MU-NLPC/Calc-aqua_rat huggingface dataset:
If 1 kilometer is approximately 0.6 mile, which of the following best approximates the number of kilometers in 3 miles?  Answers.
A) 12/3  B) 1/3  C) 9/5  D) 2/3  E) 4/3

Solution: 1 km is approxmately equal to 0.6 miles   So 3 km = 3*0.6= 
3*0.6 = 1.8
1.8 miles . Multiple & divide by 10   i.e 1.8*10/10= 18/10 = 9/5   Answer : 9/5
Answer: C
A coin is tossed live times. What is the probability that there is at the least one tail? Pick one:  A) 31/32  B) 31/38  C) 31/36  D) 31/34  E) 34/32

Solution: 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.   31/32nswer:31/32
Answer: A
A customer using a certain telephone calling plan pays a fee of $25 per month, and then receives a discount of 40% on the regular charge for all calls made to country R. If calls to country R are regularly charged at $1.60 per minute for the first 3 minutes, and $0.80 per minute for each minute thereafter, what is the maximum the customer could have saved over regular prices if he was charged for 1 hour of calls made to country R in a certain month?
Choose the correct choice from the following choices
A) $8.75 B) $12 C) $13.40 D) $17.40 E) $24.40

Solution: Discount = 40% of spending   We want to maximise discount so we will need to maximise spending. We do that by assuming that 60 calls were made of 1 min each because the first minute is the most expensive.   Max discount = (40/100)* 60 * 1.6 = (40/100)*96   This would be slightly less than 40. About 38 to 39.   Saving = (Slightly less than 40) - 25 = Slightly less than 15 charged in R country   Answer ($13.40)
Answer: C
20 litres of mixture of acid and water contain 10% water. How much water should be added so that percentage of water becomes 20% in this mixture? Choose the correct choice from the following answers.
A) 2 L	B) 3 L	C) 2.5 L	D) 4 L	E) 5 L

Solution: total mixture =20ltr   water contain = 10% of 20ltr => 2ltr water   it means 18ltr is acid in that mixture   we have to make 20% water so..20% of 20 = 4ltr water must be there in the new mixture   we have already 2 ltr water so we have to add 2 ltr more   2 LNSWER:2 L
Answer: A
Due to construction, the speed limit along an 4-mile section of highway is reduced from 55 miles per hour to 35 miles per hour. Approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?	Choose the correct choice from the following answers:  A) 5  B) 8  C) 10  D) 15  E) 2

Solution: 4/35 - 4/55 = 4/5 * ( 11 - 7)/77   = 4/5 * 4/77 * 60 min   = 4 * 12 * 4/77   = 192/77 ~ 2.4   Answer - 2
Answer: E
The average salary of a person for the months of January, February, March and April is Rs.8000 and that for the months February, March, April and May is Rs.8400. If his salary for the month of May is Rs.6500, find his salary for the month of January?	Pick one.
A) s.4580
B) s.4570
C) s.4500
D) s.4550
E) s.4900

Solution: Sum of the salaries of the person for the months of January, February, March and April   = 4 * 8000= 
4 * 8000 = 32_000
32000 ----(1)   Sum of the salaries of the person for the months of February, March, April and May= 4 * 8400= 
4 * 8400 = 33_600
33600 ----(2)   (2)-(1) i.e. May - Jan= 1600   Salary of May is Rs.6500   Salary of January = Rs.4900   Answer:s.4900
Answer: E
Q is a set of four distinct prime numbers. If the sum of the integers in Q is even and the number x is a member of Q, then what is the least value that x can be?
Options:
A) 2	B) 3	C) 4	D) 5	E) 7

Solution: Sum of 4 prime integers is Even   So all four integers should be odd numbers as including 2 in the set will make the sum Odd   Smallest odd prime number is 3   So Answer: 3
Answer: B
In how many ways can 5 boysand 2 girls be arranged at a table if 2 girls are never together? Options:  A) 350  B) 390  C) 400  D) 420  E) 480

