mathewhe/aqua_rat huggingface dataset:
Question: If Rs. 782 be divided into three parts, proportional to 1/2:1/3:3/4, then the first part is?
(A) A)426
(B) B)526
(C) C)247
(D) D)204
(E) E)297
Rationale: Given ratio
= 1/2:2/3:3/4 = 6:4:9
1st part = 782 * 6/19
= Rs. 247
Answer:C
Answer: (C) C)247
Question: The total age of A and B is 15 years more than the total age of B and C. C is how many year younger than A
(A) 11
(B) 12
(C) 13
(D) 14
(E) 15
Rationale: Explanation:
Given that A+B = 15 + B + C
=> A ? C = 15+ B ? B = 15
=> C is younger than A by 15 years
Answer: Option E
Answer: (E) 15
Question: In a sequence of 12 numbers, each term, except for the first one, is 12^14 less than the previous term. If the greatest term in the sequence is 12^15, what is the smallest term in the sequence?
Thus, A12 = A1+12-1d
Where d is the difference between each pairs of consecutive terms. Since each term is 1211 less than the previous term, d=-1211Click individual answer choices for specific explanations.
From what I undersltand the formula for an arithmetic sequence represents
some-number-in-the-sequence= first-number-in-sequence +the-place-of-that-number - 1x the-difference-of-each-#-in-the-sequence
(A) 12^14
(B) 0
(C) 12^11
(D) 11·12^11
(E) 12^12
Rationale: there are total 12 terms. andgreatestterm is 12^15. Each term is 12^14 less than previous one. What does this signify? This shows it is an AP - a decreasing one. (NoticeEach term is 12^14 less than previous one')
Therefore, 12^15 is the first term of the AP and -12^14 is the difference between successive terms, the smallest term should be the last one.
Last term = First term + (n-1)*d
therefore, Last term = 12^15 + 11*(-12^14)
=> Last term = 12^15 - 11*12^14
=> Last term = 12^14 (12-11) = 12^14
Which is the smallest term.
Hence Ans A it is.
Answer: (A) 12^14
Question: The sequence a1, a2, a3, a4. a5 is such that an = a n-1 +5 for 2≤ n ≤ 5. If a5 = 35 what is the value of a1 ?
(A) 1
(B) 6
(C) 15
(D) 16
(E) 21
Rationale: Here, each value of an is the previous value plus 5
Since the numbers are less, the fastest way to solve this problem is to successively subtract 5 from a5 till you reach a1
a5 = 35
a4 = 30
a3 = 25
a2 = 20
a1 = 15 <<<< Ans C
Answer: (C) 15
Question: A milk vendor has 2 cans of milk. The first contains 25% water and the rest milk. The second contains 50% water. How much milk should he mix from each of the containers so as to get 12 litres of milk such that the ratio of water to milk is 3 : 5?
(A) 6 litres, 6 litres
(B) 6 litres, 7 litres
(C) 7 litres, 5 litres
(D) 5 litres, 5 litres
(E) None
Rationale: Let the cost of 1 litre milk be Re. 1
Milk in 1 litre mix. in 1st can =	3	litre, C.P. of 1 litre mix. in 1st can Re.	3
4	4
Milk in 1 litre mix. in 2nd can =	1	litre, C.P. of 1 litre mix. in 2nd can Re.	1
2	2
Milk in 1 litre of final mix. =	5	litre, Mean price = Re.	5
8	8
By the rule of alligation, we have:
C.P. of 1 litre mixture in 1st can C.P. of 1 litre mixture in 2nd can
3
4
Mean Price
5
8
1
2
1
8
1
8
Ratio of two mixtures =	1	:	1	= 1 : 1.
8	8
So, quantity of mixture taken from each can = 1/2	x 12 = 6 litres
Option A
Answer: (A) 6 litres, 6 litres
Question: Ram professes to sell his goods at the cost price but he made use of 900 grms instead of a kg, what is the gain percent?
