mathewhe/aqua_rat huggingface dataset:
Question: Find the probability that a leap year selected at random will not have 53 Sundays or Mondays.
(A) 6/7
(B) 5/7
(C) 4/7
(D) 3/7
(E) 2/7
Rationale: There are 366 days in a leap year: 52 weeks and 2 more days. So, 52 Sundays, 52 Mondays and 2 days.
These 2 days can be: {Mon, Tue}, {Tue, Wed}, {Wed, Thu}, {Thu, Fri}, {Fri, Sat}, {Sat,Sun} and {Sun, Mon} (7 cases). In order to have 53 Sundays or 53 Mondays we should have either {Mon, Tue}
{Sat,Sun} or {Sun, Mon} case.
The probability of that is 3/7.
So probability of not having 53 Sundays or Mondays, probability is 1 - 3/7 = 4/7
Answer: C.
Answer: (C) 4/7
Question: There are 5 couples. If they will sit 10 chairs in a row such that each couple sits side by side, how many possible cases are there?
(A) 120
(B) 240
(C) 1,200
(D) 2,460
(E) 3,840
Rationale: Tie the couples. Then we have 5 persons that have to be arranged in 5 places. 5! ways.
Now the couples can change position with each other. 2! ways.
5! * (2!)^2 = 120 *32 = 3840
Answer is E.
5! * 2! = 240 ways.
Answer: (E) 3,840
Question: How many bricks, each measuring 25 cm x 11.25 cm x 6 cm, will be needed to build a wall of 8.5 m x 6 m x 22.5 cm?
(A) 6400
(B) 6410
(C) 6440
(D) 6500
(E) 6800
Rationale: Number of bricks = Volume of Wall/Volume of Bricks
=850x600x22.5/25x11.25x6= = 6800
answer :E
Answer: (E) 6800
Question: Positive integer x is 50 percent of 50 percent of positive integer y, and x percent of y equals 100. What is the value of y?
(A)  50
(B)  100
(C)  400
(D)  200
(E)  2,000
Rationale: x = 50% of 50% 0f y
= y/4
and
x/100 of y = 100
x /100 *4x =100
x = 50
and y= 200
Answer - D
Answer: (D)  200
Question: A train passes a station platform in 35 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) 248 m
(B) 225 m
(C) 277 m
(D) 765 m
(E) 176 m
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)/35 = 15 ==> x + 300 = 525 ==> x
= 225 m.
Answer: B
Answer: (B) 225 m
Question: The average of first four multiples of 4 is :
(A) 3
(B) 9
(C) 10
(D) 15
(E) 17
Rationale: Solution
Average = 4(1+2+3+4)/4 =40/4 =10 Answer C
Answer: (C) 10
Question: How many integers from 101 to 900, inclusive, remains the value unchanged when the digits were reversed?
(A)  50
(B)  60
(C)  70
(D)  80
(E)  90
Rationale: question is asking for palindrome
first digit possibilities - 1 through 8 = 8
9 is not possible here because it would result in a number greater than 9 (i.e 909 , 919..)
second digit possibilities - 0 though 9 = 10
third digit is same as first digit
=>total possible number meeting the given conditions = 8 *10 = 80
Answer is D.
Answer: (D)  80
Question: Two numbers A and B are such that the sum of 8% of A and 4% of B is two-third of the sum of 6% of A and 8% of B. Find the ratio of A : B.
(A) 2 : 1
(B) 1 : 2
(C) 4 : 3
(D) 1 : 3
(E) 3 : 2
Rationale: Explanation:
8% of A + 4% of B = 2/3(6% of A + 8% of B)
8A/100 + 4B/100 = 2/3(6A/100+8B/100)
⇒8A + 4B = 2/3(6A + 8B)
⇒24A + 12B = 12A + 16B
⇒ 12A = 4B
⇒ AB = 4/12
⇒ A:B=1:3
Answer: Option D
Answer: (D) 1 : 3
Question: Three models (M, N, and O) of cars are distributed among three showrooms. The number of cars in each showrooms must be equal and each model must be represented by at least one car in every showroom. There are 19 cars of Model M, 17 cars of Model N, and 15 cars of Model O. What is the maximum number of cars of model M in any showroom ?