Solution: Total ways of arranging 7 person in a circle = 6! = 720 ways   If we consider two women as one, then we have   5+1= 
  5+1 = 6
6 persons. Arranging these six persons in circle will take= 5! = 120 ways   And two women can arrange themselves in 2! ways   Total ways in which two women sit together in circle = 5!*2! = 240 ways   Total ways in which two women doesn’t sit together in circle = 6! - 5!*2! = 720 - 240= 
720 - 240 = 480
480 ways   480
Answer: E
The area of a square field 3136 sq m, if the length of cost of drawing barbed wire 3 m around the field at the rate of Rs.3.50 per meter. Two gates of 1 m width each are to be left for entrance. What is the total cost?
Choose one
A) s.1014
B) s.1140
C) s.999
D) s.1085
E) s.2331

Solution: a2 = 3136 => a = 56   56 * 4 * 3= 
56 * 4 * 3 = 672
672 – 6= 666 * 3.5= 
666 * 3.5 = 2_331
2331   ANSWs.2331R:s.2331
Answer: E
Evaluate: 60 - 9÷3×6 =  Choose the most appropriate option
A) 52
B) 18
C) 42
D) 102
E) 36

Solution: According to order of operations, 9÷3×6 (division and multiplication) is done first from left to right   9÷3×6 = 3 × 6 = 18   Hence   60 - 9÷3×6 = 60 - 18= 
60 - 18 = 42
42   correct answer 42)42
Answer: C
On tuesday, the original price of a shirt was discounted by 20%. On Monday, the price of the shirt was marked up H percent so that the new price on Monday was 20% more than the original price before the discount. What is the value of H?
Choose the correct choice from the following answers:
A) 20% B) 30% C) 33 1⁄3% D) 40% E) 50%

Solution: Let the original price be 100   discounted Price = 80   New Price = 20 +100= 
20 +100 = 120
120   H=(40/80)*100   Ans:50%
Answer: E
A,B,C invested the capitals in a business. If A invested Rs. 20,000 more than B and C invested Rs.10,000 more than A, then how should a profit of Rs.14,000 be divided among A,B and C? Given : Capital of B is Rs.10,000
Choices
A) 5500, 2500, 6000
B) 5200, 2800, 6000
C) 4250, 2250, 7500
D) 5250, 1750, 7000
E) 5300, 2700, 6000

Solution: A==30,000   B==10,000   C==40,000   so, ration are3:1:4   profit 14000   so,, 14000/8==1750   so,, A==5250, B==1750,, C==7000   ANSWER:5250, 1750, 7000
Answer: D
If the perimeter of a rectangular garden is 600 m, its length when its breadth is 100 m is? Answers
A) 827 m
B) 876 m
C) 200 m
D) 256 m
E) 197 m

Solution: 2(l + 100) = 600   => l = 200 m   Answer: 200 m
Answer: C
Find the unit's digit in 264^102+264^103  Pick:
A) 0  B) 1  C) 2  D) 3  E) 5

Solution: Required unit's digit = unit's digit in 4102+4103.4102+4103.   Now, 4242 gives unit digit 6.   ⇒ 41024102 gives unit digit 6.   ⇒ 41034103 gives unit digit of the product 6×46×4 i.e., 4.   Hence, unit's digit in 264102+264103264102+264103   = unit's digit in (6+4)=0   0
Answer: A
Kim has 7 pairs of shoes; each pair is a different color. If Kim randomly selects 2 shoes without replacement from the 14 shoes, what is the probability that she will select 2 shoes of the same color?  Choose the correct answer:
A) 2/5
B) 1/5
C) 1/9
D) 1/10
E) 1/13

