mathewhe/aqua_rat huggingface dataset:
Question: Mr. Smith calculated the average of 10 three digit numbers. But due to a mistake he reversed the digits of a number and thus his average increased by 19.8 The difference between the unit digit and hundreds digit of that number is :
(A) 2
(B) 6
(C) 5
(D) 3
(E) 4
Rationale: Since the average increased by 29.7 and there were a total of 10 numbers, it means the incorrect number was 198 greater than the correct number.
Say, the correct number was abc (where a, b and c are the digits of the 3 digit number)
Then the incorrect number was cba.
100c + 10b + a - (100a + 10b + c) = 198
99c - 99a = 99(c - a) = 198
198 = 99*2 = 99(c - a)
So c - a = 2
Answer (A)
Answer: (A) 2
Question: A man whose speed is 5.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey?
(A) 3kmph
(B) 4kmph
(C) 5.1kmph
(D) 6kmph
(E) 7kmph
Rationale: M = 5.5
S = 1.5
DS = 7
US = 4
AS = (2 * 7 * 4) /11 = 4
Answer:C
Answer: (C) 5.1kmph
Question: A bag contains 4 white, 5 red and 6 blue balls. Three balls are drawn at random from the bag. The probability that all of them are red, is:
(A) 2/91
(B) 3/52
(C) 5/25
(D) 8/45
(E) 7/56
Rationale: n(s)=no of ways of drawing 3 balls out of 15
15C3 = 15*14*13/3*2*1
==>455
n(E)=5C3=5C2 = 5*4/2*1 = 10
p(E) =n(E)/n(S)=10/455 = 2/91
ANSWER A
Answer: (A) 2/91
Question: Working alone, pump A can empty a pool in 4 hours. Working alone, pump B can empty the same pool in 6 hours. Working together, how many minutes will it take pump A and pump B to empty the pool?
(A) 132
(B) 138
(C) 144
(D) 150
(E) 156
Rationale: Pump A can empty (1/4) of the pool per hour.
Pump B can empty (1/6) of the pool per hour.
Together the pumps can empty 1/4+1/6=5/12 of the pool per hour.
1 pool / (5/12) pool per hour = 12/5 hours = 144 minutes.
The answer is C.
Answer: (C) 144
Question: The ratio of spinsters to cats is 2 to 7. If there are 55 more cats than spinsters, how many spinsters are there?
(A) 20
(B) 21
(C) 22
(D) 23
(E) 24
Rationale: Let 2x be the number of spinsters. Then 7x is the number of cats.
7x-2x=55
x=11 and the number of spinsters is 2(11)=22.
The answer is C.
Answer: (C) 22
Question: If a point (x,y) is randomly selected within the square shown in the figure above, (the vertices are on 1,1 1,-1, -1,1 -1,-1) what are
the E odds that x^2+y^2>1?
(A) 1. pi/4
(B) 2. E=pi/16
(C) 3. E=1-pi/4
(D) 4. 1-pi/16
(E) 5.4-pi
Rationale: area of the square will be 4, and the area of circle with center (0,0) and radius 1 will be pi.
then succesful outcomes = 4 - pi (the area where x2+y2 will be greater than 1)
total outcomes = 4
therefore probability = (4-pi)/4
C
Answer: (C) 3. E=1-pi/4
Question: A charity collected $1,299 from donors during the last month. If each donor gave at least $20, what is the greatest possible number of donors the charity could have?
(A) 60
(B) 64
(C) 66
(D) 68
(E) 69
Rationale: Min fund = 20
Total = 1299
The closest multiple of 20 to 1299 is : 63
Which implies 63 people gave 20 and 1 person gave 39
Ans. B
Answer: (B) 64
Question: (168% of 1265) ÷ 6 = ?
(A) A)354
(B) B)175
(C) C)225
(D) D)375
(E) E)524
Rationale: Explanation :
? = (168 x 1265/100) ÷ 6 = 212520/600 = 354
Answer : Option A
Answer: (A) A)354
Question: A 13% stock yields 8%.The market value of the stock is :
(A) Rs. 72
(B) Rs. 92
(C) Rs. 162.50
(D) Rs. 116.50
(E) None of these
Rationale: solution
To obtain Rs. 8, investment = Rs. 100.