(A) 17
(B) 16
(C) 15
(D) 14
(E) 13
Rationale: The total number of cars is 51. So each showroom has 17 cars(since the number of cars in each showrooms should be equal 51/3=17).
Moreover that the number of model M is maximum means that the numbers of model N and O should be minimum. Since each model must be represented by at least one car in every showroom that minimum number should be 1.
So Maximum number of model M is 17-2= 15.
The answer is (C)
Answer: (C) 15
Question: If x is an integer and (x)(x^2)(x^3) is positive, which of the following could be negative?
(A) x^4
(B) (x)(x^3)
(C) (x)(x)
(D) x + x^3
(E) 3x^2
Rationale: Assuming) x is negative (makes it easier)
(-2)(-2^2)(-2^3)
(-2)^3.(-2)^3
The two negative numbers will remain negative, so they will both cancel out.
So we need an equation where x^n with n being odd.
a) not sufficient -> will always be positive
b) not sufficient -> equals x^4 which will always be positive
c) not sufficient -> equals x^2 which will always be positive
d) -2+-8 = -10!!!
e) 3*4=12 is positive (pemdas!)
Answer is D
Answer: (D) x + x^3
Question: A bat is bought for Rs.420 and sold at a gain of 20% find its selling price
(A) s.430/-
(B) s.480/-
(C) s.400/-
(D) s.504/-
(E) s.600/-
Rationale: 100 % ------> 420
120 % ------> 420*120/100
Selling price = Rs.504
D
Answer: (D) s.504/-
Question: The diagonals of a rhombus are 14 cm and 20 cm. Find its area?
(A) 176
(B) 140
(C) 150
(D) 179
(E) 172
Rationale: 1/2 * 14 * 20
= 140
Answer:B
Answer: (B) 140
Question: A certain class of students is being divided into teams. The class can either be divided into 15 teams with an equal number of players on each team or 24 teams with an equal number of players on each team. What is the lowest possible number of students in the class?
(A) 6
(B) 36
(C) 48
(D) 60
(E) 120
Rationale: Let total no of students in the class be N
So, we are told that N is divisible by both 15 24
So, Lets find the least common multiple of 15 24 , ie 120
So our answer is (E) 120
Answer: (E) 120
Question: The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is:
(A) 230
(B) 240
(C) 245
(D) 250
(E) 260
Rationale: Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (130 + x)/30 = 25/2 => 2(130 + x) = 750 => x = 245 m.
Answer: Option C
Answer: (C) 245
Question: Anand and Deepak started a business investing Rs. 22,500 and Rs. 35,000 respectively. Out of a total profit of Rs. 15,6400, Deepak's share is:?
(A) s.9520
(B) s.8428
(C) s.8400
(D) s.8429
(E) s.8420
Rationale: Ratio of their shares
= 22500 : 35000
= 9:14
Deepak's share
= 15640 * 14/23
= Rs.9520.
Answer:A
Answer: (A) s.9520
Question: Which of the following numbers has neither 3 or 5 as a distinct prime factor?
(A) 77
(B) 80
(C) 125
(D) 132
(E) 210
Rationale: 77=7*11
80=2^4*5
125=5^3
132=2^2*3*11
210=2*3*5*7
77 has distinct prime factors of 7 and 11.
Answer A
Answer: (A) 77
Question: The salary of a typist was at first raised by 10% and then the same was reduced by 5%. If he presently draws Rs.2090.What was his original salary?
(A) 2277
(B) 2999
(C) 1000
(D) 2651
(E) 2000
Rationale: X * (110/100) * (95/100) = 2090
X * (11/10) * (1/100) = 22
X = 2000
Answer: E
Answer: (E) 2000
Question: A bag contains five white and four red balls. Two balls are picked at random from the bag. What is the probability that they both are different color?
