mathewhe/aqua_rat huggingface dataset:
Question: A fair coin is to be tossed twice and an integer is to be selected at random from one of the integers 3, 8, and 10. What is the probability that at least one head is tossed and an even integer is selected?
(A) 1/6
(B) 1/4
(C) 1/3
(D) 1/2
(E) 7/12
Rationale: 1) Let us simply state the possibilities. This method works for this problem due to the limited number of possibilities
Ways of getting at least a head and an even number =6
HT8
TH8
HT10
TH10
HH8
HH10
Ways of not getting at least one head and an even number=6
TT8
TT10
HT3
TH3
HH3
TT3
Total probability=6/12=1/2
Answer:D
Answer: (D) 1/2
Question: Elizabeth bought a dress with a 35% off coupon. If the dress cost her $87.61, what is the original selling price of the dress?
(A) $134.78
(B) $250.31
(C) $118.27
(D) $87.61
(E) None of these.
Rationale: Explanation:CP of Elizabeth is 35% of the Original SP.:. Original SP = $87.61x100/65 = $134.78.Answer: Option A.
Answer: (A) $134.78
Question: In a set of numbers from 100 to 400 inclusive, how many integers are odd and do not contain the digit 5?
(A) 180
(B) 196
(C) 286
(D) 288
(E) 324
Rationale: We have to find the total number of 3-digit odd numbers not having 5 as a digit.
Units digits will be among 1,3,5,7,9
Tenth digits will be among 0,1,2,3,4,6,7,8,9
Hundredth digits will be among 1,2,3,4
So total numbers = 5*9*4 =180
Answer : A
Answer: (A) 180
Question: How many seconds will a train 100 meters long take to cross a bridge 150 meters long if the speed of the train is 36 kmph?
(A) 22 sec
(B) 77 sec
(C) 25 sec
(D) 18 sec
(E) 17 sec
Rationale: D = 100 + 150 = 250
S = 36 * 5/18 = 10 mps
T = 250/10 = 25 sec
Answer:C
Answer: (C) 25 sec
Question: A discount of 20 percent on an order of goods followed by a discount of 30 percent amounts to
(A) the same as one 44 percent discount
(B) the same as one 40 percent discount
(C) the same as one 36 percent discount
(D) the same as one 30 percent discount
(E) the same as one 25 percent discount
Rationale: 0.8*0.7*x=0.56x from initial value, meaning 0.44 or 44% discount
A
Answer: (A) the same as one 44 percent discount
Question: Car A runs at the speed of 60 km/hr and reaches its destination in 8 hours. Car B runs at the speed of 70 km/h and reaches its destination in 4 hours. What is the ratio of distances covered by Car A and Car B?
(A) 3 : 7
(B) 4 : 9
(C) 12 : 7
(D) 5 : 7
(E) 6 : 11
Rationale: Car A travels 60 × 8 = 480 km
Car B travels 70 × 4 = 280 km
The ratio is 480 : 280 = 48 : 28 = 12 : 7
The answer is C.
Answer: (C) 12 : 7
Question: A person distributed 20% of his income to his 3 children each. He deposited 30% of his income to his wife's account. He donated 5% of remaining amount to an orphan house.Finally he has $40000. Find his total income?
(A) 452000
(B) 562000
(C) 800000
(D) 500000
(E) 652000
Rationale: 3 children got = 3*20% = 60%
wife got = 30%
orphan house = 5%
total = 60+30+5 = 95%
remaining = 100-95 = 5%
5% = 40000
100% = 40000*100/5 = $800000
Answer is C
Answer: (C) 800000
Question: A man rows his boat 95 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream?
(A) 6
(B) 7
(C) 10
(D) 8
(E) 9
Rationale: Speed downstream = d/t = 95/(2 1/2) = 38 kmph
Speed upstream = d/t = 45/(2 1/2) = 18 kmph
The speed of the stream = (38 - 18)/2
= 10 kmph
Answer: C
Answer: (C) 10
Question: How many 3 digit numbers can be formed from the digits 2,3,5,6,7 and 9 which are divisible by 5 and none of the digits is repeated?