To obtain Rs. 13, investment = Rs.(100/8X13)= Rs. 162.50
∴ Market value of Rs. 100 stock = Rs.162.50
Answer C
Answer: (C) Rs. 162.50
Question: In what ratio must tea of Rs.42 per kg be mixed with tea of Rs.50 per kg so that cost of mixture is Rs.45 per kg?
(A) 5:3
(B) 3:5
(C) 2:3
(D) 3:4
(E) 1:2
Rationale: 50-45:45-42=5:3
ANSWER:A
Answer: (A) 5:3
Question: The average amount with a group of seven numbers is Rs. 30. If the newly joined member has Rs. 70 with him, what was the average amount with the group before his joining the group?
(A) s. 25.6
(B) s. 70/3
(C) s. 16.6
(D) s. 26/3
(E) s. 25
Rationale: Total members in the group = 7
Average amount = Rs. 30
Total amount with them = 7 * 30 = Rs. 210
One number has Rs. 70. So, the amount with remaining 6 people = 210 - 70 = Rs. 140
The average amount with them = 140/6 = Rs. 70/3
ANSWER:B
Answer: (B) s. 70/3
Question: The average price of 10 oranges is Rs. 12 while the average price of 8 of these oranges is Rs. 11.75. Of the remaining two oranges, if the price of one orange is 60% more than the price of the other, what is the price of each of these two oranges?
(A) Rs 5, Rs 7.50
(B) Rs 8, Rs 12
(C) Rs 10, Rs 16
(D) Rs 12, Rs 14
(E) None of these
Rationale: Explanation :
Total price of the two oranges = Rs. [(12 x 10) (11.75 x 8)]
= Rs. (120 - 94) = Rs. 26.
Let the price of one orange be Rs. x.
Then, the price of other orange = Rs. (x + 60% of x) = Rs. x + 3/5x = Rs. 8x/5
So, x + 8x/5 = 26
13x = 130
x = 10.
The prices of the two oranges are Rs. 10 and Rs. 16
Answer : C
Answer: (C) Rs 10, Rs 16
Question: A man can row with a speed of 20 kmph in still water. If the stream flows at 10 kmph, then the speed in downstream is?
(A) 29
(B) 378
(C) 20
(D) 30
(E) 121
Rationale: M = 20
S = 10
DS = 20 + 10 = 30
Answer: D
Answer: (D) 30
Question: The edges of a cuboid are 4 cm, 5 cm and 6 cm. Find the volume of the cuboid?
(A) 120
(B) 298
(C) 272
(D) 827
(E) 278
Rationale: 4*5*6
= 120
Answer:A
Answer: (A) 120
Question: Pipe A can fill a tank in 2 hours, pipe B in 4 hours and pipe C in 4 hours. If all the pipes are open, in how many hours will the tank be filled?
(A) 2
(B) 1
(C) 3
(D) 4
(E) 5
Rationale: Answer:	Part filled by A + B + C in 1 hour = 1/2 + 1/4 + 1/4= 1/1
All the three pipes together will fill the tank in 1 hours.
Answer: B
Answer: (B) 1
Question: If a person walks at 10 km/hr instead of 5 km/hr, he would have walked 20 km more. The actual distance traveled by him is?
(A) 50 km
(B) 76 km
(C) 20 km
(D) 16 km
(E) 97 km
Rationale: Let the actual distance traveled be x km. Then,
x/5 = (x + 20)/10
5x - 100 =>x = 20 km.
Answer: C
Answer: (C) 20 km
Question: A two digit number, digits interchange places and the new number is added to the original number, then the resulting number will be divisible by?
(A) 10
(B) 11
(C) 13
(D) 15
(E) 16
Rationale: Let the ten's digit be x and unit's digit be y.
Then, number = 10x + y.
Number obtained by interchanging the digits = 10y + x.
(10x + y) + (10y + x) = 11(x + y), which is divisible by 11.
B
Answer: (B) 11
Question: if 5 boys take two hours to water the garden, then how long should 10 boys take to water the same type of garden?