(A) 5/5
(B) 5/1
(C) 5/9
(D) 5/2
(E) 5/7
Rationale: Two balls can be picked from nine balls in 9C2 ways.
We select one white ball and one red ball from five white balls and four red balls. This can be done 5C1 . 4C1 ways.
The required probability
= (5 * 4)/9C2
= 20/36
= 5/9
Answer:C
Answer: (C) 5/9
Question: The difference between a two-digit number and the number obtained by interchanging the two digits is 63. Which is the smaller of the two numbers?
(A) 2
(B) 3
(C) 9
(D) 7
(E) 1
Rationale: Explanation:
Let the ten's digit be x and units digit by y.
Then,
(10x + y) - (10y + x) = 63
9(x - y) = 63
x - y = 7
Thus, none of the numbers can be determined.
Answer: D
Answer: (D) 7
Question: By walking at 3/4th of his usual speed, a man reaches office 5 minutes later than usual. What is his usual time?
(A) 15min
(B) 50min
(C) 65min
(D) 60min
(E) 70min
Rationale: let T be the usual time.
time spent=4T/3
therefore, 4T/3=T+5
4T=3T+15...therefor T=15min
ANSWER:A
Answer: (A) 15min
Question: A hostel had provisions for 250 men for 44 days. If 50 men left the hostel, how long will the food last at the same rate?
(A) 55
(B) 40
(C) 50
(D) 60
(E) 65
Rationale: A hostel had provisions for 250 men for 44 days
If 50 men leaves the hostel, remaining men = 250 - 50 = 200
We need to find out how long the food will last for these 200 men.
Let the required number of days = x days
More men, Less days (Indirect Proportion)
(men) 250 : 200 :: x : 44
250×44=200x
5×44=4x
x=5×11=55
ANSWER A
Answer: (A) 55
Question: I live X floors above the ground floor of a high-rise building. It takes me 30 s per floor to walk down the steps and 2 s per floor to ride the lift. What is X, if the time taken to walk down the steps to the ground floor is the same as to wait for the lift for 7 min and then ride down?
(A) 4
(B) 7
(C) 14
(D) 15
(E) 17
Rationale: Explanation :
Since I live X floors above the ground floor and it takes me 30 s per floor to walk and 2 s per floor to ride, it takes 30X s to walk down and 2X s to ride down after waiting 420 s
=> 30X = 2X + 420
=> X = 15.
Answer : D
Answer: (D) 15
Question: Tough and Tricky questions: Remainders.
1^1 + 2^2 + 3^3 + ... + 7^7 is divided by 7. What is the remainder?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: a number is divisible by 5, if its last digit is divisible by 5
let's look into the sum of last digits of each term of the given expression
1^1=1
2^2=4
3^3=7
4^4=6
5^5=5
6^6=6
7^7=3
adding all these numbers we get 32 which gives a remainder of4 when divided by 7. so answer must be 4.
bunuel, can you please confirm the answer of this question.
Yes, the OA is C. Clicked the wrong button when posting. Edited. Thank you.
E
Answer: (E) 4
Question: What is the next number: 2, 17, 257, __
(A) 2977
(B) 3837
(C) 4097
(D) 4847
(E) 5387
Rationale: 4^0 + 1 = 2
4^2 + 1 = 17
4^4 + 1 = 257
4^6 + 1 = 4097
The answer is C.
Answer: (C) 4097
Question: Square X is inscribed in circle Y. If the perimeter of X is 64, what is the circumference of Y?
(A) 16√ 2π
(B) 8√ 2π
(C) 22√ 2π
(D) 12√ 2π
(E) 9
Rationale: square forms two right angled triangles.
Any time we have a right angle triangle inside a circle, the hypotenuse is the diameter.
hypotenuse here = diagonal of the square = 16 sqrt(2) = diameter
=> radius = 8 sqrt(2)
Circumference of the circle = 2pi r = 16 pi sqrt(2)
Answer is A.