Solution: Total pairs = 14C2 = 91; Same Color Pairs= 7C1*1C1=7; Prob = 1/13   Ans 1/13
Answer: E
When Tom works alone he chops 3 lb. salad in 2 minutes, and when Tammy works alone she chops 2 lb. salad in 3 minutes. They start working together, and after some time finish chopping 65 lb. of salad. Of those 80 lb., the salad quantity chopped by Tom is what percent greater than the quantifying chopped by Tommy?.	Choose the correct choice from the following
A) 44%	B) 100%	C) 125%	D) 225%	E) 400%

Solution: Tammy chops 4 lbs in 6 minutes   Tom chops 9 lbs in 6 minutes   So in the same amount of time, Tammy chops 125% more than Tom, since 9 is 125% greater than 4. So 125% is the answer.   Note that the actual time doesn't matter. If you multiply the time each work by x, you'll multiply the work each does by x, and 9x is still 125% greater than 4x.   Ans :125%
Answer: C
At what price must an article costing Rs.47.50 be marked in order that after deducting 6% from the list price. It may be sold at a profit of 25% on the cost price?
Choose the correct choice from the following.
A) 63.16
B) 62.6
C) 62.1
D) 62.7
E) 62.2

Solution: CP = 47.50   SP = 47.50*(125/100)= 
47.50*(125/100) = 59.375
59.375   MP*(94/100)= 59.375   MP = 63.16   63.16nswer: 63.16
Answer: A
A car started running at a speed of 30 km/hr and the speed of the car was increased by 2 km/hr at the end of every hour. Find the total distance covered by the car in the first 8 hours of the journey.
Pick: A) 296 km B) 352 km C) 642 km D) 742 km E) 382 km

Solution: The total distance covered by the car in the first 8 hours = 30 + 32 + 34 + 36 + 38 + 40 + 42 + 44 = sum of 8 terms in AP whose first term is 30 and last term is 44 = 8/2 [30 + 44] = 296 km.   296 kmNSWER:296 km
Answer: A
A man takes twice as long to row a distance against the stream as to row the same distance in favour of the stream. The ratio of the speed of the boat in still water and stream is	Select.
A) 3:1	B) 1:3	C) 2:4	D) 4:2	E) None of these

Solution: Explanation:   Let speed downstream = x kmph   Then Speed upstream = 2x kmph   So ratio will be,   (2x+x)/2 : (2x-x)/2   => 3x/2 : x/2 => 3:1   Option 3:1
Answer: A
20 is subtracted from 80% of a number, the result is 60. Find the number?
Select the correct option:  A) 150  B) 997  C) 100  D) 288  E) 271

Solution: (80/100) * X – 20 = 60   8X = 800   X = 100   Answer:100
Answer: C
The ages of 2 persons differ by 18 years. If 12 years ago the elder one be 6 times as old as the younger one, find the present age of elder person.	Select the correct option:  A) 33.6  B) 47  C) 50.4  D) 52.4  E) 47.9

Solution: age of the younger person = x   age of the elder person = x+18   6(x-12) = x+18-12   x= 15.6   age of elder person = 15.6+18= 
15.6+18 = 33.6
33.6   33.6nswer is 33.6
Answer: A
How many 3-digit numerals begin with a digit that represents a odd prime and end with a digit that represents a prime number?  Options: A) 16 B) 80 C) 160 D) 120 E) 240

Solution: prime digits 2,3,5 and 7.   three digit numbers _ _ _   1st place can be filled in 3 ways   2nd place can be filled in 10 ways   3rd place can be filled in 4 ways   Total=3*10*4= 
3*10*4 = 120
120   Ans : 120
Answer: D
X is a set containing 8 different positive odd numbers. Y is a set containing 7 different numbers, all of which are members of X. Which of the following statements CANNOT be true?  Choose the correct choice from the following options.
A) The range of Y is even.  B) The mean of X is even.  C) The mean of Y is even.  D) The range of X is equal to the range of Y.  E) The median of Y is equal to the mean of Y.