(A) 30
(B) 20
(C) 10
(D) 45
(E) 50
Rationale: Since each desired number is divisible by 5,
so we much have 5 at the unit place.
The hundreds place
can now be filled by any of the remaining 4 digits .
so, there4 ways of filling it.
Required number of numbers = (1 * 5 * 4)
= 20
Ans: B
Answer: (B) 20
Question: A Jar contains a mixture of AB in the ratio 4:1. When 30 L of Mixture is replaced with liquid B, ratio becomes 2:3. How many liters of liquid A was present in mixture initially.
(A) 12
(B) 48
(C) 16
(D) 20
(E) 25
Rationale: 30 litres of mixture that is replaced will contain 24 litres of A and 6 litres of B (as A:B = 4:1)
Let the initial volume of the mixture be 4K + 1K = 5K
So by condition ,
[ 4K-24]/ [ K-6+30 ] = 2/3 = > 12K-72 = 2K-12+60 => 10K = 120
Solve for K which is K = 12
So initial volume of liquid A = 4K = 48 litres
Answer : B
Answer: (B) 48
Question: The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 20000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is:
(A) 23
(B) 49
(C) 22
(D) 20
(E) 21
Rationale: Let the total number of workers be x. Then,
8000x = (20000 * 7) + 6000(x - 7)
= 2000x = 98000
= x = 49.
ANSWER:B
Answer: (B) 49
Question: In the faculty of Reverse-Engineering, 500 second year students study numeric methods, 300 second year students study automatic control of airborne vehicles and 300 second year students study them both. How many students are there in the faculty if the second year students are approximately 50% of the total?
(A) 1100
(B) 1200
(C) 1150
(D) 1000
(E) 1050
Rationale: Total number of students studying both are 500 + 300 - 300 = 500 (Subtracting the 300 since they were included in the both the other numbers already).
So 50% of total is 500, so 100% is 1000
Answer is D
Answer: (D) 1000
Question: What is the units digit of 32! + 50! + 4! + 4!?
(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 + 4 + 4 = 8
The units digit is 8.
The answer is E.
Answer: (E) 8
Question: Look at this series: 36, 34, 30, 28, 24, ... What number should come next?
(A) 20
(B) 22
(C) 23
(D) 26
(E) 28
Rationale: Explanation: This is an alternating number subtraction series. First, 2 is subtracted, then 4, then 2, and so on.
Answer: Option B
Answer: (B) 22
Question: If a rectangular room measures 10 meters by 5 meters by 4 meters, what is the volume of the room in cubic centimeters? (1 meter=100 centimeters)
(A) 24,000
(B) 240,000
(C) 2,400,000
(D) 200,000,000
(E) 240,000,000
Rationale: D. 200,000,000
10*100*5*100*4*100 = 200,000,000
Answer: (D) 200,000,000
Question: One room length is 16 m and breadth 12m.outside this room there is corridor 3.5 m wide.in this corridor how much stone will be used of size 7 decimeter× 5 decimeter?
(A) 600
(B) 700
(C) 800
(D) 900
(E) 400
Rationale: Area of room = (16*12) sq.m= 192 sq.m
Area of room along with corridor=[(16+2*3.5)×(12+2*3.5)] sq.m=(23×19)=437 sq.m.
Area of corridor=[437-192]=245 sq.m
Area of one stone=[7/10*5/10]=7/20sq.m
No. of stone=245×20/7=700
Answer B
Answer: (B) 700
Question: Baker Ram is storing cake boxes in cartons that measure 25 inches by 42 inches by 60 inches. If the measurement of each cake box is 8 inches by 7 inches by 5 inches, then what is the maximum number of cake boxes that can be placed in each carton?
(A) 330
(B) 300
(C) 252
(D) 225
(E) 210
Rationale: Baker Ram is storing cake boxes in cartons The dimensions of the carton are 25x 42x 60and those of each cake box are 8x 7x 5.