(A) 80 min
(B) 50 min
(C) 30 min
(D) 65 min
(E) 60 min
Rationale: if 5 boys take an hour to water the garden, then
10 boys will take 5*120/10 = 60 mins to water the same type of garden.
ANSWER:E
Answer: (E) 60 min
Question: A train 125 m long passes a man, running at 6 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is?
(A) 40
(B) 50
(C) 51
(D) 79
(E) 80
Rationale: Speed of the train relative to man = 125/10 = 25/2 m/sec.
= 25/2 * 18/5 = 45 km/hr
Let the speed of the train be x km/hr. Then, relative speed = (x - 6) km/hr.
x - 6 = 45 => x = 51 km/hr.
Answer: Option C
Answer: (C) 51
Question: Eight family members are seated around their circular dinner table. If only arrangements that are considered distinct are those where family members are seated in different locations relative to each other, and Michael and Bobby insist on sitting next to one another, then how many distinct arrangements around the table are possible?
(A) 1040
(B) 1240
(C) 1440
(D) 1640
(E) 1840
Rationale: Let's consider Michael and Bobby as one unit.
There are 7! possible arrangements of 7 units.
Around a table, there would be repetitions of each arrangement, so we divide by 7.
Then there are 6! arrangements around a circular table.
For each arrangement, Michael and Bobby can switch places, so we multiply by 2.
The number of arrangements is 6!*2 = 1440.
The answer is C.
Answer: (C) 1440
Question: Two trains of equal lengths take 10 sec and 15 sec respectively to cross a telegraph post. If the length of each train be 160 m, in what time will they cross other travelling in opposite direction?
(A) 17 sec
(B) 12 sec
(C) 16 sec
(D) 15 sec
(E) 18 sec
Rationale: Speed of the first train = 120/10 = 12 m/sec.
Speed of the second train = 120/5 = 8 m/sec.
Relative speed = 12 + 8 = 20 m/sec.
Required time = (160 + 160)/20 = 16 sec.
Answer:C
Answer: (C) 16 sec
Question: Excluding stoppages, the speed of a train is 50 kmph and including stoppages it is 30 kmph. Of how many minutes does the train stop per hour?
(A) 82
(B) 17
(C) 12
(D) 24
(E) 18
Rationale: Explanation:
T = 20/50 * 60 = 24
Answer: Option D
Answer: (D) 24
Question: How many arrangements can be made out of the letters of the word 'ENGINEERING' ?
(A) 277200
(B) 92400
(C) 69300
(D) 23100
(E) 45380
Rationale: The word 'ENGINEERING' contains 11 letters, namely 3E, 3N, 2G, 2I and 1R.
∴ Required number of arrangements = 11!/(3!)(3!)(2!)(2!)(1!) = 277200.
Answer is A
Answer: (A) 277200
Question: From January 1, 1991, to January 1, 1993, the number of people enrolled in health maintenance organizations increased by 10 percent. The enrollment on January 1, 1993, was 45 million. How many million people, to the nearest million, were enrolled in health maintenance organizations on January 1, 1991 ?
(A)  38
(B)  39
(C)  40
(D)  41
(E)  42
Rationale: 1.10x=45 --> 11/10*x=45 --> x=45*10/11=450/11=~41.
Answer: D.
Answer: (D)  41
Question: On a map, 1 centimeter represents 17 kilometers. Two cities 663 kilometers apart would be separated on the map by how many centimeters?
(A) 15
(B) 27
(C) 39
(D) 270
(E) 480
Rationale: X=663/17= 39
Answer: C
Answer: (C) 39
Question: In a group of 68 students, each student is registered for at least one of three classes – History, Math and English. Twenty-one students are registered for History, twenty-six students are registered for Math, and thirty-four students are registered for English. If only three students are registered for all three classes, how many students are registered for exactly two classes?
(A) 13
(B) 10
(C) 9
(D) 8
(E) 7
Rationale: A U B U C = A + B + C - AB-BC-AC + ABC
68 = 21 + 26+ 34 -AB-BC-AC +3 => AB+BC+AC = 16
Exactly Two classes = AB+BC+AC - 3ABC = 16 -3*3 = 7
Hence E
Answer: (E) 7
Question: The average marks scored by Ganesh in English, Science, Mathematics and History is less than 18 from that scored by him in English, History, Geography and Mathematics. What is the difference of marks in Science and Geography scored by him?