A. 11%
(A) 11 1/9%
(B) 11 1/8%
(C) 11 9/9%
(D) 11 5/9%
(E) 11 1/5%
Rationale: 900 --- 100
100 --- ? => 11 1/9%
Answer:A
Answer: (A) 11 1/9%
Question: The average age of a class of 32 students is 16 yrs. if the teacher's age is also included, the average increases by one year. Find the age of the teacher
(A) 28 Years
(B) 30 Years
(C) 32 Years
(D) 37 Years
(E) 49 Years
Rationale: Total age of students is 32X16 = 512 Years
Total age inclusive of teacher = 33X (16+1) = 561
So, Teacher's age is 561-512 = 49 Yrs
There is a shortcut for these type of problems
Teacher's age is 16+(33X1) = 49 Years
E
Answer: (E) 49 Years
Question: Three pipes of same capacity A,B,C can fill a tank in 24 hours. If there are only two pipes A and B of same capacity, the tank can be filled in?
(A) 12
(B) 24
(C) 6
(D) 36
(E) 8
Rationale: The part of the tank filled by three pipes in one hour
= 1/24
=> The part of the tank filled by two pipes in 1 hour
= 2/3 * 1/24 = 1/36.
The tank can be filled in 36 hours.
Answer:D
Answer: (D) 36
Question: The difference of two numbers is 1565. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder. What is the smaller number ?
(A) A)270
(B) B)280
(C) C)290
(D) D)300
(E) E)310
Rationale: Let the smaller number be x. Then larger number = (x + 1565).
x + 1565 = 6x + 15
5x = 1550
x = 310
Smaller number = 310.
E)
Answer: (E) E)310
Question: Twenty percent of Country Y's yearly exports come from fruit exports. One-sixth of all fruit exports from Country Y are orange exports. If country Y generates $3 million from its orange exports, how much money does it generate from its yearly total of exports?
(A) $21.25m
(B) $25.5m
(C) $90m
(D) $127.5m
(E) $153m
Rationale: 2/10*1/6*(total) = 3
1/30*(total) = 3
(total) = 3*30 = 90
Answer: C.
Answer: (C) $90m
Question: Among 500 people, 56% like strawberry jam, 44% like apple jam, and 40% like raspberry jam. If 30% of the people like both strawberry and apple jam, what is the largest possible number of people who like raspberry jam but do not like either strawberry or apple jam?
(A) 20
(B) 60
(C) 80
(D) 86
(E) 150
Rationale: 56%+44%-30%=70% who like either Strawberry, Apple, or both.
That means 100%-70% = 30% do not like either Apple of Strawberry jam.
30% is the most possible that like raspberry jam but do not like either strawberry or apple (assuming nobody in the group does not like any)
E
Answer: (E) 150
Question: Becky, Merry and John want to share a chocolate bar evenly.
What part of the bar will each of them take?
What part of the bar will Becky and Merry have together?
(A) 1/3
(B) 2/3
(C) 2/4
(D) None of these
(E) Cannot be determined
Rationale: Solution
The children need to divide the bar into three pieces. So everyone will take 1/3 of the chocolate bar.
Two girls together will have two pieces, hence, mathematically speaking, they will have 2/3 of the bar
Answer B
Answer: (B) 2/3
Question: Two employees A and B are paid a total of Rs. 450 per week by their employer. If A is paid 150 percent of the sum paid to B, how much is B paid per week?
(A) 130
(B) 140
(C) 150
(D) 170
(E) 180
Rationale: Let the amount paid to A per week = x
and the amount paid to B per week = y
Then x + y = 450
But x = 150% of y = 150y/100 = 15y/10
∴15y/10 + y = 450
⇒ y[15/10 + 1] = 450
⇒ 25y/10 = 450
⇒ 25y =4500
⇒ y = 4500/25 =Rs.180
E
Answer: (E) 180
Question: A man jogging inside a railway tunnel at a constant speed hears a train approaching the tunnel from behind at a speed of 30 km/h, when he is one third of the way inside the tunnel. Whether he keeps running forward or turns back, he will reach the end of the tunnel at the same time the train reaches that end. The speed at which the man is running is:
(A) 6 km/hr
(B) 8 km/hr
(C) 10 km/hr
(D) 12 km/hr
(E) None of these
Rationale: Explanation :
Let the train is at distance y km from the tunnel and the length of the tunnel is x km. Man is at point C which is x/3 km away from B.