To maximize number of boxes try and fit maximum into the base of the box. If you take the base as 25x 42and fit 5 x 6 boxes of 5x 7, then the total number of boxes is 5 x 6 x integer(60/8) = 5 x 6 x 7 = 210.
Alternatively you could try taking the base as 60x 42and fit 12 x 6 boxes of 5x 7, then the total number of boxes is 12 x 6 x integer(25/8) = 12 x 6 x 3 = 216. But since that is not an answer option, I go with (E) 210.
Answer: (E) 210
Question: The length of each side of square A is increased by 100 percent to make square B. If the length of the side of square B is increased by 75 percent to make square C, by what percent is the area of square C greater than the sum of the areas of squares A and B?
(A) 75%
(B) 80%
(C) 145%
(D) 150%
(E) 180%
Rationale: Let length of each side of square A be 10
Area of A = 10^2 = 100
Since , length of each side of square A is increased by 100 percent to make square B
length of each side of square B = 2*10 = 20
Area of B = 20^2 = 400
Since , length of the side of square B is increased by 75 percent to make square C
length of each side of square C= 1.75*20 = 35
Area of C= 35^2 = 1225
Difference in areas of C and cummulative areas of A and B = 1225 -(400+100) = 725
percent is the area of square C greater than the sum of the areas of squares A and B = (725/500) * 100 % = 145%
Answer C
Answer: (C) 145%
Question: A girl sitting in a train which is travelling at 100 kmph observes that a goods train travelling in a opposite direction, takes 6 seconds to pass him. If the goods train is 560 m long, find its speed.
(A) 230
(B) 232
(C) 234
(D) 236
(E) 238
Rationale: Relative speed = (560/6)m/s = (560/6)*(18/5) = 336 kmph
speed of goods train = 336-100 = 236 kmph
Answer is E
Answer: (E) 238
Question: A certain deck of cards contains 2 blue cards, 2 red cards, 2 yellow cards, and 2 green cards. If two cards are randomly drawn from the deck, what is the probability that they will both be not Yellow?
(A) 15/28
(B) 1/4
(C) 9/16
(D) 1/32
(E) 1/16
Rationale: The question asks they will both be not Yellow. Considering that these are draws without replacement there are following possibilities :
draw 1, draw 2
===== =====
1) Not Yellow, Yellow;
2) Yellow, Not Yellow;
3) Yellow, Yellow;
4) Not Yellow, not Yellow;
The answer has to be either P(4) OR all exclusion of the 3 previous conditions i.e. 1- [P(1) + P(2) + P(3)] => neither of the draws are Yellow
P(4) = 6/8*5/7=15/28
1- [P(1) + P(2) + P(3)] = 1 - [ (6/8 * 2/7) + (2/8*6/7) + (2/8*1/7)] = 1 - [26/8*7] = 1 - [13/28] = 15/28
A
Answer: (A) 15/28
Question: A set of numbers has an average of 30. If the largest element is 4 greater than 3 times the smallest element, which of the following values cannot be in the set?
(A)  85
(B)  95
(C)  23
(D)  50
(E)  55
Rationale: Ans: B
Solution: we are given the relation between smallest and the largest term. so let the smallest a and largest be 3a+4
so the avg = 50
which tells us that any value of a must be less than 30
so a<50 means, largest value 3a+4 <(3*30)+4
=largest value must be <94
so 95 can not be the value in the set.
Answer: (B)  95
Question: John had a stock of 1400 books in his bookshop. He sold 75 on Monday, 50 on Tuesday, 64 on Wednesday, 78 on Thursday and 135 on Friday. What percentage of the books were not sold?
(A) 50.4%
(B) 71.3%
(C) 66.5%
(D) 34.9%
(E) 43.5%
Rationale: Let N be the total number of books sold. Hence
N = 75 + 50 + 64 + 78 + 135 = 402
Let M be the books NOT sold
M = 1400 - N = 1400 - 402 = 998
Percentage
Books not sold / total number of books = 998/1400 = 0.713 = 71.3%
correct answer B
Answer: (B) 71.3%
Question: Ram borrowed some money at the rate of 6% p.a. for the first three years, 8% p.a.for the next six years and 10% p.a.for the period beyond nine years If the total interest paid by him at the end of 12 years is 19200, how much money did he borrow?