Answer: (A) 16√ 2π
Question: The sum of three integers A, B and C is 300. A is one third of the sum of B and C and B is one fifth of the sum of A and C. What is C?
(A) 175
(B) 180
(C) 185
(D) 190
(E) 195
Rationale: A is one third of the sum of B and C..
or A=1/3(B+C)...
But A+B+C=300
so 1/3(B+C)+B+C=300
4(B+C)/3= 300
B+C =300*3/4 = 225
A=300-225=75
2)B is one fifth of the sum of A and C
or B=1/5(A+C)...
But A+B+C=300
so 1/5(A+C)+A+C=300
A+C=300*5/6=250
but A=75, so C=250-75=175
Answer : A
Answer: (A) 175
Question: For every $20 that a billionaire spends, a millionaire spends the equivalent of 20 cents. For every $8 that a millionaire spends, a yuppie spends the equivalent of $1. The ratio of money spent by a yuppie, millionaire, and billionaire can be expressed as
(A) 1 : 8 : 800
(B) 1 : 4 : 100
(C) 20 : 4 : 1
(D) 100 : 4 : 1
(E) 400 : 4 : 1
Rationale: B.........M........Y
20.....0,20......Y
B.........8........1
What I did first was to turn 0.20 to 2 (by multiplying by 10), so that it is easy to find the LCM. This led me to this:
B.........M........Y
200.....2.........Y
B........80......10
Then I multiplied every row by 80 (the LCM of 2 and 80), which led me to this:
B.........M........Y
8000...80.......10
Then I got rid of the extra zero, and in the correct order this is Y:M:B=1:8:800
ANS A
Answer: (A) 1 : 8 : 800
Question: Two mixtures of X and Y have X and Y in the ratio 3:2 and 3:4. In what proportion should these two mixtures be mixed to get a new mixture in which the ration of X to Y is 5:4?
(A) 6:1
(B) 5:4
(C) 20:7
(D) 10:9
(E) 14:11
Rationale: I got C but with a different, yet slightly longer approach, which I constantly use for proportion problems such as this one. Usually, this approach is very efficient when used with slightly difficult questions, but this problem is quite hard so I had to slightly tweak it. I will show you how I usually use the approach and later show you how to use it with this specific problem.
Example.
1 Liter of Solution A contains 45% alcohol, while 1 Liter of Solution B contains 20% alcohol. In what ratio must the two solutions be used to get a solution with 30% alcohol
Solution:
1.	45/100*[A/(A+B)]+20/100*[B/(A+B)] = 30/100
2.	Multiply 100 to both sides to arrive at 45A/(A+B) + 20B/(A+B) = 30
3.	Multiply (A+B) to both sides to arrive at 45A + 20B = 30A + 30B
4.	Distribute to arrive at 15A = 10B
5.	Thus the ratio is A/B = 10/15 = 2/3
Now using this same approach, we tackle Gopu106’s question. It is important to first think of X in the mixture as the alcohol in the problem above; hence, a mixture of X and Y in the ratio of 3:2 translates to X is 3/5 of the solution. Applying this concept to all three equations, we write:
1.	3/5*[A/(A+B)]+3/7*[B/(A+B)] = 5/9
2.	Now here is the tweak that must be made to continue with this approach. You must find the common denominator for all three numbers and organize the fractions accordingly. By finding the common denominator of 5,7,9 (or 315) we re-write the equations as follows
3.	189/315*[A/(A+B)]+135/315*[B/(A+B)] = 175/315
4.	Multiply 315 to both sides to arrive at 189A/(A+B) + 135B/(A+B) = 175
5.	Multiply (A+B) to both sides to arrive at 189A + 135B = 175A + 175B
6.	Distribute to arrive at 14A = 40B
7.	Thus the ratio is A/B = 40/14 = 20/7 or answer C
Answer: (C) 20:7
Question: In assembling a Bluetooth device, a factory uses one of two kinds of modules. One module costs $10 and the other one, that is cheaper, costs $2.5. The factory holds a $62.50 worth stock of 22 modules. How many of the modules in the stock are of the cheaper kind?