A ----------- B -------------- C ----------------D
<---- y------><------x/3-------><------2x/3------->
AB=y, BC =x/3 and CD =2x/3.
Let, M km/h be the speed of man.
Now, train is at A and man is at C and both will take same time for reaching from B.
=>y/30=x/3M.
=>M=10x/y . ----------------------(i)
Also, train and man will take some time for reaching at D.
=>(x+y)/30=2x/M.
=>M=20x/(x+y). ---------------------(ii)
From both the equations we get: x=y
And on putting value in any equation we get: M = 10 km/hr.
Answer : C
Answer: (C) 10 km/hr
Question: If 45-[28-{37-(15-*)}]= 58, then * is equal to:
(A) -29
(B) -19
(C) 19
(D) 29
(E) 39
Rationale: 45-[28-{37-(15-*)}]= 58 => 45-[28-{37-15+*}]=58
45-[28-37+15-*]=58 => 45[43-37-*]=58
45-[6-*]=58 => 45-6+*=58
39+*=58 => *=58-39
= 19
ANSWER:C
Answer: (C) 19
Question: X and Y invest Rs.21000 and Rs.17500 respectively in a business. At the end of the year, they make a profit of Rs.26400. What is the share of X in the profit?
(A) Rs.14400
(B) Rs.26400
(C) Rs.12000
(D) Rs.12500
(E) None of these
Rationale: Explanation :
Ratio of the investment = 21000 : 17500 = 210 : 175 = 42 : 35 = 6 : 5
Share of X in the profit = 26400 * (6/11) = 2400 * 6 = 14400 .. Answer : Option A
Answer: (A) Rs.14400
Question: If 0.75: x :: 5:8, then x is equal to:
(A) 1.29
(B) 1.28
(C) 1.20
(D) 1.21
(E) 1.22
Rationale: Explanation:
(x * 5) = (0.75 *8)
X=6/5 = 1.20
Answer: C) 1.20
Answer: (C) 1.20
Question: A train running at the speed of 60 km/hr crosses a pole in 5 seconds. Find the length of the train.
(A) 83.33
(B) 882
(C) 772
(D) 252
(E) 121
Rationale: Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (Distance) = Speed * Time
(50/3) * 5 = 83.33 meter.Answer: A
Answer: (A) 83.33
Question: Difference of two numbers is 1660. If 7.5% of the number is 12.5% of the other number , find the number ?
(A) 2490 and 4150
(B) 249 and 415
(C) 2400 and 4100
(D) 2290 and 4350
(E) 229 and 435
Rationale: Let the numbers be x and y. Then , 7.5 % of x =12.5% of y
X = 125*y/75 = 5*y/3.
Now, x-y =1660
5*y/3 –y =1660
2*y/3= 1660
y =[ (1660*3)/2] =2490.
One number = 2490, Second number =5*y/3 =4150
Answer is A.
Answer: (A) 2490 and 4150
Question: Helen went to the stationers and bought things worth Euro 26, out of which 30 paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
(A) uro 16.70
(B) uro 15.70
(C) uro 13.70
(D) uro 18.70
(E) uro 20.70
Rationale: E
Euro 20.70
Let the amount taxable purchases be Euro x.
Then, 6% of x = 30/100
x = (30/100 x 100/6) = 5.
Cost of tax free items = Euro [26 - (5 + 0.30)] = Euro 20.70
Answer: (E) uro 20.70
Question: A set of numbers has an average of 40. 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)  90
(C)  125
(D)  50
(E)  55
Rationale: Ans: C
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 40
so a<50 means, largest value 3a+4 <(3*40)+4
=largest value must be <124
so 125 can not be the value in the set.
Answer: (C)  125
Question: How many numbers can be formed from 1, 2, 3, 4, 5 (without repetition), when the digit at the unit’s place must be greater than that in the ten’s place?
(A) 54
(B) 60
(C) 50
(D) 2 x 4!