(A) 18,000
(B) 10,000
(C) 25,000
(D) 20,000
(E) None of these
Rationale: Let the sum be x. Then,
(x×3×6/100)+(x×6×8/100)+(x×3×10/100)=19200
⇒ 18x + 48x + 30x = (19200 × 100)
⇒ 96x = 1920000
⇒ x = 20000.
Answer D
Answer: (D) 20,000
Question: If (d-5)(y+2) = 0 which of the following must be true?
(A)  d = y
(B)  d > y
(C)  d < y
(D)  dy = -10
(E)  None of the above
Rationale: From (d-5)(y+2) = 0 it follows that either d=5 or y=-2.
(A) d = y --> not necessarily true. Consider d=5 and y=0.
(B) d > y --> not necessarily true. Consider d=5 and y=10.
(C) d < y --> not necessarily true. Consider d=5 and y=0.
(D) dy = -10 --> not necessarily true. Consider d=5 and y=0.
Thus, none of the statements must be true.
Answer: E.
Answer: (E)  None of the above
Question: The length of the bridge, which a train 130 meters long and travelling at 45 km/hr can cross in 30 seconds, is:
(A) 200 m
(B) 225 m
(C) 245 m
(D) 250 m
(E) 280 m
Rationale: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (130 + X)/30 = 25/2 ==> 2(130 + X) = 750 ==> X = 245 m.
ANSWER:C
Answer: (C) 245 m
Question: Can you find the missing number in the sequence given below?
10 14 18 11 15 ? 12 16 20 13 17 21
(A) 25
(B) 23
(C) 20
(D) 18
(E) 19
Rationale: Let's break the given series as below:
10 14 18
11 15 ?
12 16 20
13 17 21
Now read the number from left hand side from top to bottom as :
So the number that will replace '?' is 19
Answer : E
Answer: (E) 19
Question: A box contains 4 black, 3 red and 6 green marbles. 3 marbles are drawn from the box at random. What is the probability that both the marbles are of the same color?
(A) 24/286
(B) 25/709
(C) 25/286
(D) 24/268
(E) 24/226
Rationale: Explanation:
Total marbles in a box = 4 black + 3 red + 6 green marbles = 13 marbles
3 marbles are drawn from 13 marbles at random. Therefore,
n(S) = 13C3= 286 ways
Let A be the event that 2 marbles drawn at random are of the same color. Number of cases favorable to the event A is
n(A) = 4C3 + 3C3+ 6C3 = 4 +1 + 20 = 25
Therefore, by definition of probability of event A,
P(A) = n(A)/n(S) = 25/286
ANSWER:C
Answer: (C) 25/286
Question: The average score of a cricketer for five matches is 45 runs. If the average for first three matches is 30, then average for last two matches is
(A) 33.25
(B) 32.25
(C) 67.5
(D) 60.5
(E) 45.5
Rationale: Explanation:
=(45×5)−(30×3)/2
=(225 −90)4=67.5
Answer: Option C
Answer: (C) 67.5
Question: By selling 16 pencils for a rupee a man loses 20%. How many for a rupee should he sell in order to gain 20%?
(A) 28
(B) 25
(C) 24
(D) 23
(E) 21
Rationale: 80% --- 16
120% --- ?
80/120 * 16 = 24
Answer:C
Answer: (C) 24
Question: What is the place value of 4 in the numeral 4125
(A) 2500
(B) 3400
(C) 3500
(D) 3000
(E) 4000
Rationale: Option 'E'
4 * 1000 = 4000
Answer: (E) 4000
Question: A man performs 1/2 of the total journey by rail, 1/3 by bus and the remaining 5km on foot. His total journey is
(A) 16km
(B) 10km
(C) 12km
(D) 30km
(E) 25km
Rationale: Explanation:
Let the journey be x km
Then, 1x/2 + 1x/3 +5 =x
5x +30 =6x
X = 30km
Answer: Option D
Answer: (D) 30km
Question: In a division sum, the remainder is 6 and the divisor is 5 times the quotient and is obtained by adding 17 to the thrice of the remainder. The dividend is
(A) 74
(B) 146
(C) 86
(D) 92
(E) 98
Rationale: Divisor = (6 * 3) + 17 = 35
5 * Quotient = 35
Quotient = 7.