Solution: Option C.   Given: X is a set containing 8 different positive odd numbers   Easily inferred: Y is a set containing 7 different odd numbers   (A) The range of Y is even. - Always even, since it is a difference of two odd numbers   (B) The mean of X is even. - can be. suppose 8 numbers consist of 4 pairs of (16n-1,16n+1) for different values of n. Adding these will give a multiple of 16, which when divided by 8 (to arrive at mean), will give an even number   (C) The mean of Y is even. - Cannot be. Mean = (sum of 7 odd numbers)/7 = Odd number/odd number thus cannot be even.   (D) The range of X is equal to the range of Y.   (E) The median of Y is equal to the mean of Y   The mean of Y is even.
Answer: C
If x > 1, which of the following decreases as x decreases?
I. 1/(x + x^2)
II. 2x^2 − x
III. 1/(x + 1)  Pick one
A) I only B) II only C) III only D) I and II only E) II and III only

Solution: let x= 4 and 3 b old and new values   ST1: x= 4 -> 4+16 =1/ 20   x=3-> 3+9 = 1/12 ...increased   ST2:x= 4-> 2*16-4 = 28   x=3->2*9-3 = 15   decreased   St3: x=4-> 1/4 = .25   x=3->1/3 = .33   Ans: II only
Answer: B
A watch passes through three hands and each person gains 25%. If the third person sells it for $187.50, what did the first person pay for it?  Pick:	A) $84	B) $88	C) $92	D) $96	E) $100

Solution: 1.25*1.25*1.25 * original price = 187.5   (5/4)^3 * original price = 187.5   original price = 64*187.5 / 125= 
64*187.5 / 125 = 96
$96   The answer is $96.
Answer: D
There are 18 stations between Hyderabad and Bangalore. How many second class tickets have to be printed, so that a passenger can travel from any station to any other station?	Choose the correct choice from the following choices:
A) 827	B) 234	C) 246	D) 346	E) 380

Solution: The total number of stations = 20   From 20 stations we have to choose any two stations and the direction of travel (i.e., Hyderabad to Bangalore is different from Bangalore to Hyderabad) in ²⁰P₂ ways.   ²⁰P₂ = 20 * 19= 
20 * 19 = 380
380.   Answer: 380
Answer: E
One ton has 2500 pounds, and one pound has 16 ounces. How many packets containing wheat weighing 16 pounds and 4 ounces each would totally fill a gunny bag of capacity 13 tons?
Choose the correct choice from the following choices:
A) 2000  B) 1700  C) 2350  D) 2500  E) 8000

Solution: 16 pounds and 4 ounces= 16*16 + 4= 
16*16 + 4 = 260
260 ounces.   13 tons= 13*2500 pound = 13*2500*16 ounces.   Hence the answer is   (13*2500*16)/260= 
  (13*2500*16)/260 = 2_000
2000.   2000nswer: 2000.
Answer: A
96 is divided into two parts in such a way that seventh part of first and ninth part of second are equal. Find the smallest part? Choices:
A) 66	B) 26	C) 42	D) 27	E) 11

Solution: x/7 = y/9 => x:y = 7:9   7/16 * 96= 
7/16 * 96 = 42
42   Answer: 42
Answer: C
x, y, a, and b are positive integers. When x is divided by y, the remainder is 6. When a is divided by b, the remainder is 10. Which of the following is NOT a possible value for y + b?	Choose the correct choice from the following choices
A) 24 B) 21 C) 20 D) 16 E) 15

Solution: Important note: remainder is ALWAYS less than divisor, thus y>6 and b>10 --> y+b>16.   Answer: 16.
Answer: D
A train running at a speed of 36 kmph crosses an electric pole in 12 seconds. In how much time will it cross a 360 m long platform? Choose the correct answer:  A) 19  B) 27  C) 29  D) 48  E) 28