(E) 51 / 3
Rationale: The digit in the unit’s place should be greater than that in the ten’s place. Hence if digit 5 occupies the unit place then remaining four digits need not to follow any order. Hence the required numbers = 4!. However, if digit 4 occupies the unit place then 5 cannot occupy the ten’s position. Hence digit at the ten’s place will be one among 1, 2 or 3. This can happen in 3 ways. The remaining 3 digits can be filled in the remaining three places in 3! ways. Hence, in all we have (3 x 3!) numbers ending in 4. Similarly, if we have 3 in the unit’s place, the ten’s place can be either 1 or 2. This can happen in 2 ways. The remaining 3 digits can be arranged in the remaining 3 places in 3! ways. Hence, we will have (2 x 3!) numbers ending in 3. Similarly, we can see that there will be 3! numbers ending in 2 and no number ending with 1.
Hence, the total number of numbers = 4! + (3 x 3!) + (2 x 3!) + 3!
= 4! + 6 x 3! = 24 + (6 x 6) = 60
ANSWER:B
Answer: (B) 60
Question: Find the length of the longest pole that can be placed in a room 12 m long 8m broad and 9m high.
(A) 13
(B) 14
(C) 15
(D) 16
(E) 17
Rationale: Length of longest pole = Length of the diagonal of the room
= sqrt(12^2+8^2+9^2= sqrt(289)= 17 m.
Answer is E.
Answer: (E) 17
Question: The speed of a boat in upstream is 60 kmph and the speed of the boat downstream is 80 kmph. Find the speed of the boat in still water and the speed of the stream?
(A) 10 kmph
(B) 23 kmph
(C) 75 kmph
(D) 56 kmph
(E) 46 kmph
Rationale: Speed of the boat in still water
= (60+80)/2
= 70 kmph. Speed of the stream
= (80-60)/2
= 10 kmph.
Answer:A
Answer: (A) 10 kmph
Question: In how many ways can a group of 22 friends be seated round 2 tables if one of the tables can seat 12 and the other can seat 10 people?
(A) 15C5 * 9! *4!
(B) 15C3 * 8! *3!
(C) 15C4 * 9! *3!
(D) 22C2 * 11! *9!
(E) 26C5 * 10! *4!
Rationale: 12 people can be selected from 22 people in 22C12 ways.
Remaining 10 people can be selected from 10 people in 10C10 ways.
Now, arranging 12 people on a round table = (12-1) ! = 11!
Arranging 10 people on a round table = (10-1) ! = 9!
Hence, total number of ways = 22C12 * 11! * 10C10 * 9!
= 22C2 * 11! * 9!
D
Answer: (D) 22C2 * 11! *9!
Question: A coin is tossed live times. What is the probability that there is at the least one tail?
(A) 31/32
(B) 31/38
(C) 31/30
(D) 31/37
(E) 31/31
Rationale: Let P(T) be the probability of getting least one tail when the coin is tossed five times.
= There is not even a single tail.
i.e. all the outcomes are heads.
= 1/32 ; P(T) = 1 - 1/32 = 31/32
Answer:A
Answer: (A) 31/32
Question: Two trains 170 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?
(A) 10.6 sec
(B) 18.8 sec
(C) 14.8 sec
(D) 10.88 sec
(E) 11.88 sec
Rationale: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other = 170 + 160 = 330 m.
Required time = 330 * 9/250 = 297/25= 11.88 sec.
Answer: E
Answer: (E) 11.88 sec
Question: Henry got a weekly raise of $963. If he gets paid every other week, write an integer describing how the raise will affect his paycheck.
(A) 693
(B) 396
(C) 963
(D) 691
(E) 961
Rationale: Let the 1st paycheck be x (integer).
Henry got a weekly raise of $ 963.
So after completing the 1st week she will get $ (x+963).
Similarly after completing the 2nd week she will get $ (x + 963) + $ 963.
= $ (x + 963 + 963)
= $ (x + 1926)
So in this way end of every week her salary will increase by (C)$ 963.
Answer: (C) 963
Question: Present ages of X and Y are in the ratio 2:3 respectively. Four years hence this ratio will become 3:4 respectively. What is X's present age in years?
(A) 8
(B) 36
(C) 37
(D) 39
(E) 40
Rationale: Let the present ages of X and Y be 2x and 3x years respectively.