Dividend = (Divisor * Quotient) + Remainder
Dividend = (20 * 7) + 6 = 146.
B)
Answer: (B) 146
Question: Calculate how many ways a woman who has 5 bags and 4 books can put the books in her bag?
(A) 625
(B) 635
(C) 615
(D) 325
(E) 125
Rationale: First paper can be put in 5 ways, similarly second, third, and forth books also can be put in 5 ways.
So total number of ways = 5 x 5 x 5 x 5 = 625
A
Answer: (A) 625
Question: Solve below question 2x + 1 = -17
(A) -8
(B) -9
(C) 9
(D) 8
(E) -7
Rationale: 1. Subtract 1 from both sides:
2x + 1 - 1 = -17 - 1
2. Simplify both sides:
2x = -18
3. Divide both sides by 2:
4. Simplify both sides:
x = -9
B
Answer: (B) -9
Question: A machine manufactures notebooks in a series of five colors: red, blue, black, white, and yellow. After producing a notebook of one color from that series, it produces a notebook of the next color. Once five are produced, the machine repeats the same pattern. If the machine began a day producing a red notebook and completed the day by producing a black notebook, how many notebooks could have been produced that day?
(A) 27
(B) 34
(C) 50
(D) 61
(E) 78
Rationale: A machine manufactures notebooks in a series of five colors: red, blue, black, white, and yellow.
Machine starts manufacturing Red and ended on Black.
This means that either machine has manufactured 3, 8, 13, 18, 23, 28, 33, 38, 43, 48, 53, 58, 63, 68, 73, 78
Only 78 is given in the options. So answer = 78
ANSWER:E
Answer: (E) 78
Question: The ratio of the amount of the oil bill for the month of February to the amount of the oil bill for the month of January was 5:4. If the oil bill for February had been $45 more, the corresponding ratio would have been 3:2. How much was the oil bill for January?
(A) $60
(B) $90
(C) $120
(D) $150
(E) $180
Rationale: 5:4 = 15:12 and 3:2 = 18:12.
An increase in $45 increases the ratio by 3:12.
Therefore an increase in $15 increases the ratio by 1:12.
Therefore, January's bill was 12($15) = $180.
The answer is E.
Answer: (E) $180
Question: The area of an isosceles trapezoid with sides of length 5 and bases of length 8 and 14 is?
(A) 22
(B) 32
(C) 44
(D) 55
(E) 56
Rationale: we can divide the trapezoid into two triangles and a rectangle
sides of triangle , t1 --> h1 =5 , b1 =3 , s1= root(25-9) = 4 = s2 of triangle t2
area of triangle = (1/2)*4*3=6
side of the rectangle = 8*4=32
total area of the trapezoid= 32+6+6=44
ANSWER:C
Answer: (C) 44
Question: A man can row with a speed of 15 kmph in still water. If the stream flows at 1 kmph, then the speed in downstream is?
(A) 10 kmph
(B) 5 kmph
(C) 20 kmph
(D) 16 kmph
(E) 25 kmph
Rationale: M = 15
S = 1
DS = 15 + 1 = 16
ANSWER:D
Answer: (D) 16 kmph
Question: A person is traveling at 25km/hr and reached his destiny in 9hr find the distance?
(A) A)100km
(B) B)95km
(C) C)135km
(D) D)80km
(E) E)225km
Rationale: speed = 25km/hr
time = 9hr
distance = 25*9 = 225km
Answer is E
Answer: (E) E)225km
Question: Which of the following correctly lists the data sets in order of greatest to least standard deviation?