(A) 31
(B) 35
(C) 21
(D) 40
(E) 45
Rationale: So the number of $2.50 modules must be 21 so that the leftover 1 modules are of $10 which will give a total value $62.50. 21*2.50+1*10 = 52.50+10=62.50
Answer : C
Answer: (C) 21
Question: A train travelled from station P to Q in 8 hours and came back from station Q to P is 6 hours. What would be the ratio of the speed of the train while traveling from station P to Q to that from station Q to P?
(A) 3:5
(B) 3:3
(C) 3:1
(D) 3:4
(E) 3:2
Rationale: :
Since S # 1/t
S1 : S2 = 1/t1 : 1/t2 =1/8 :1/6
=3:4
Answer:D
Answer: (D) 3:4
Question: A series S1 of five positive integers is such that the third term is half the first term and the fifth term is 20 more than the first term. In series S2, the nth term defined as the difference between the (n+1) term and the nth term of series S1, is an arithmetic progression with a common difference of 30.
First term of S1 is
(A) 80
(B) 90
(C) 100
(D) 120
(E) 130
Rationale: Explanation :
According to the question,
S1:- 2a, b, a, c, 2a + 20
And,
S2:- b - 2a, a - b, c - a, 2a + 20 - c
Also,
=> b - 2a + 30 = a - b i.e. 3a - 2b = 30 .
=> a - b + 30 = c - a
=> c - a + 30 = 2a + 20 - c i.e. 3a - 2c = 10
Solving them, we get a = 50, b = 60, c = 70
So series S1: 100, 60, 50, 70, 120 and series S2: -40, -10, 20.
Answer : C
Answer: (C) 100
Question: How many sides does the polygon have if the total angles measures up to 900 degrees?
(A) 3
(B) 7
(C) 4
(D) 6
(E) None of these
Rationale: 7 sides...answer is B
Answer: (B) 7
Question: Average weight of 15 boys in a class is 48 kgs. The average weight of the class of 25 students is 45 kgs. What is the average weight of the 15 girls in the class?
(A) 45
(B) 47.3
(C) 39.8
(D) 45.5
(E) 40.5
Rationale: total weight of boys in class 15 X 48=720kg
total weight of all student in the class room 25 X45=1125kg
total no of girls in the class 1125-720= 405kg
average weight of girls 405/10= 40.5kg
correct ans is E
Answer: (E) 40.5
Question: A train having a length of 240 m passes a post in 24 seconds. How long will it take to pass a platform having a length of 670 m?
(A) 120 sec
(B) 91 sec
(C) 89 sec
(D) 80 sec
(E) 85 sec
Rationale: Explanation:
v = 240/24 (where v is the speed of the train) = 10 m/s
t = (240+670)/10 = 91 seconds
Answer: Option B
Answer: (B) 91 sec
Question: A train passes a man standing on the platform. If the train is 245 meters long and its speed is 126 kmph, how much time it took in doing so?
(A) 2 sec
(B) 67 sec
(C) 5 sec
(D) 9 sec
(E) 7 sec
Rationale: D = 245
S = 126 * 5/18 = 35 mps
T = 245/35 = 7 sec
Answer:E
Answer: (E) 7 sec
Question: 3+333+333+3.33=?
(A) 362.33
(B) 672.33
(C) 702.33
(D) 702
(E) None of them
Rationale: 3
333
333
3.33
----------
672.33
----------
Answer is B
Answer: (B) 672.33
Question: The age of man is three times the sum of the ages of his two sons.Nine years hence,his age will be double of the sum of the ages of his sons.The fatherâ€™s present age is :
(A) 40 years
(B) 45 years
(C) 50 years
(D) 55 years
(E) 81 years
Rationale: Solution
Let the sum of present ages of the two sons be x years.
Then,father's present age = 3x years.
âˆ´ (3x + 9)=2 (x +18) â‡” 3x + 9 = 2x + 36 â‡” x =27
Hence,father's present age = 81 years. Answer E
Answer: (E) 81 years
Question: If a radio is purchased for Rs 490 and sold for Rs 465.50 Find the loss%?