Then, (2x + 4)/(3x + 4) = 3/4
4(2x + 4) = 3(3x + 4) =>8x+16=9x+12 => x=4
X's present age = 2x = 2*4 = 8
ANSWER:A
Answer: (A) 8
Question: A tree increases annually by 1/8th of its height. By how much will it increse after 2 years, if it stands today 64 cm high?
(A) 72 cm
(B) 74 cm
(C) 75 cm
(D) 81 cm
(E) 83 cm
Rationale: Increase % = (1/8 x 100)%
= 12 1/2 % = 25/2 %
height after 2 years =(64 x(1+(25/2x100)power of 2)) cm
= (64 x 9/8 x 9/8 ) cm= 81 cm
Answer is D
Answer: (D) 81 cm
Question: If 32455 × 3145208 × m^100 is divisible by 5, which of the following could be the value of m?
(A) 6000209
(B) 5644564
(C) 2345678
(D) 1000000
(E) 2355232
Rationale: The first two terms are not divisible by 5, so we need the third term to be divisible by %. The only way that (m^10) is going to be a multiple of 5 is if m is a multiple of 5. Therefore, we need the single answer that is a multiple of 5.
Answer =(D)
Answer: (D) 1000000
Question: ABCD is a parallelogram on xy rectangular coordinate plane, three of the four vertices of parallelogram are (5,15) , (5,45) and (-5,15). Which can be the coordinate of fourth vertex?
(A) (-5,-5)
(B) (5,45)
(C) (-5,-25)
(D) (-5,10)
(E) (15,25)
Rationale: A(-5, 15)
B(5, 15)
C(5, 45)
X(-5, 45): Parallelogram=Square=AXCB, where AX||CB, AX=CB, XC||AB, XC=AB
Y(-5, 5): Parallelogram=AYBC, where AY||BC, AY=BC, AC||YB, AC=YB
Z(15, 45): Parallelogram=ACZB, where AC||ZB, AC=ZB, CZ||AB, CZ=AB
Ans:B
Answer: (B) (5,45)
Question: {3, 5, 8, y}
For the above mentioned Set, Mean of the set is equal to Range of the set then find out possible values of y
(A) 16/5, 28/3
(B) 4, 16/5
(C) 4, 16/5, 28/3
(D) 4, 28/3
(E) 3, 4, 5
Rationale: The set can have the following forms:
1. {3,5,8,y} , range = y-3 and mean = 4+y/4, y= 28/3
2. {3,5,y,8} , range = 5 and mean = 4+y/4, y=4
3. {3,y,5,8} , range = 5 and mean = 4+y/4, y=4
4. {y,3,5,8} , range = 8-yand mean = 4+y/4, y=16/5. But as y<3 (assumed here), y=3.2 can not be true. Hence reject this case.
Thus the possible values are 4 and 28/3.
D is the correct answer.
Answer: (D) 4, 28/3
Question: A small college reduced its faculty by approximately 23 percent to 195 professors. What was the original number of faculty members?
(A) 253
(B) 208
(C) 224
(D) 254
(E) 302
Rationale: If x is the original number of faculty members, then after 23% reduction in faculty members number is .77x
but we are given .77x = 195
x = 253
So the original number of faculty members is 253
Correct Answer - A
Answer: (A) 253
Question: A book is bought for $32 and sold for $56. What is the profit in percentage?
(A) 15
(B) 35
(C) 75
(D) 25
(E) 85
Rationale: 56/32 = 1.75
The answer is C.
Answer: (C) 75
Question: When a plot is sold for Rs. 18,700, the owner loses 15%. At what price must that plot be sold in order to gain 15%?
(A) Rs. 21,000
(B) Rs. 22,500
(C) Rs. 25,300
(D) Rs. 25,800
(E) Rs. 28,800
Rationale: 85 : 18700 = 115 : x
x = (18700 x 115)/85 = 25300.
Hence, S.P. = Rs. 25,300.
Answer: Option C
Answer: (C) Rs. 25,300
Question: There are many numbers that can be expressed as the sum of three squares in three different ways.
Can you find out the smallest of such number?
