: A sum of Rs.4800 is invested at a compound interest for three years, the rate of interest being 10% p.a., 20% p.a. and 25% p.a. for the 1st, 2nd and the 3rd years respectively. Find the interest received at the end of the three years.
(A) Rs.3128
(B) Rs.3120
(C) Rs.3123
(D) Rs.3122
(E) Rs.3144
Rationale: Let A be the amount received at the end of the three years.
A = 4800[1 + 10/100][1 + 20/100][1 + 25/100]
A = (4800 * 11 * 6 * 5)/(10 * 5 * 4)
A = Rs.7920
So the interest = 7920 - 4800 = Rs.3120
Answer:B
Answer: (B) Rs.3120
Question: A die is rolled twice. What is the probability of getting a sum equal to 9?
(A) 2/9
(B) 1/9
(C) 5/9
(D) 4/9
(E) 3/9
Rationale: Total number of outcomes possible when a die is rolled = 6 (∵ any one face out of the 6 faces)
Hence, total number of outcomes possible when a die is rolled twice, n(S) = 6 × 6 = 36
E = Getting a sum of 9 when the two dice fall = {(3, 6), {4, 5}, {5, 4}, (6, 3)}
Hence, n(E) = 4
P(E) = n(E)/n(S)=4/36=1/9
Answer is B.
Answer: (B) 1/9
Question: Tanks A and B are each in the shape of a right circular cylinder. The interior of tank A has a height of 10 meters and a circumference of 11 meters, and the interior of tank B has a height of 11 meters and a circumference of 10 meters. The capacity of tank A is what percent of the capacity of tank B?
(A) 75%
(B) 80%
(C) 100%
(D) 110%
(E) 125%
Rationale: The radius of tank A is 11/(2*pi).
The capacity of tank A is 10*pi*121 / (4*pi^2) = 605 / (2*pi)
The radius of tank B is 10 / (2*pi).
The capacity of tank B is 11*pi*100 / (4*pi^2) = 550 / (2*pi)
Tank A / Tank B = 605/550 = 11/10 = 110%
The answer is D.
Answer: (D) 110%
Question: A, B and C are entered into a partnership. A invested Rs.6500 for 6 months, B invested Rs.8400 for 5 months and C invested for Rs.10000 for 3 months. A is a working partner and gets 5% of the total profit for the same. Find the share of C in a total profit of Rs.7400.
(A) 1750
(B) 1900
(C) 8600
(D) 10300
(E) 8000
Rationale: 65 * 6 : 84 * 5 : 100 * 3
26:28:20
C share = 74000 * 95/100 = 7030 * 20/74 => 1900
ANSWER:B
Answer: (B) 1900
Question: A reduction of 40% in the price of bananas would enable a man to obtain 64 more for Rs.40, what is reduced price per dozen?
(A) 2
(B) 8
(C) 7
(D) 3
(E) 1
Rationale: Explanation:
40*(40/100) = 16 --- 64
? --- 12 => Rs.3
Answer: D
Answer: (D) 3
Question: At Joel’s bookstore, the current inventory is 40% historical fiction. Of the historical fiction books, 40% are new releases, while 70% of the other books are new releases. What fraction of all new releases are the historical fiction new releases?
(A) 4/25
(B) 8/29
(C) 2/5
(D) 8/15
(E) 2/3
Rationale: let there be 100 books in all
Historic fiction books = 40% of total = 40
Other books = 60
New historic fiction = 40% of 40 = 16
Other new books = 70% of 60 = 42
total new books = 58
fraction = 16/58 = 8/29
Ans: B
Answer: (B) 8/29
Question: Scotty B is helping his brother Jimmy B with math patterns. Jimmy's paper has 12, 24, 36, 48, and a blank space.
What number should Jimmy B put in the blank space?
(A) 50
(B) 58
(C) 60
(D) 62
(E) 96
Rationale: C) 60- because the pattern is adding 12 each time.
Answer: (C) 60
Question: A car covers a distance of 1122 km in 6 ½ hours. Find its speed?
(A) 104 kmph
(B) 187 kmph
(C) 164 kmph
(D) 175 kmph
(E) 106 kmph
Rationale: 1122/6
= 187 kmph
Answer: B
Answer: (B) 187 kmph
Question: There are 2000 employees working in abc limited. out of them 40% of the employees using i phone and out of them 12% having BMW car out of them 70% are boys. Then find out the number of boys how many of the having BMW car and i phone?
(A) 96
(B) 84
(C) 59
(D) 67
(E) 45
Rationale: Total number of employees = 2000; Out of them 40% of the employees using i phone =800; out of them 15% of the employees having BMW car = 120; Out of them 70% are boys =84.
Answer: (B) 84
Question: A train 280 m long, running with a speed of 36 km / hr will pass a tree in
(A) 12 sec
(B) 15 sec
(C) 16 sec
(D) 28 sec
(E) None
Rationale: Sol.