(A) 3%
(B) 4%
(C) 5%
(D) 6%
(E) None of these
Rationale: Explanation :
Loss = 490 – 465.5 = 24.5 loss in % = 24.5/ 490 x 100 = 5%.
Answer : C
Answer: (C) 5%
Question: A batsman in his 17th innings makes a score of 85 and their by increasing his average by 3. What is his average after the 17th innings?
(A) 12
(B) 13
(C) 46
(D) 37
(E) 26
Rationale: 16x + 85 = 17(x + 3)
x = 34 + 3 = 37
Answer: D
Answer: (D) 37
Question: if page of chemistry book is 30 more than page of physics book.if ratio of pages is
5:3.a child torn 15 pages of chemistry book.calculate new ratio.
(A) 1:1
(B) 2:1
(C) 5:4
(D) 4:3
(E) 2:3
Rationale: chemistry page=5x, physics page=3x
5x-3x=30,2x=30,x=15
chemistry page=75, physics page=45
after torn 15 page of chemistry=60
ratio become 60/45=4:3
answer D
Answer: (D) 4:3
Question: Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is?
(A) 12
(B) 77
(C) 48
(D) 99
(E) 11
Rationale: Relative speed = 60 + 90 = 150 km/hr.
= 150 * 5/18 = 125/3 m/sec.
Distance covered = 1.10 + 0.9 = 2 km = 2000 m.
Required time = 2000 * 3/125 = 48 sec.
Answer: C
Answer: (C) 48
Question: In the equation 2x â€“ cy = 18, c is a constant. If the value of y is 2 when x is 6, what is the value of x when y is 4 ?
(A) âˆ’9/2
(B) -4
(C) 3
(D) 4
(E) 9/2
Rationale: 2x - cy = 18
x=6, y=2;
12-2c=18
c=-3
2x-cy=18
when y=4, c=-3, x=
x=3
ANSWER:C
Answer: (C) 3
Question: 0.0203 x 2.92/0.0073 x 14.5 x 0.7 = ?
(A) 0.7
(B) 0
(C) 0.8
(D) 8
(E) 7
Rationale: = 0.0203 x 2.92/0.0073 x 14.5 x 0.7
= 203 x 292/73 x 145 x 7
= 4/5
= 0.8
Answer is C.
Answer: (C) 0.8
Question: If two sides of a triangle have lengths 3 and 8, which of the following could be the perimeter of the triangle? I. 9 II. 15 III. 19
(A) None
(B) I only
(C) II only
(D) III only
(E) I, II, and III
Rationale: The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.
Therefore:
(8-3) < {third side} < (8+3).
5 < {third side} < 11.
Perimeter = {third side} + 8 + 3 = {third side} + 11.
16 < {perimeter} < 22.
answer D
Answer: (D) III only
Question: A boy wants to go abroad by boat and return by flight. He has a choice of 4 different boat to go and 5 flight to return. In how many ways, can the boy perform his journey?
(A) 20
(B) 24
(C) 25
(D) 26
(E) 30
Rationale: Ans.(A)
Sol. Number of choices to go by ship = 4 Number of choices to return by airline = 5 From, fundamental principle, total number of ways of performing the journey = 4 x 5 = 20 ways
Answer: (A) 20
Question: A is the average (arithmetic mean) of the first 7 positive multiples of 5 and B is the median of the first 3 positive multiples of positive integer n. If the value of A^2 – B^2 is zero, what is the value of n?
(A) 5
(B) 6
(C) 10
(D) 15
(E) 20
Rationale: If A^2 - B^2 = 0, then let's assume that A = B.
A must equal the 4th positive multiple of 4, thus A = 20, which also equals B.
B is the second positive multiple of n, thus n = 20/2 = 10.
The answer is C.
Answer: (C) 10
Question: A school give scholarship of a total of $940,000 to students, the scholarship consist of 3 types $95,000, $35,000, and $10,000. What is the smallest possible number of students who take the scholarship?