(A) 72
(B) 50
(C) 60
(D) Data inadequate
(E) None of these
Rationale: E+H+G+M/4âˆ’E+S+M+H/4=18
â‡’ G - S = 72
Answer A
Answer: (A) 72
Question: Which is longest: a foot, a yard or an inch?
(A) a yard
(B) inch
(C) foot
(D) feet
(E) cm
Rationale: 3 feet = 1 yard
12 inches = 1 foot
answer A
Answer: (A) a yard
Question: If p and q are integers, such that p < 3 < q, and s is a nonnegative integer, which of the following must be true?
(A) p^2 < q^2
(B) p + q = 0
(C) sp < sq
(D) sp ≠ sq
(E) p/q < s
Rationale: We're told that P < 0 < Q and that S is a NON-NEGATIVE INTEGER. We're asked which of the following MUST be true.
P = -2
Q = 2
S = 0
Answer A: P^2 < Q^2.... 4 < 1 NOT TRUE
Answer B: P+Q=0... -2+1 = -1 NOT TRUE
Answer C: SP < SQ... 0 < 0 NOT TRUE
Answer D: SP ≠ SQ... 0 = 0 NOT TRUE
Answer E: P+Q=0 This IS TRUE
B
Answer: (B) p + q = 0
Question: A grocer stacked apples in a pile. The bottom layer was rectangular with 3 rows of 5 apples each. In the second layer from the bottom, each apple rested on 4 apples from the bottom layer, and in the third layer, each apple rested on 4 apples from the second layer. Which of the following is the maximum number of apples that could have been in the third layer?
(A)  5
(B)  3
(C)  6
(D)  2
(E)  1
Rationale: Bottom Layer = 5 x 3 = 15
IInd Layer = (5-1) x (3-1) = 8
IIIrd Layer = (4-1) x (2-1) = 3
Answer = 3 = B
Answer: (B)  3
Question: The radius of a sphere is increased by 50%. The increase in surface area of the sphere is :
(A) 168
(B) 125
(C) 186
(D) 197
(E) 191
Rationale: Explanation:
Take radius 100. Then surface area is 4 × ππ × 100 × 100.
After increase radius by 50% the radius becomes100 + 50% of 100 = 150
Then new surface area is 4 × ππ × 150 × 150
Then put the values into formula of percentage = 4π1502−4π10024π1002×1004π1502−4π10024π1002×100 = 125%
Answer: B
Answer: (B) 125
Question: If a man lost 4% by selling oranges at the rate of 12 a rupee at how many a rupee must he sell them to gain 44%?
(A) 9
(B) 8
(C) 7
(D) 6
(E) 65
Rationale: 96% ---- 12
144% ---- ?
96/144 * 12 = 8
Answer: B
Answer: (B) 8
Question: How much is 80% of 40 is greater than 2/5 of 25?
(A) 22
(B) 27
(C) 18
(D) 12
(E) 81
Rationale: (80/100) * 40 â€“ (2/5) * 25
32 - 10 =22
Answer:A
Answer: (A) 22
Question: Given two sets A = {1,1,2,2,7,7} and B = {0,1}, if one number is chosen from each set at random, what is the probability that the sum of both numbers is an even number
(A) 1/5
(B) 1/6
(C) 1/2
(D) 1/3
(E) 1/4
Rationale: One way to look at it:
The number from set A can be ANYTHING.
The number selected from set B will determine whether the sum is odd or even.
For example, if a 2 is selected from set A, we need a 0 from set B to get an even sum.
If a 7 is selected from set A, we need a 1 from set B to get an even sum.
And so on.
So, P(sum is even) = P(select ANY number from set AANDselect the number from set B that makes the sum even)
= P(select ANY number from set A)xP(select the number from set B that makes the sum even)
= 1x1/2
= 1/2
= C
Answer: (C) 1/2
Question: Of the three-digit integers greater than 700, how many have distinct digits?