Solution: Let the length of the train be x m.   When a train crosses an electric pole, the distance covered is its own length.   So, x = 12 * 36 * 5 /18= 
12 * 36 * 5 /18 = 120
120 m.   Time taken to cross the platform= (120 +360)/ 36 * 5/18   = 48 min.   Answer:48
Answer: D
At a certain laboratory, chemical substance are identified by an unordered combination of three different colors. If no chemical may be assigned the same three colors as any other, what is the maximum number of substances that can be identified using six colors? Choose the correct choice from the following options
A) 20  B) 35  C) 105  D) 135  E) 210

Solution: The prompt tells us that substance is identified by an UNORDERED combination of 3 colors and that no chemical may be assigned the same 3 colors as any other chemical.   20s an example, a chemical with the colors 20/B/C means that the following combinations C20NNOT be used by any other chemical:   20BC   20CB   B20C   BC20   C20B   CB20   By extension, the first part of your calculation would be the number of possible substances that could be identified with 6 colors: 6c3 = 20 possible substances   20
Answer: A
Lane can make a handcrafted drum in 4 weeks. Zane can make a similar handcrafted drum in 6 weeks. If they both work together, how many weeks will it take for them to produce 15 handcrafted drums?
Choose one:
A) 30
B) 36
C) 70
D) 80
E) 150

Solution: Method I: the rates solution   “Lane can make a handcrafted drum in 4 weeks. Zane can make a similar handcrafted drum in 6 weeks.” Lane’s rate is (1 drum)/(4 weeks) = 1/4. Zane’s rate is (1 drum)/(6 weeks) = 1/6. The combined rate of Lane + Zane is   R = 1/4 + 1/6 = 3/12 + 2/12 = 5/12   That’s the combined rate. We need to make 15 drums — we have a rate and we have an amount, so use the “art” equation to solve for time:   T = A/R = 15/(5/12) = 15*(12/5) = (15/5)*12 = 3*12= 
3*12 = 36
36   BTW, notice in the penultimate step, the universal fraction strategy: cancelbeforeyou multiply (Tip #3:http://magoosh.com/gmat/2012/can-i-use- ... -the-gmat/. Lane and Zane need 36 weeks to make 15 drums.   Answer= 36.
Answer: B
Two trains are approaching each other at 60 mph each. The length of each train is 1/6 miles. When
the two locomotives(engines) meet, how many seconds will it take for them to pass each other
completely?
Select:	A) 15 sec	B) 12 sec	C) 10 sec	D) 18 sec	E) None of these

Solution: Explanation :   Total distance to cover = 2*(1/6) = 2/6 miles   Relative speed = 60+60= 
60+60 = 120
120mph   Time taken= (2/6)/120*3600= 
(2/6)/120*3600 = 10
10 sec.   Hence (C) is the answer.   Answer : 10 sec
Answer: C
There are 14 people in a room. If each person shakes hands with exactly 3 other people, what is the total number of handshakes?  Choices
A) 18	B) 21	C) 35	D) 42	E) 56

Solution: Note that each handshake includes two people.   The total number of handshakes is  14*3/2= 
 14*3/2 = 21
21   The answer is 21.
Answer: B
How many numbers between 100 and 900 begin or end with 3?
Choose the correct choice from the following answers.
A) 80
B) 100
C) 150
D) 170
E) 190

Solution: How many numbers between 100 and 900 begin or end with 3?   Just think that those numbers are:   i) The ones ending in 3: 103, 113, 123, ... , 893 --> 80 numbers   ii) The ones beginning in 3: 300, 301, 302, 303, ... , 393, ... , 399 --> 100 numbers   BUT 10 out of the first 80 numbers are repeated in the second set.   THEREFORE, the solution is 170 numbers.   Answer: 170
Answer: D
If 4x + y = 12 and −x + y = 44, then what is the value of 3x + 2y?
Choose the correct answer:
A) 1/7	B) 3	C) 15	D) 52/7	E) 56