I. 8, 9, 10, 11, 12, 13
II. 12, 12, 12, 12, 12, 12
III. 47, 56, 58, 60, 64, 69
(A) I, II, III
(B) I, III, II
(C) III, I, II
(D) II, III, I
(E) II, I, III
Rationale: out of three given sets,
II has all numbers same, so it has zero standard deviation hence it is Least
I has consecutive numbers , hence all are closedly spaced hence std deviation will be less
while in III,numbers are spread widely hence std deviation should be more than II
hence order should be II, I,III
IMO E
Answer: (E) II, I, III
Question: Given two fair dice, what is the probability E that the sum of their numbers is 4 if exactly one die shows a 3?
(A) a) 2/11
(B) b) 1/18
(C) c) 3/11
(D) d) 2/39
(E) e) 1/5
Rationale: If exactly one die shows 3, there are 10 such combinations (given that we have 2 fair dice).
1:3, 2:3, 4:3, 5:3, 6:3,
3:1, 3:2, 3:4, 3:5, 3:6
The sum of numbers would be 4 for two events: 1:3, 3:1.
E=2/11 would be the answer if 'at least one of the die shows a 3'.A
Answer: (A) a) 2/11
Question: If a and b are odd integers which of the following must be an even integer?
(A) a/b
(B) ab
(C) (ab)^2
(D) ab + b
(E) (a + b)/b
Rationale: Certainly (D)
ab+b=b(a+1)
Sine both a & b are ODD , we can say ( a + 1 ) is EVEN as ODD + 1 = EVEN
Hence there is no doubt that the OA must be (D)
ANSWER:D
Answer: (D) ab + b
Question: if the price of a book is first decreased by 20% and then increased by 20%, then the net change in the price will be :
(A) 10
(B) 388
(C) 4
(D) 29
(E) 22
Rationale: Explanation:
Let the original price be Rs. 100.
Decreased by 20% = 80
Then increased 20% on Rs 80 = 80 + 16 = 96
Net change in price = 100 - 96 = 4
Answer : C
Answer: (C) 4
Question: The ratio of three numbers is 6:7:5 and their sum is 108. The second number of the three numbers is?
(A) 12
(B) 42
(C) 30
(D) 36
(E) None of these
Rationale: Explanation:
6:7:5
Total parts = 18
18 parts --> 108
1 part ---->6
The second number of the three numbers is = 7
7 parts ----> 42
Answer: Option B
Answer: (B) 42
Question: If x and y are both odd prime numbers and x < y, how many distinct positive R integer factors does 2xy have?
(A) 3
(B) 4
(C) 6
(D) 8
(E) 12
Rationale: Since 2xy prime R factors are x^1*y^1*2^1, its total number or factors must be (1+1)(1+1)(1+1)=2^3=8. Thus, I think D would be the correct answer.
Answer: (D) 8
Question: Three students appear at an examination of Mathematics. The probability of their success are 1/3, 1/4, 2/5 respectively. Find the probability of success of at least two.
(A) 1/4
(B) 2/5
(C) 3/4
(D) 3/5
(E) 4/5
Rationale: The probability of success of at least two students will involve the following possibilities.
The first two students are successful, the last two students are successful, the first and third students are successful and all the three students are successful.
Therefore, the required probability = 1/3 x 1/4 x 3/5 + 1/4 x 2/5 x 2/3 + 1/3 x 2/5 x 3/4 + 1/3 x 1/4 x 2/5 = 1/4
ANSWER:A
Answer: (A) 1/4
Question: Which of the following is closer to (24!+23!)/(24!-23!)?
(A) 49
(B) 36
(C) 25
(D) 1
(E) 16
Rationale: Notice that 24! = (24)(23!), so we can factor out 23! from top and bottom.
(24!+23!)/(24!-23!)=[23!(24+1)]/[23!(24-1)]
= (24+1)/(23-1)
= 25/23
≈ 1
Answer: D
Answer: (D) 1
Question: Molly can do a task in 15 days while Sandy can do the task in 30 days. How many days will it take to complete the task if both work together?
