MU-NLPC/Calc-aqua_rat huggingface dataset:
If 12 men or 20 women can do a piece of work in 54 days, then in how many days can 9 men and 21 women together do the work?  Select the correct option:	A) 10 days	B) 30 days	C) 20 days	D) 80 days	E) 40 days

Solution: B 30 days   Given that 12m = 20w => 3m = 5w   9 men + 21 women = 15 women + 21 women = 36 women   20 women can do the work in 54 days. So, 36 women can do it in   (20 * 54) /36= 
  (20 * 54) /36 = 30
30 days.
Answer: B
If 13 = 13w/(1-w) ,then (3w)2 =	Choose the correct answer:
A) 1/4  B) 1/2  C) 1  D) 2  E) 3

Solution: 13-13w=13w   26w=13   w=1/2   3w=3/2   3w*2=3/2*2= 
3/2*2 = 3
3   ANSW3R:3
Answer: E
Find the odd man out
892, 444, 220, 112, 52, 24  Answers:
A) 52 B) 112 C) 220 D) 444 E) 544

Solution: 24x2+4=52   52x2+4=108   108x2+4=220   220x2+4=444   ANSWER:112
Answer: B
Find the area of a parallelogram with base 26 cm and height 12 cm?	Choose the correct option:
A) 281  B) 284  C) 288  D) 255  E) 312

Solution: Area of a parallelogram = base * height   = 26 * 12= 
26 * 12 = 312
312 cm2   Answer: 312
Answer: E
January 1, 2004 was a Thursday, what day of the week lies on January 1 2005.	Choose the correct choice
A) Saturday  B) Monday  C) Saturday  D) Tuesday  E) None of these

Solution: Explanation :   Given that January 1, 2004 was Thursday.   Odd days in 2004 = 2 (because 2004 is a leap year)   (Also note that we have taken the complete year 2004 because we need to find out the odd days from 01-Jan-2004 to 31-Dec-2004, that is the whole year 2004)   Hence January 1, 2005 = (Thursday + 2 odd days) = Saturday. Answer : Option Saturday
Answer: C
A football coach must choose 4 freshers from a team of 11 players. How many different ways can the coach choose the freshers? Choose the correct option.
A) 330	B) 650	C) 729	D) 800	E) 890

Solution: Choose 4 starters from a team of 11 players. Order is not important.   \inline {\color{Black} 11C_{4}}= 330   330
Answer: A
There are seven thieves. They stole diamonds from a diamond merchant and ran away. While running, night sets in and they decide to rest in the jungle.
When everybody was sleeping, two of them woke up and decided to divide the diamonds equally among themselves. But when they divided the diamonds equally, one diamond is left.
So they woke up the 3rd thief and tried to divide the diamonds equally again but still one diamond was left. Then they woke up the 4th thief to divide the diamonds equally again, and again one diamond was left. This happened with the 5th and 6th thief – one diamond was still left.
Finally, they woke up the 7th thief and this time the diamonds were divided equally.
How many diamonds did they steal in total? Choose the correct choice from the following answers:	A) 2397	B) 2401	C) 2411	D) 2423	E) None of the above

Solution: We need a number that is a multiple of 7 that will give a remainder of 1 when divided by 2, 3, 4, 5, and 6. The least common multiple of these numbers is 60. So, we need a multiple of 7 that is 1 greater than a multiple of 60.   Answer 2401
Answer: B
Three is the largest number that can be divided evenly into 27 and the positive integer x, while 10 is the largest number that can be divided evenly into both 100 and x. Which of the following is the largest possible number that could be divided into x and 2100  Answers: A) 30 B) 70 C) 210 D) 300 E) 700

Solution: Since 3 is the GCF of 27 (3.3.3) and x => x has only one "3 in its prime box.   Since 10 (2.5) is the GCF of 100 (2.2.5.5) and x => x has only one 2 and one 5 in its primebox.   So x = 2.3.5.n (n=something that is not 2, 3, 5)   2100 = 2.3.5.7 =210   The GCF of x and 2100 is the product of the common factors of x and 2100 => the max possible is 2100.   ANSWER:210
Answer: C
Increasing the original price of an article by 15% and then increasing the new price by 15% again is equivalent to increasing the original price by what %?  Choose one.
A) 34 B) 40 C) 68 D) 88 E) 102