Speed = (36 x 5/18) m/sec.
= 10 m / sec.
Time taken = (280 x 1/10) sec = 28 sec
Answer D
Answer: (D) 28 sec
Question: In a jar there are 28 white balls, 30 green balls and 42 blue balls. How many balls must be taken out in order to make sure we have 25 balls of the same color?
(A) a)	23
(B) b)	46
(C) c)	57
(D) d)	71
(E) e)	77
Rationale: Here, we need to find minimum number of marbles to be taken out to get 25 marbles of same color.
For a instance, if we take 24 white marbles 1st and followed by 23 Green and then 23 Blue.
Total will be 24 + 23+ 23= 70 draws.
If we choose either Green or Blue next time. This will bring the total of either of these colored marble to 25.
So Minimum we need to take 70+1 = 71 Times to get 25 marbles of same color(either Green or Blue).
Answer : D.
Answer: (D) d)	71
Question: In order to fulfill a local club charitable function request for x cakes, B parents agreed to each bake an equal number of cakes. If p of the parents did not bake any cakes, which of the following represents the additional number of cakes that each of the other parents had to bake in order for the school’s request for x cakes to be fulfilled?
(A) px/B
(B) px
(C) Bp/x
(D) B-p/x
(E) px/(B(B - p)
Rationale: No of cakes each parent has to bake : x/B
No of parents did not bake cake = p
No of cakes that were not baked by p parents = p*x/B
No of parents has to bake additional cakes = B-p
additional number of cakes that each of the other parents had to bake in order for the school’s request for x cakes = px/(B(B - p))
Answer E
Answer: (E) px/(B(B - p)
Question: Of the mutual funds on a “select list,” 1/3 have 5-star ratings, and 2/5 of the remaining funds have 4-star ratings. If the remaining 400 funds on the list have 3-star ratings, how many funds are on the list?
(A) 500
(B) 750
(C) 1,000
(D) 1,200
(E) 1,500
Rationale: C
Fraction of 5- and 4-star funds: 1/3 + (2/5)*(2/3) = 5/15 + 4/15 = 9/15
Fraction of 3-star funds = 1 - 9/15 = 6/15
(6/15)*Total = 400
Total = 1000
Answer: (C) 1,000
Question: The price of a certain truck this year is $36,000, which is 20 percent greater than the cost of the truck last year. What was the price of the truck last year?
(A) $29,000
(B) $30,000
(C) $31,000
(D) $32,000
(E) $33,000
Rationale: The price of the truck last year was $36,000/1.2=$30,000
The answer is B.
Answer: (B) $30,000
Question: Find the value of y from (12)^3 x 6^4 ÷ 432 = y?
(A) 2567
(B) 3589
(C) 3789
(D) 4890
(E) 5184
Rationale: Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184
432 12 x 62
E
Answer: (E) 5184
Question: Arun house area is the 10% more than of Akash house .if Akash House area is 144 Sqr m .then what is the area of Arun house?
(A) 138.4 sq m
(B) 148.4 sq m
(C) 158.4 sq m
(D) 168.4 sq m
(E) 178.4 sq m
Rationale: arun house=akash house area+10% askash house area=144+14.4=158.4 sq m
ANSWER:C
Answer: (C) 158.4 sq m
Question: A student chose a number, multiplied it by 2, then subtracted 152 from the result and got 102. What was the number he chose?
(A) 127
(B) 100
(C) 129
(D) 160
(E) 200
Rationale: Solution:
Let x be the number he chose, then
2*x*152=102
2x=254
x=127
correct answer A
Answer: (A) 127
Question: What investment must be made to obtain Rs 650 income from 10% stock at Rs 96?
(A) 6240
(B) 6248
(C) 2727
(D) 6212
(E) 6172
Rationale: Explanation:
Given market value = Rs 96
Required income = Rs 650
We assume the face value to be Rs 100.
To obtain 10% of face value, investment had to be Rs 96. So, in order to receive Rs 650, required investment is:
9.6*650=6240
Thus the investment should be Rs 6240.
ANSWER:A
Answer: (A) 6240
Question: In a bag containing 5balls, a white ball was placed and then 1ball was taken out at random. What is the probability that the extracted ball would turn on to be white, if all possible hypothesis concerning the color of the balls that initiallyin the bag wereequally possible ?
(A) 2/3
(B) 5/8
(C) 5/4
(D) 5/6
(E) 6/7
Rationale: Since, all possible hypothesis regarding the colour of the balls are equally likely, therefore these could be 3 white balls, initially in the bag.
∴ Required probability = 1/4 [1 + 3/4 + 1/2 + 1/4]
= 1/4 [(4 + 3 + 2 + 1)/4] = 5/8
B
Answer: (B) 5/8