(A) 8
(B) 10
(C) 11
(D) 12
(E) 14
Rationale: Each day, Molly can do 1/15 of the task.
Each day, Sandy can do 1/30 of the task.
Each day, they can do 1/15 + 1/30 = 1/10 of the task.
The task will be completed in 10 days.
The answer is B.
Answer: (B) 10
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) 288
(B) 668
(C) 240
(D) 299
(E) 121
Rationale: Speed = [54 * 5/18] m/sec = 15 m/sec.
Length of the train = (15 * 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:C
Answer: (C) 240
Question: A store reduced the price of all items in the store by 15% on the first day and by another 10% on the second day. The price of items on the second day was what percent of the price before the first reduction took place?
(A) 76.5
(B) 80.9
(C) 81.0
(D) 81.1
(E) 81.9
Rationale: consider price of the all items as $100
after a initial reduction of 15% price becomes = 0.85 *100 = $ 85
after the final reduction of 10% price becomes = 0.9* 85 = $ 76.5
price of all items on second day is 76.5% of price on first day
correct answer option A
Answer: (A) 76.5
Question: What is his percentage profit made by Osborn if he purchased 30 dozen watches at Rs. 50 per dozen. He sold 12 dozens at 12% profit and the remaining 18 dozens with 17% profit?
(A) 12.6%
(B) 13.6%
(C) 16.6%
(D) 15.6%
(E) 14.6%
Rationale: Explanation :
C.P of 30 dozen = Rs.(50 x 30) = Rs.1500
C.P of 12 dozen = Rs. (50 x12) = Rs. 600.
C.P of 18 dozen =Rs. (50 x18) = Rs. 900
profit on 12 dozen at 12% = 12/100*600 = 72
profit on 18 remaining dozen at 18% = 18/100*900 = 162
total profit = 72 + 162 = 234
% profit = ?/100*1500 = 234
= 15.6%
Answer : D
Answer: (D) 15.6%
Question: A box contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the box, if at least one black ball is to be included in the draw?
(A) 54
(B) 58
(C) 62
(D) 64
(E) 68
Rationale: We may have(1 black and 2 non-black) or (2 black and 1 non-black) or (3 black).
Required number of ways	= (3C1 x 6C2) + (3C2 x 6C1) + (3C3)
= 3 x	6 x 5 + 3 x 2	x 6 + 1
2 x 1	2 x 1
= (45 + 18 + 1)
= 64
Answer: D.
Answer: (D) 64
Question: A sock drawer contains five socks, each one a different solid color. The colors of the socks are red, orange, yellow, 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) 10
(B) 15
(C) 21
(D) 36
(E) 42
Rationale: Since here order of socks is not important then we'll have 5C2 i.e. 10 combinations.
Answer : A
Answer: (A) 10
Question: A Fruit store sells four varieties of Mangoes. A,B,C & D. IF A Costs 15% less than B, and C costs 20% less than A,and D costs 25% less than C what percent of B's cost is D?
(A) 40%
(B) 38%
(C) 44%
(D) 46%
(E) 51%
Rationale: Soln:-
B=100
A 15% less than B = 85
C 20% less than A = 68
D 25% less than C = 51
D is what percent of B = D/B * 100
= 51/100 * 100 = 51%
ANSWER:E
Answer: (E) 51%
Question: A number consists of two digits whose sum is 11. If 27 is added to the number, then the digits change their places. What is the number ?
(A) 47
(B) 65
(C) 83
(D) 92
(E) 82
Rationale: If number is xy , then x +y =11
and
10x+y +27 = 10y+x
solving these eqns, we get
x=4 and y =7
so number is 47.
ANSWER:A
Answer: (A) 47
Question: 8 x 5.4 - 0.6 x 10/1.2 = ?
(A) 30
(B) 45
(C) 50
(D) 31
(E) 21
Rationale: Given Expression
= (43.2 - 6)/1.2
= 37.2/1.2
= 31
Answer is D.
Answer: (D) 31