Solution: Let the price of a commodity is increased by a% and then b% then the final increment will be   1 + a/100 + b/100 + ab/10000   Now the same logic can be applied with decrements also with just changing the signs.   Let for example price of commodity is increased by a% and then decreased by b% then the resulting increase/decrease will be   1 + a/100 - b/100 -ab/10000   For the above question the approach will be    1 + 0.15 + 0.15 + 0.0225= 
 1 + 0.15 + 0.15 + 0.0225 = 1.3225
1.3225==> 32.25%   Closest answer is 34
Answer: A
Which of the following is a prime number ?
Choose the correct option
A) 33
B) 81
C) 97
D) 93
E) none

Solution: 97learly, 97 is a prime number
Answer: C
The average of first seven prime numbers which are between 30 and 70 is	Answers
A) 35.4 B) 42 C) 44.4 D) 57 E) 67

Solution: Explanation :   first seven prime numbers which are between 30 and 70 = 31, 37, 41, 43, 47, 53, 59   average = (31 + 37 +41 + 43 + 47 + 53 + 59)/7   = 44.4   Answer : 44.4
Answer: C
Mark has to visit towns B and C in any order. The roads connecting these towns with his house are shown on the diagram. How many different routes can he take starting from A and returning to A, going through both B and C and not traveling any road twice on the same trip?
Options.
A) 5 B) 8 C) 9 D) 10 E) 12

Solution: Mark can travel clockwise or anticlockwise on the diagram.   Clockwise, he has no choice of route from A to B, a choice of one out of two routes from B to C, and a choice of one out of two routes from C back to A. This gives four possible routes.   Similarly, anticlockwise she has four different routes.   Total routes = 8   8
Answer: B
When Professor Wang looked at the rosters for this term's classes, she saw that the roster for her economics class (E) had 26 names, the roster for her marketing class (M) had 26, and the roster for her statistics class (S) had 18. When she compared the rosters, she saw that E and M had 9 names in common, E and S had 7, and M and S had 10. She also saw that 4 names were on all 3 rosters. If the rosters for Professor Wang's 3 classes are combined with no student's name listed more than once, how many names will be on the combined roster?	Choose the correct choice from the following answers
A) 30  B) 34  C) 48  D) 46  E) 50

Solution: Total # of students 26+26+18-(9+7+10)+4= 
26+26+18-(9+7+10)+4 = 48
48.   Answer: 48.
Answer: C
A dealer purchased an article at 3/4 of its list price and sold 50% more than the list price. Find his gain percent?
Choose the correct choice from the following answers:
A) 106%	B) 200%	C) 100%	D) 170%	E) 104%

Solution: MP = 100   100%P = 75   SP = 150   ------   75 ---- 75   100 ---- ? => 100%   Answer: 100%
Answer: C
If n and y are positive integers and 450y = n^3, which of the following must be an interger
I. y/ (3 * 2^2 * 5)
II. y/ (3^2 * 2 * 5)
III. y/ 3 * 2 * 5^2
Choose the correct choice from the following options
A) None.  B) I only.  C) II only.  D) III only.  E) I, II, and III

Solution: 450 y = n^3 -> y = n3/450 -> n3 is divisible by 450 & n is +ve integer. look for values of n^3 such that n is integer and n is divisible by 450. Clearly we have to look in the order of 1000's to find a value such that n3 is divisible by 450 and n is integer.   n3=1000 n =10 not divisible by 450   n3=8000 n =20 not divisible by 450   n3=27000 n =30 divisible by 450 y = 2700/45= 
2700/45 = 60
60   Look for I, II , III which have denominators 60,90,150.   only I does and hence I only.
Answer: B
The ratio of three numbers is 3:4:5 and the sum of their squares is 1250. The sum of the numbers is:  Select:
A) 30  B) 50  C) 60  D) 70  E) 80