(A)  216
(B)  82
(C)  80
(D)  45
(E)  36
Rationale: Three digit number can have only following 3 patterns:
A. all digits are distinct;
B. two digits are alike and third is different;
C. all three digits are alike.
We need to calculate B. B=Total - A - C
Total numbers from 700 to 999 = 299 (3-digit numbers greater than 700);
A. all digits are distinct = 3*9*8=216
Answer: A
Answer: (A)  216
Question: Find the compound interest on $ 10,000 in 2 years at 4% per annum, the interest being compounded half-yearly
(A) 824
(B) 824.36
(C) 824.32
(D) 824.24
(E) 824.26
Rationale: Principal = $ 10000; Rate = 2% per half-year; Time = 2 years = 4 half-years.
Amount = $ [10000 * (1+(2/100))4] = $(10000 * (51/50) * (51/50) * (51/50) * (51/50))
= $ 10824.32.
:. C.I. = $ (10824.32 - 10000) = $ 824.32.
Answer C.
Answer: (C) 824.32
Question: There are n cities. What is the number of airlines that connected 5 different cities (airline from city A to city B is different with airline from city B to city A)?
(A) n(n-1)
(B) n(n+1)
(C) n(n-1)/2
(D) n(n-3)
(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-4). Hence, the answer is n(n-4), which makes A an answer choice.
D
Answer: (D) n(n-3)
Question: What is the probability that a two digit number selected at random is a multiple of 3 and not a multiple of 5 ?
(A) 1/15
(B) 2/15
(C) 4/15
(D) 7/15
(E) None of these
Rationale: Explanation :
Since every third number starting from 10 will be divisible by 3, so total number of numbers divisible by 3 are 90/3 = 30
Numbers which are divisible by 3 and 5 both are numbers which are multiple of 15.
For the range 10 to 99, 15 is the first number divisible by 15 and 90 is the last number.
So total number of numbers divisible by 15 are: (90-15)/15 + 1 = 5 + 1 = 6
Number of numbers which are divisible by 3 are 30 and number of numbers which are divisible by 3 and 5 both are 6. So number of numbers divisible by 3 and not by 5 are: 30-6=24
So total probability = 24/90 = 4/15
Answer : C
Answer: (C) 4/15
Question: The sale price of a trolley bag including the sale tax is Rs. 280. The rate of sale tax is 12% . If the shopkeeper has made a profit of 25%, the cost price of the trolley bag is:
(A) Rs 200
(B) Rs 220
(C) Rs 260
(D) Rs 280
(E) None of these
Rationale: Explanation :
112% of S.P. = 280
S.P. = Rs.(280x 100/112) = Rs.250.
C.P. = Rs (100/125x 250) = Rs 200
Answer : A
Answer: (A) Rs 200
Question: How many factors of 990 are odd numbers greater than 1?
(A) 13
(B) 14
(C) 15
(D) 16
(E) 17
Rationale: When factorized, 990 has 5 prime factors. Of these prime factors 4 are odd and 1 is even. Hence total number of odd factors is 2*2*2*2(16), which includes 1. The total number of odd factors greater than 1 are 15.(option C)
Answer: (C) 15
Question: A sum of Rs.1420 is divided into 13 students so that each boy gets Rs.120 while each girl gets Rs.100. Find the number of boys and number of girls
(A) 8B, 5G
(B) 5B, 8G
(C) 4B, 9G
(D) 9B, 4G
(E) 6B, 7G
Rationale: 120B+100G=1420-----i
B+G=13-------ii
from i
100B+20B+100G=1420
100(B+G)+20B=1420
100(13)+20B=1420
By simplifing we get
B=6;G=7
ANSWER:E
Answer: (E) 6B, 7G
Question: For some integer p, p^2 - 5 is divisible by all of the following EXCEPT
(A) 30
(B) 38
(C) 41
(D) 29
(E) 31
Rationale: Hint: p^2-5 (p is an integer) is never multiple of 3 (try to prove this), hence 30 is out.
Answer: A
Answer: (A) 30
Question: The length of a room is 5.5 m and width is 3.75 m. Find the cost of paving the floor by slabs at the rate of Rs. 1200 per sq. metre.