Solution: 4x + y = 12   −x + y = 44   Adding both the equations --> 3x + 2y = 56   Answer: 56
Answer: E
A box contains ten bulbs out of which 5 are defective. If five bulbs are chosen at random, find the probability that atleast one bulb is good Options: A) 225/226 B) 225/229 C) 225/228 D) 225/224 E) 251/252

Solution: Required probability = 1- 5C5/10C5=1 - 1/252 = 251/252.Answer:251/252
Answer: E
Two alloys A and B are composed of two basic elements. The ratios of the compositions of the two basic elements in the two alloys are 5 : 3 and 1 : 2, respectively. A new alloy X is formed by mixing the two alloys A and B in the ratio 4 : 3. What is the ratio of the composition of the two basic elements in alloy X ? Select the correct option.
A) 1 : 1
B) 2 : 3
C) 5 : 2
D) 4 : 3
E) 7 : 9

Solution: Mixture A has a total of 5 + 3= 
5 + 3 = 8
8 parts. If in the final mixture this represents 4 parts, then the total number of parts in mixture B should be  (8/4)*3= 
 (8/4)*3 = 6
6.   So, we should take of mixture B a quantity with 2 and 4 parts, respectively.   This will give us in the final mixture (5 + 2) : (3 + 4), which means 7:7, or 1:1.   1 : 1nswer 1 : 1.
Answer: A
How many combinations of three letters taken from letters (a, a, b, c, c, d) are possible?	Select the correct option:
A) 12	B) 13	C) 10	D) 36	E) 56

Solution: So 4103 for abcd - 4 choices   3 more for aa(b,c or d)   3 more for cc(a,b or d)   total 10   Ans :10
Answer: C
A, B and C can do a piece of work in 11 days, 20 days and 55 days respectively, working alone. How soon can the work be done if A is assisted by B and C on alternate days?
Pick:  A) 7 days  B) 8 days  C) 9 days  D) 10 days  E) None of these

Solution: (A+B)'s 1 day's work=(1/11+1/20)=31/220;   (A+C)'s 1 day's work=(1/11+1/55)=6/55;   work done in 2 days=(31/220+6/55)=55/220=1/4   Now, 1/4 work is done by A in 2 days.   Whole work will be done in (2*4)= 
(2*4) = 8
8days.   Correct Option: 8 days
Answer: B
What approximate value should come in place of the question mark (?) in the following equation?
1.542 × 2408.69 + 3134.632 = ?
Choose the correct choice
A) 6800  B) 4800  C) 5200  D) 6400  E) 3600

Solution: Explanation 3700 + 3100= 
3700 + 3100 = 6_800
6800   6800nswer 6800
Answer: A
Each digit in the two-digit number G is halved to form a new two-digit number H. Which of the following numbers could be the sum of G and H? Choose the most appropriate option
A) 153 B) 150 C) 140 D) 138 E) 89

Solution: Let x be the original 2-digit number.   If each digit is halved, then the sum of G and H is 3x/2.   Note the sum must be a multiple of 3 and less than 150.   Of these five choices, only 138 satisfies these two conditions.   The answer is 138.
Answer: D
Ten cards numbered 1 to 10 are placed in a box, mixed up thoroughly and then one card is drawn
randomly. If it is known that the number on the drawn card is more than 3, what is the probability
that it is an even number? Select the correct option:
A) 1/4	B) 4/7	C) 2/3	D) 2/5	E) 3/5

Solution: Let A be the event ‘the number on the card drawn is even’ and B be the   event ‘the number on the card drawn is greater than 3’. We have to find P(A|B).   Now, the sample space of the experiment is S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}   Then A = {2, 4, 6, 8, 10}, 4/7 = {4, 5, 6, 7, 8, 9, 10}   and A n 4/7 = {4, 6, 8, 10}   Also P(A) = 5/2, P(4/7) = 7/10 and P(A n 4/7) = 4/10   Then P(A|4/7) = P(A n 4/7)/P(4/7) = (4/10)/(7/10) = 4/7   4/7
Answer: B
A large field of 700 hectares is divided into two parts. The difference of the areas of the two parts is one-fifth of the average of the two areas. What is the area of the smaller part in hectares?  Choose the correct choice from the following options.
A) 315 B) 339 C) 288 D) 299 E) 111