Solution: Let the numbers be 3x, 4x and 5x   Then, 9x2+16x2+25x2=1250   50x2=1250   X=5   Sum of numbers= 3x+4x+5x=12x3 +4 +5= 
3 +4 +5 = 12
12x=60   ANSWER 60 60
Answer: C
A company assigns product codes consisting of all the letters in the alphabet.How many product codes are possible if the company uses at most 2 letters in its codes, and all letters can be repeated in any one code? Choices:
A) A.702 B) B.16226 C) C.17576 D) D.18278 E) E.28572

Solution: The no of ways in which the company can make codes of 1 letter : 26   # for 2 letters :   26*26= 
  26*26 = 676
676   The total : By adding all of them , 676+26= 702   A.702.
Answer: A
A bike covers a certain distance at the speed of 81km/h in 7 hrs. If the bike was to cover the same distance in approximately 9 hrs, at what approximate speed should the bike travel? Select:	A) 80 km/h	B) 67 km/h	C) 90.14 km/h	D) 63 km/h	E) 92 km/h

Solution: Ans.(D)   Sol. Total distance = 81 × 7 = 567 km   Now speed = 567/9= 
567/9 = 63
63 km/h
Answer: D
There are k-2 members in a certain band, including Jim and Ellen. Two members are to be selected to attend the Grammy awards ceremony. If there are 21 possible combinations in which Jim and Ellen are not selected, what is the value of k?
Pick one:	A) 8	B) 9	C) 10	D) 11	E) 12

Solution: There are k-2 members in the band, and k-4 members without Jim and Ellen.   (k-4)C2 = 21   (k-4)(k-5)/2 = 21   (k-4)(k-5) = 42 = 7*6   k = 11   The answer is 11.
Answer: D
A number when divided by 6 leaves a remainder 3. When the square of the same number is divided by 6, the remainder is:
Choose the correct option
A) 0
B) 1
C) 2
D) 3
E) 4

Solution: Let x=6q+3. Then, x2= (6q+3)2= 36q2+36q+9= 6(6q2+6q+1)+3.   So, when 2n is divided by 4, remainder =3.   Answer: 3
Answer: D
When n is divided by 20, the remainder is 6. What is the remainder when n + 16 is divided by 5?  Select the correct option
A) 1 B) 3 C) 4 D) 5 E) 6

Solution: 1ssume n = 14   Remainder (n/20) = 6   n+16 = 36   Remainder (36/5) = 1   Option 1
Answer: A
Carol and Jordan draw rectangles of equal area. If Carol's rectangle measures 5 inches by 24 inches and Jordan's rectangle is 4 inches long, how wide is Jordan's rectangle, in inches?  Choices:
A) 25
B) 23
C) 32
D) 30
E) 18

Solution: Area of Carol's rectangle = 24*5= 
24*5 = 120
120   Let width of Jordan's rectangle= w   Since , the areas are equal   4w = 120   =>w = 30   Answer 30
Answer: D
A man can row 3.6 km/hr in still water. It takes him twice as long to row upstream as to row downstream. What is the rate of the current ?  Pick one:
A) 1.9
B) 1.7
C) 1.2
D) 1.5
E) 1.1

Solution: Speed of boat in still water (b) = 3.6 km/hr. Speed of boat with stream (Down Stream), D = b + u Speed of boat against stream (Up stream), U = b – u It is given upstream time is twice to that of down stream. ⇒ Downstream speed is twice to that of upstream. So b + u = 2(b – u) ⇒ u =b/3 = 1.2 km/hr.   Answer: 1.2
Answer: C
A, B and C have Rs.500 between them, A and C together have Rs.200 and B and C Rs.350. How much does C have? Options:
A) 50  B) 76  C) 27  D) 26  E) 54

Solution: 50+B+C = 500   50+C = 200   B+C = 350   --------------   50+B+2C = 550   50+B+C = 500   ----------------   C = 50   50nswer:50
Answer: A
Ayesha's father was 58 years of age when she was born while her mother was 42 years old when her brother four years younger to her was born. What is the difference between the ages of her parents? Answers:  A) 6  B) 40  C) 50  D) 10  E) 20