(A) 87
(B) 54
(C) 29
(D) 30
(E) 70
Rationale: B
54
7^2 + 2^2 + 1^1
6^2 + 3^2 + 3^2
2^2 + 5^2 + 5^2
Answer: (B) 54
Question: In Cliff’s impressive rock collection, there are half as many igneous rocks as sedimentary rocks. Of the igneous rocks, 3/4 are shiny and the rest are matte, while 1/5 of the sedimentary rocks are shiny. If there are 30 shiny igneous rocks, how many total rocks does Cliff have?
(A) 30
(B) 45
(C) 60
(D) 120
(E) 135
Rationale: We can start with the known quantity and then go on to find the others.
Shiny igneous ricks are 30. These are (3/4) of total igneous rocks.
(2/3)*Total igneous rocks = 30
Total igneous rocks = 30 * (4/3) = 40
Total sedimentary rocks = 2*Total igneous rocks = 2*40 = 80
Total number of rocks = 40 + 80 = 120
Answer (D)
Answer: (D) 120
Question: Tough and Tricky questions: Probability.
Medical analysts predict that half of all people who are infected by a certain biological agent could be expected to be killed for each day that passes during which they have not received an antidote. What fraction of a group of 1,000 people could be expected to be killed if infected and not treated for three full days?
(A) 16/81
(B) 7/8
(C) 2/3
(D) 19/27
(E) 65/81
Rationale: At the end of each day we will have 1/2 alive. So after 3 days we will have (1/2)^3 people alive. Therefore, fraction of dead people will be 1-(1/2)^3=7/8.
The correct answer is B.
Answer: (B) 7/8
Question: If the mean of numbers 28, x, 50, 78 and 104 is 62, what is the mean of 48, 62, 98, 124 and x?
(A) 76.5
(B) 58
(C) 39.8
(D) 90.3
(E) 66.67
Rationale: Mean = (Sum of all no. in series)/(no. in series)
M1 = 62 = (X+28+50+78+104)/(5)
62 x 5 = 260 + X
X = 50
Therefore mean of 2nd series
M2 = (X+48+62+98+124)/5
M2 = 76.5
Answer = A
Answer: (A) 76.5
Question: 10 men can prepare 20 toys in 12 days working 15 hours a day. Then in how many days can 24 men prepare 32 toys working 20 hrs a day?
(A) 4 days
(B) 10 days
(C) 20 days
(D) 25 days
(E) 26 days
Rationale: Explanation:
10*12*15/20 = 24*20*x/32
X=4
Answer: Option A
Answer: (A) 4 days
Question: Five bells begin to toll together at 12:00 noon and toll respectively at intervals of 4, 5, 6, 8, and 9. seconds. Not including the toll at 12:00 noon, how many more times will all five bells toll together before 3:01 pm (i.e. three hours and one minute later)?
(A) 25
(B) 30
(C) 35
(D) 40
(E) 45
Rationale: The least common multiple is 2*2*2*3*3*5=360.
10860 seconds / 120 = 30 + remainder.
The answer is B.
Answer: (B) 30
Question: The curved surface of a sphere is 64 pi cm2. Find its radius?
(A) 1 cm
(B) 4 cm
(C) 2 cm
(D) 3 cm
(E) 5 cm
Rationale: 4 Ï€r2 = 64 => r = 4
ANSWER B
Answer: (B) 4 cm
Question: Three times the first of three consecutive odd integers is 3 more than twice the third. The third integer is :
(A) 15
(B) 30
(C) 45
(D) 60
(E) 65
Rationale: Sol.
Let the three integers be x, x + 2 and x + 4. Then, 3x = 2(x + 4) + 3 = ⇔ x = 11.
∴ Third integer = x + 4 =15.
Answer A
Answer: (A) 15
Question: In what time will a train 120 m long cross an electric pole, it its speed be 144 km/hr?
(A) 2.5 sec
(B) 3 sec
(C) 8.9 sec
(D) 6.9 sec
(E) 2.9 sec
Rationale: Speed = 144 * 5/18
= 40 m/sec
Time taken = 120/40
= 3 sec.
Answer: B
Answer: (B) 3 sec
Question: The average score of a cricketer in 2 matches is 27 and in other 3 matches is 32. Then find the average score in all the 5 matches?