(A) 13
(B) 14
(C) 15
(D) 16
(E) 17
Rationale: The number of first-place students=f
The number of second-place students=s
The number of third-place students=t
Then, an equation 95,000f+35,000s+10,000t=940,000 is derived.
In order for f+s+t to be minimum, f should be maximum followed by s and t.
Then, f=9, s=1, t=5 are derived and f+s+t=9+1+5=15.
ANSWER:C
Answer: (C) 15
Question: How much pure alcohol should be added to 400ml of a 15% solution to make the strength of solution 25%?
(A) 100 ml
(B) 60 ml
(C) 125 ml
(D) 130 ml
(E) 150 ml
Rationale: we can also go by answer choices
Tke 100 ml for eg
400 (old)+100 (new concentr)ml
500*25/100 = 125 ml (25ml is de old concentration +100 ml (newly added)
Answer C
Answer: (C) 125 ml
Question: At garage sale, all of the prices of the items sold were different. If the price of a radio sold at the garage sale was both the 9th highest price and the 35th lowest price among the prices of the items sold, how many items were sold at the garage sale?
(A) 43
(B) 28
(C) 44
(D) 49
(E) 46
Rationale: 8+34+1= 43
Answer: A
Answer: (A) 43
Question: Find the one which does not belong to that group ?
(A) 3
(B) 4
(C) 5
(D) 9
(E) 7
Rationale: Explanation:
3, 5, 9 and 7 are odd numbers, but not 4.
ANSWER IS B
Answer: (B) 4
Question: If log 32 x= 0.8, then x is equal to
(A) 25.6
(B) 16
(C) 10
(D) 12.8
(E) None
Rationale: Solution
log32 x	=0.8.
x=(32)0.8
‹=›(25)4/5
‹=›24
‹=› 16.
Answer B
Answer: (B) 16
Question: When running a mile during a recent track meet, Nuria was initially credited with a final time of 5 minutes, 42 seconds. Shortly after her run, officials realized that the timing mechanism malfunctioned. The stopwatch did not begin timing her until 11/25 of a minute after she began to run. If the time was otherwise correct, how long did it actually take Nuria to run the mile?
(A) 5 minutes, 17.6 seconds
(B) 5 minutes, 21.8 seconds
(C) 5 minutes, 43.56 seconds
(D) 5 minutes, 44.44 seconds
(E) 6 minutes, 10.4 seconds
Rationale: One approach:
The watch starts to work after Nuria began his running. It means the time should be greater than credited 5 minutes, 42 seconds. The only number is 6 minutes, 10.4 seconds.
Another approach:
11/25 close to 30 second when added to the 5 minutes, 44 seconds, it means it passes 6 minute.
Answer: E
Answer: (E) 6 minutes, 10.4 seconds
Question: The average score in an examination of 10 students of a class is 50. If the scores of the top five students are not considered, the average score of the remaining students falls by 5. The pass mark was 40 and the maximum mark was 100. It is also known that none of the students failed. If each of the top five scorers had distinct integral scores, the maximum possible score of the topper is
(A) 96
(B) 97
(C) 89
(D) 98
(E) 95
Rationale: The average score in an examination of 10 students of a class is 50 --> the total score = 10*50 = 500;
The 5 smallest scores have an average of 45 --> the total score of the 5 smallest scores = 225
From above, the total score of the 5 largest scores = 500 - 225 = 275.
Say the 5 largest scores are a, b, c, d, and e (where a<b<c<d<e, since each of the top five scorers had distinct scores). We want to maximize e. To maximize e, we need to minimize a, b, c, and d. The least value of a, is 45 (The least score of the top 5 , a, should be equal to the highest of the bottom 5 and to minimize the highest of the bottom 5, all scores from the bottom 5 should be equal). In this case the least values of b, c, and d are 56, 57, and 58 respectively:
a + b + c + d + e = 45 + 46 +47 + 48 + e = 275;
e = 89.
Answer: C.
Answer: (C) 89