(A) Rs. 15000
(B) Rs. 15550
(C) Rs. 24750
(D) Rs. 16500
(E) None of these
Rationale: Solution
Area of the floor = (5.5 × 3.75) m2 = 20.625 m2
∴ Cost of paving = Rs. (1200 × 20.625) = 24750. Answer C
Answer: (C) Rs. 24750
Question: How many seconds will a 500 meter long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr
(A) 25 Seconds
(B) 28 Seconds
(C) 30 Seconds
(D) 35 Seconds
(E) 40 Seconds
Rationale: Explanation:
Relative Speed = 63-3 = 60 Km/hr
= 60 *(5/18) = 50/3 m/sec
Time taken to pass the man will be
500âˆ—3/50=30seconds
ANSWER IS C
Answer: (C) 30 Seconds
Question: What is the length of the longest pole which can be kept in a room 12 m long, 4 m broad and 3 m high?
(A) 16
(B) 4
(C) 11
(D) 12
(E) 13
Rationale: d^2 = 12^2+4^2+3^2
d^2 = 122 + 42 + 32 = 13
Answer: E
Answer: (E) 13
Question: A number is doubled and 5 is added. If the resultant is trebled, it becomes 105. What is that number?
(A) 12
(B) 29
(C) 27
(D) 15
(E) 99
Rationale: Explanation:
Let the number be x.
Therefore,
3(2x + 5) = 105
6x + 15 = 105
6x = 90
x = 15
ANSWER:D
Answer: (D) 15
Question: The Present worth of Rs.2310 due years hence ,the rate of interest being 15% per annum, is :
(A) Rs.1440
(B) Rs.1750
(C) Rs.1680
(D) Rs.1840
(E) None of these
Rationale: Explanation:
P.W.=Rs.[100×2310/100+(15×52)]=Rs.1680.
Answer: C
Answer: (C) Rs.1680
Question: All even numbers from 2 to 98 inclusive, except those ending in 0, are multiplied together what is the rightmost digit (the units digit) of the product?
(A) 0
(B) 2
(C) 4
(D) 6
(E) 8
Rationale: first multifly all numbers ending with 2 those are 2*12*22*32*42.......*92=2^10=4 is last digit
multify all numbers ending with 4=4^10=6 last digit
multify all numbers ending with 6=6^10= 6 last digit
multifly all numbers ending with 8=8^10=4 last digit
so 4*6*6*4=6 last digit
ANSWER:D
Answer: (D) 6
Question: A basket contains 5 apples of which one is rotten. If Henry is to select 2 apples from the basket simultaneously and at random what is the probability that the 2 apples selected will include the rotten apple?
(A) 1/5
(B) 3/10
(C) 2/5
(D) 1/2
(E) 3/5
Rationale: Direct probability approach:
P=15∗44+45∗14=25P=15∗44+45∗14=25: probability of {first apple rotten, second apple good} plus the probability of {first apple good, second apple rotten}.
Reverse probability approach:
Again 1- the probability of the opposite event --> P=1−45∗34=25P=1−45∗34=25.
Answer: C
Answer: (C) 2/5
Question: What is the units digit of 29! + 50! + 3! + 3!?
(A) 0
(B) 2
(C) 4
(D) 6
(E) 8
Rationale: For all N greater than 4, the units digit of N! is 0.
The sum of the four units digits is 0 + 0 + 6 + 6 = 12
The units digit is 2.
The answer is B.
Answer: (B) 2
Question: If the milk and water ware added in the ratio 5:4 then how much more water should be added so he gets the ratio of 6:7.
(A) 11/6
(B) 11/7
(C) 11/8
(D) 6/11
(E) 7/11
Rationale: let quantity of water should added be x then
A/Q
5/(4+x)= 6/7
=> 35=24+6x
=> x=11/6
ANSWER:A
Answer: (A) 11/6
Question: if 5 tomatoes are worth 8 oranges,5 oranges are worth 4 apples, 7 apples are worth 3 pineapples and 7 pineapples cost rs.203,then he approx price of each tomato is
(A) 16
(B) 5
(C) 19
(D) 20
(E) none of these
Rationale: 7 pineapples cost rs.203 means one pineapple cost is 29
7 apples are worth 3 pineapples means 7 apple cost 29*3. 1 Apple cost (29*3)/7
5 oranges are worth 4 apples. 1 orange cost is (29*3*4)/(7*5)
5 tomatoes are worth 8 oranges. 1 tomato cost is (29*3*4*8)/(7*5*5) = 2784/175 = 15.9
ANSWER:A
Answer: (A) 16
Question: A school’s annual budget for the purchase of student computers increased by 60% this year over last year. If the price of student computers increased by 20% this year, then the number of computers it can purchase this year is what percent greater than the number of computers it purchased last year?