Solution: Mother's age when Ayesha's brother was born = 42 years.   Father's age when Ayesha's brother was born = (58 + 4)= 
(58 + 4) = 62
62 years.   Required difference= (62 - 42)= 
(62 - 42) = 20
20 years.   Answer:20
Answer: E
The average score of 35 students in a class is 37. If every student is given 3 grace marks, the new average of the class is: Choose the most appropriate option.
A) 33	B) 21	C) 38	D) 40	E) 92

Solution: Explanation:   Average score = 37   Grace mark 3 is given to 35 student then its average will be 3.   Hence new average = 37 + 3= 
37 + 3 = 40
40   Answer: 40
Answer: D
The sector of a circle has radius of 21 cm and central angle 120o. Find its perimeter?  Pick
A) 91.5 cm	B) 11.5 cm	C) 91.8 cm	D) 86 cm	E) 99.5 cm

Solution: Perimeter of the sector = length of the arc + 2(radius)   = (120/360 * 2 * 22/7 * 21) + 2(21)   =44 + 42= 
44 + 42 = 86
86 cm   Answer:86 cm
Answer: D
Earl can stuff advertising circulars into envelopes at the rate of 36 envelopes per minutes and Ellen requires a minutes and half to stuff the same number of envelops.Working together,how long will it take Earl and Ellen to stuff 60 envelopes  Choose the correct choice from the following answers:
A) 1 minute	B) 5 minutes	C) 7 minutes	D) 3 minutes	E) 4 minutes

Solution: earl takes 1 min. for 36 envelopes.   ellen takes 3/2 mins for the same. so ellen can stuff ((36)/(3/2)) in 1 min. i.e., 24 envlpes a min.   so both of them when work together can stuff 36+24= 
36+24 = 60
60 envelopes in 1 min.   for 60 envelopes they will take 60/60 mins. i.e., 1 mins.   1 minuteNSWER:1 minute
Answer: A
How many times the keys of a writer have to be pressed in order to write first 200 counting no's?  Choose the correct choice from the following:
A) 452
B) 462
C) 472
D) 482
E) 492

Solution: 1 to 9 = 9 * 1= 
9 * 1 = 9
9   10 to 99= 90 * 2= 
90 * 2 = 180
180   100 to 200= 101 * 3= 
101 * 3 = 303
303   -----------   492   492
Answer: E
If x is a prime number, which of the following cannot be an integer?	Choose the correct choice from the following answers
A) x/2	B) 5x/3	C) 3x/7	D) 15x/6	E) x/6

Solution: x/2 can be an integer when x=2   5x/3 can be an integer when x=3   3x/7 can be an integer when x=7   15x/6==> 5x/2 can be an integer when x=2   x/6 can't be an integer==> when x=2, x/6=1/3 when x=3, x/6=1/2   ANSWx/6R:x/6
Answer: E
Find out the C.I on Rs.5000 at 4% p.a. compound half-yearly for 1 1/2 years.  Pick:
A) 306.05 B) 306.00 C) 306.04 D) 306.05 E) 306.01

Solution: 306.05 = 5000(51/50)3   = 5306.04   5000   -----------   306.04   306.05nswer: 306.05
Answer: A
The mean of 50 observations is 200. But later he found that there is decrements of 15 from each observations. what is the the updated mean is ?  Choose one.
A) 170	B) 185	C) 190	D) 198	E) 200

Solution: 185   Answer is 185
Answer: B
A container contains 20 liters of milk, From this container 2 liters of milk was taken out and replaced by water. This process was repeated further 2 times. How much milk is now contained by the container?	Choices:
A) 14.58 liters	B) 20.16 liters	C) 22.45 liters	D) 26.95 liters	E) 31.45 liters

Solution: 14.58 litersmount of milk left after 3 operations = 20 (1 - 2/20)^3 = 20 * 9/10 * 9/10 * 9/10= 
20 * 9/10 * 9/10 * 9/10 = 729/50 = around 14.58
14.58 liters   14.58 litersnswer is 14.58 liters
Answer: A
Calculate the percentage increase in the area of a rectangle, if each of its sides is increased by 10%?
Select:  A) 20%  B) 29%  C) 27%  D) 24%  E) 21%