Solution: Explanation:   Let the areas of the two parts be x and (700-x) hectares   therefore,   So, the two parts are 385 and 315.   Hence, 315rea of the smaller = 315 hectares   315nswer: 315) 315
Answer: A
An Tiger walks an average of 500 meters in 12 minutes. A Horse walks 20% less distance at the same time on the average. Assuming the horse walks at her regular rate, what is its speed in km/h?
Choose one:
A) 2.215.
B) 2.5.
C) 2.775.
D) 3.2.
E) 2.0

Solution: the Tiger walks an average of 500 meters in 12 minutes   500 meters in 1/5 hours   the Horse walks 20% less distance = 500-100= 
500-100 = 400
400 meters in 12 minutes   0.400 km in 12/60= 1/5 hours   speed = 0.400*5= 
0.400*5 = 2
2.00 km/h   I guess option 2.0 should be 2.00
Answer: E
A man is 26 years older than his son. In two years, his age will be twice the age of his son. What is the present age of his son?	Choose the correct choice from the following answers
A) 23 years B) 22 years C) 24 years D) 20 years E) 19 years

Solution: Let present age of the son =x years   Then, present age the man =(x+26) years   Given that, in 2 years, man's age will be twice the age of his son   â‡’(x+26)+2=2(x+2)   â‡’x=24   ANSWER:24 years
Answer: C
Out of a classroom of 4 boys and 7 girls, the teacher randomly chooses a president for the student board, a vice president, and a secretary. What is the probability that only girls will be selected for all three positions? Choose the correct option:  A) 3/11  B) 5/11  C) 5/33  D) 7/33  E) 16/165

Solution: The number of ways to choose three people is 11C3=165.   The number of ways to choose three girls is 7C3=35.   P(only girls are chosen)=35/165=7/33   The answer is 7/33.
Answer: D
Difference of two numbers is 15. Two times of the first exceeds by 2 from the three times of the other. Then the numbers will be
Choose the most appropriate option: A) 28, 43 B) 43, 28 C) 15, 30 D) 30, 15 E) 25, 10

Solution: Explanation:   x - y = 15   2x Ã¢â‚¬â€œ 3y = 2   x = 43 y = 28 Answer: 43, 28
Answer: B
A box contains 3 yellow balls and 5 black balls. One by one, every ball is selected at random without replacement. What is the probability that the fourth ball selected is black?	Pick.
A) 1/4  B) 1/2  C) 1/2  D) 5/8  E) 2/3

Solution: Let the 5 black balls be BBBBB and 3 Red Balls be RRR   They can be arranged in 8 slots _ _ _ _ _ _ _ _   in (8!)/ (5!x3!)   If the fourth slot is Black ball then the arrangement will be to fill   _ _ _ B _ _ _ _   we have 7 slots and 4 Black (BBBB) and 3 Red (RRR)   They can be arranged in (7!)/ (4!x3!)   Hence required probability = [(7!)/ (4!x3!)] / [(8!)/ (5!x3!)]   Ans = 5/8 5/8
Answer: D
Which of the following year is not a leap year?	Options
A) 1960 B) 2080 C) 2024 D) 2100 E) None of these

Solution: SOLUTION :   The two conditions that decide that a year is a leap year or not is:   • For a year to be a leap year, it should be divisible by 4.   • No century is a leap year unless it is divisible by 400.   Hence, the year 2100 is not a leap year as it is not divisible by 400.   ANSWER IS 2100
Answer: D