(A) 33.33%
(B) 40%
(C) 42%
(D) 48%
(E) 60%
Rationale: If last year, the budget was B and the price of one computer was P, then B/P was the number of purchased computers.
This year, 1.6B/(1.2P) = 4/3(B/P) = 1.33(B/P) computers can be purchased, which is 33.33% greater than the number of computers purchased last year.
Answer A.
Answer: (A) 33.33%
Question: An unbiased cubic die is thrown.What is the probabiltiy of getting a multiple of 3 or 4?
(A) 1/9
(B) 1/12
(C) 1/2
(D) 3/4
(E) 3/8
Rationale: Explanation :
Total numbers in a die=6P(mutliple of 3) = 2/6 = 1/3P(multiple of 4) = 1/6P(multiple of 3 or 4) = 1/3 + 1/6 = 1/2
Answer : C
Answer: (C) 1/2
Question: In a class there are 55 pupil, out of them 10 are in debate only and 18 in singing only. Then how many in both?
(A) 132
(B) 26
(C) 17
(D) 11
(E) 12
Rationale: Explanation:Total pupil = 55
Debate + Singing = 10 + 18 = 28
The intersection for two = 55 â€“ 10 â€“ 28 = 17 play both games.
Answer: C
Answer: (C) 17
Question: Anna left for city A from city B at 5.20 a.m. She traveled at the speed of 80 km/hr for 2 hrs 15 min. After that the speed was reduced to 60 km/hr. If the distance between two cities is 350 kms, at what time did Anna reach city A?
(A) 9.20 a.m
(B) 9.25 a.m
(C) 9.35 a.m
(D) 10.05 a.m
(E) None of these
Rationale: Explanation:
Distance covered in 2 hrs 15 min i.e., 2 1/4 hrs = 80 * 9/4 = 180 hrs.
Time taken to cover remaining distance = (350 - 180)/60 = 17/6 hrs
= 2 5/6 = 2 hrs 50 min
Total time taken = (2 hrs 15 min + 2 hrs 50 min) = 5 hrs 5 min.
So, Anna reached city A at 10.25 a.m.
ANSWER IS E
Answer: (E) None of these
Question: If point A coordinates are (-6, -3) point B coordinates are (8 ,4 ) if C is along the line A-B so that AC = 1/2 CB. What are the coordinates of point C.
(A) (-2, - 2/3)
(B) (2, -2/3)
(C) (2/3, -2)
(D) (0, 2)
(E) (2, 2/3)
Rationale: Look at the diagram below:
Line segment.pngSince, AC= 1/2 CB, then AC = 1/3 AB. This implies that point C is closer to A than to B, which on the other hand implies that the x-coordinate of C must be less than (-6+8)/2=0.5. Only D and A fits, but as (0 , 2) is clearly not on line segment AB, then the answer must be B.
Answer: B.
Answer: (B) (2, -2/3)
Question: Of the 420 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) 200 to 260
(B) 160 to 260
(C) 220 to 260
(D) 220 to 300
(E) 40 to 100
Rationale: W=260
P=300
ALL=420
N(NEITHER)=AT LEAST 60
BOTH=?
W+P-BOTH+N=ALL
260+300-BOTH+60=420
BOTH=200
now pay attention to the fact, that both at most can be 260, since W=260
so, the answer is A
Answer: (A) 200 to 260
Question: A seller of used cars has 10 cars to sell and each of his clients selected 2 cars that he liked most. If each car was selected exactly thrice, how many clients visited the garage?
(A) 8
(B) 10
(C) 15
(D) 14
(E) 16
Rationale: IfNo caris selected more than once then the number of clients = 10/2 =5
But since every car is being selected three times so No. of Clients must be thrice as well =5*3 = 15
Answer: option C
Answer: (C) 15