Solution: Assume original length = 100m by 50m   original area = 100*50= 
100*50 = 5_000
5000   10% increase on each side   l= 100 + 10= 
100 + 10 = 110
110   w= 50 + 5= 
50 + 5 = 55
55   new area= 110*55= 
110*55 = 6_050
6050   increase in area= 6050 - 5000= 
6050 - 5000 = 1_050
1050   %increase=21%   Answer 21%
Answer: E
Tough and Tricky questions: Arithmetic.
(8^2 + 8^2)/4^2 =	Pick.
A) 4  B) 29  C) 8  D) 58  E) 116

Solution: Ans is 8   my approach was:   (8^2 + 8^2)/4^2 =8(8+8)/4*4   =8*16/4*4=2*4= 
2*4 = 8
8   8
Answer: C
Two trains 140 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? Choose the most appropriate option.
A) 10.6
B) 10.9
C) 10.4
D) 10.8
E) 10.1

Solution: Relative speed = 60 + 40= 
60 + 40 = 100
100 km/hr.= 100 * 5/18 = 250/9 m/sec.   Distance covered in crossing each other = 140 + 160= 
140 + 160 = 300
300 m.   Required time= 300 * 9/250 = 54/5= 
54/5 = 54/5 = around 10.8
10.8 sec.   Answer: 10.8
Answer: D
If -y^2= 2xy, then (x+y)^2 = Choose the correct choice.
A) x^2 B) 3x^2 C) 4xy D) 2y^2 E) -y^2

Solution: Its B   -y^2 = 2xy   0 = 2xy + y^2   x^2dd x^2 on both sides we get   x^  2 +0= 
  2 +0 = 2
x^2 +y^2 +2xy   x^2= (x+y)^2   Correct Option : x^2
Answer: A
Lion, rat stay in jungle happily. Lion lies on: Mon, Tue, Wed. Rat lies on: Wed, Thurs , Sat. If lion says: I didn't lie yesterday. Rat says: I didn’t lie yesterday. So what day is today?
Pick one.
A) Tuesday
B) wednesday
C) Thursday
D) Friday
E) Sunday

Solution: Tuesday -- lion ll tell lie on tuesday   lion is saying lie that he didn't lie sday [ again a lie... bcozzz lion ll say lie on monday also]   Tuesday -- Rat ll not say lie on tuesday   TuesdayNSWER:Tuesday
Answer: A
337.62+5.628+33.4=?  Choices.
A) 376.648 B) 112.6 C) 258.69 D) 5874.3 E) 269.88

Solution: 337.62   5.628   33.4   ----------   376.648   376.648nswer is 376.648
Answer: A
What is the least common multiple of 12,27 and 40	Pick:
A) 8521  B) 1080  C) 368  D) 8979  E) 6584

Solution: factors of 12 =2*2*3   factors of 27= 3*3*3   factors of 40 =2*2*2*5   thus the l.c.m is 2^3*3^3*5=1080   the answer is 1080
Answer: B
A right triangle STU has an area=30. If the longest side of the triangle is SU and value of ST=5. What are the lengths of sides TU and SU?
Pick one:
A) 12, 13
B) 5, 13
C) 24, 26
D) 12, 24
E) None of the above

Solution: Area=30 and ST=5. By applying Area=STxTU, we get that TU=12, which is the first part of our answer.   By Pythagorean Theorem, we can now find the value of SU since we have value of ST and we found value of TU. So the correct answer is 12, 13.
Answer: A
If one-third of one-fourth of a number is 20, then three-tenth of that number is:
A. 35 Choose the most appropriate option.
A) 23 B) 87 C) 26 D) 54 E) 72

Solution: 72xplanation:   The number is 1/3 of 1/4 is =15 then 1/3 Ã— 1/4 = 20   Number is 240 then 240 Ã— 3/10 = 72   Answer: 72
Answer: E
If two trains are 120 miles apart and are traveling toward each other at constant rate of 30 miles per hour and 40 miles per hour, respectively, how far apart will they be 1 hour before they meet?
Choose the correct option:
A) 10	B) 30	C) 40	D) 50	E) 70