(A) 25
(B) 27
(C) 30
(D) 35
(E) 42
Rationale: Average in 5 matches = (2*27 + 3*32)/2+3 = 54+96 / 5 = 30
Answer is C
Answer: (C) 30
Question: The radius of the two circular fields is in the ratio 3: 5 the area of the first field is what percent less than the area of the second?
(A) 84%
(B) 94%
(C) 65%
(D) 64%
(E) 34%
Rationale: r = 3 πr2 = 9
r = 5 πr2 = 25
25 π – 16 π
100 ---- ? => 64%
Answer:D
Answer: (D) 64%
Question: A certain library assesses fines for overdue books as follows. On the first day that a book is overdue, the total fine is $0.07. For each additional day that the book is overdue, the total fine is either increased by $0.30 or doubled, whichever results in the lesser amount. What is the total for a book on the fifth day it is overdue?
(A) $0.60
(B) $0.70
(C) $0.86
(D) $0.90
(E) $1.00
Rationale: 1st day fine - 0.07
2nd day fine - 0.07*2 = 0.14 (as doubling gives lower value)
3rd day fine - 0.14*2 = 0.28 (as doubling gives lower value)
4rd day fine - 0.28*2 = 0.56 (as doubling gives lower value)
5th day fine - 0.56 + 0.3 = 0.86 (as doubling gives higher value we add 0.3 this time)
Answer: C.
Answer: (C) $0.86
Question: (2^2+4^2+6^2+.....+20^2)=?
(A) 770
(B) 1155
(C) 1540
(D) 385x385
(E) None of them
Rationale: =(1x2)^2+(2x2)^2,+(2x3)^3+......(2x10)^2
=2^2 x (1^2+2^2+3^2+.......+10^2)
formula is =1/6 n(n+1)(2n+1)
=(4x1/6x10x11x21)
=(4x5x77)=1540
Answer is C
Answer: (C) 1540
Question: If 3 spiders make 3 webs in 3 days, then 1 spider will make 1 web in how many days?
(A) 7
(B) 6
(C) 5
(D) 4
(E) 3
Rationale: Let the required number days be x.
Less spiders, More days (Indirect Proportion)
Less webs, Less days (Direct Proportion)
spiders 1:3
Webs 3:1
1 x 3 x x = 3 x 1 x 3
=> x= 3
Answer is E
Answer: (E) 3
Question: How many three digits numbers can be formed by using the digits 1,2,3,4,5.
(A) 255
(B) 135
(C) 225
(D) 125
(E) 175
Rationale: We have to determine the total number of three digits numbers formed by using the digits 1,2,3,4,5. Clearly the repetition of digits allowed.Units place can be filled by any of the digits in 5 ways. Simillarly each one of the tens and hundreds place can be filled in 5 ways. Total number of required number =5x5x5 =125 Answer : D
Answer: (D) 125
Question: If 4 people are selected from a group of 5 married couples, what is the probability that none of them would be married to each other?
(A) 1/33
(B) 2/33
(C) 1/3
(D) 16/33
(E) 8/21
Rationale: If we are to select 4 people from 5 couples WITHOUT any restriction, how many ways can we make the selection? 10!/4!6! = 210
If we are to select 4 people from 5 couples WITH restriction that no married couple can both make it to the group, only a representative?
5!/4!1! = 5
But we know that to select a person from each couple, take 2 possibilities
5*2*2*2*2 = 80
Probability = Desired/All Possibilities = 80/210 = 8/21
Answer: E
Answer: (E) 8/21
Question: What is the probability that a leap year has 53 Sundays and 52 Mondays?
(A) 1/8
(B) 1/7
(C) 1/3
(D) 1/5
(E) 1/2
Rationale: A leap year has 52 weeks and two days
Total number of cases = 7
Number of favourable cases = 1
i.e., {Saturday, Sunday}
Required Probability = 1/7
Answer: B
Answer: (B) 1/7
Question: If a * b * c =(√(a + 2)(b + 3)) / (c + 1), find the value of 6 * 15 * 3.
(A) 8
(B) 5
(C) 11
(D) 3
(E) 4
Rationale: 6 * 15 * 3 = (√(6 + 2)(15 + 3) )/ (3 + 1)
= (√8 * 18) / 4
= (√144) / 4
= 12 / 4 = 3.
Answer is D.
Answer: (D) 3