Solution: They would meet in 120/70 = 12/7 hours   1 hour earlier 5/7 hours   distance between trains = total distance -(distance covered by train A + distance covered by train B)   = 120-(5/7(40+30)) [ distance of A = 5/7* 40; like wise distance by B]   = 70 Km   ANSW70R:70
Answer: E
The total car population in a Mumbai is 2,94,00 out of which 1,50,00 are made by Honda. Out of every 100 Honda cars, 98 are red in color, but only 53% of the total car population is red. Find the % of non-Honda cars that are red Options.
A) 2.54% B) 4.56% C) 6.125% D) 7.134% E) 8.341%

Solution: Total Car.29.10 i.e., Honda +non Honda = 29400 Given: Whim. tractor .150W   Now,5346 of 2..00 = Honda +Red Non-Honda 29400 .:4 =15582 Thus...El Mall... 1.0 Now Honda 15582 flow, Non-. Honda =15582 - 15.582-14700=8B2 96 non-Honda =1=1.100 = 6.125%   6.125%
Answer: C
A train 100 meters long completely crosses a 300 meters long bridge in 45 seconds. What is the speed of the train is?
Choose the correct answer: A) 32 B) 27 C) 88 D) 26 E) 12

Solution: S = (100 + 300)/45 = 400/45 * 18/5= 
400/45 * 18/5 = 32
32   32nswer:32
Answer: A
the difference between a positive fraction and its reciprocal is 9/20 find the sum of that fraction and its reciprocal.
Choose the correct choice from the following options:	A) 41/20	B) 17/20	C) 11/20	D) 9/20	E) None of these

Solution: Explanation :   Let the fraction = x   Then x − (1/x) = 9/20   ⇒ (x2 − 1)/x = 9/20   ⇒ x2 − 1 = 9x/20   ⇒ 20x2 − 20 = 9x   ⇒ 20x2 − 9x − 20 = 0   x=−b±b2−4ac√2ax=−b±b2−4ac2a =9±(−9)2−4×20×(−20)√2×20=9±(−9)2−4×20×(−20)2×20 =9±81+1600√40=9±4140=5040Or−3240=9±81+160040=9±4140=5040Or−3240   Given that the fraction is positive. Hence   x = 50/40 = 5/4   1/x = 4/5   x + (1/x) = (5/4) + (4/5) = (5 × 5 + 4 × 4)/20 = 41/20. 41/20nswer : Option 41/20
Answer: A
Find the least number must be subtracted from 5264 so that remaining number is divisible by 17.  Choose the correct option
A) 11	B) 14	C) 18	D) 20	E) 29

Solution: When dividing 5264 by 17, we get the remainder 11, so 11 should be subtracted. The answer is 11.
Answer: A
The probability of a lottery ticket being a prized ticket is 0.2. When 4 tickets are purchased, the probability of winning a prize on atleast one ticket is
Choose one.
A) 0.5928 B) 0.5904 C) 0.5297 D) 0.5297 E) 0.5101

Solution: P(winning prize atleast on one ticket)   = 1 - P("Losing on all tickets")   = 1 - (0.8)4 = (1 + (0.8)2)(1 - (0.8)2)   = (1.64)(0.36)   = 0.5904   Answer:0.5904
Answer: B
Find the greatest number which on dividing 6215 and 7373, leaves a reminder of 23 and 29 respectively  Choose the correct choice from the following answers
A) 125  B) 127  C) 129  D) 131  E) 144

Solution: 144xplanation:   In this type of question, its obvious we need to calculate the HCF, trick is   HCF of (6215 - 23) and (7373 -29)   = HCF (6192, 7344) = 144   Option 144
Answer: E
The sum of the ages of a father and son is 45 years. Five years ago, the product of their ages was four times the fathers age at that time. The present age of father and son  Choose the correct choice from the following answers:
A) 6	B) 7	C) 9	D) 2	E) 5

Solution: Let sons age = x years. Then fathers age = (45 - x)years.   (x—5)(45—x—5) = 4(45- x - 5) hence (x—5) = 4 so x = 9   Their ages are 36 years and 9 years.   Answer: 9
Answer: C
There are 20,6 and 9 rupees notes. you have to form 99 rupees with minimum number of notes.At what minimum number of notes you can achieve this?	Choose the correct option.
A) 9  B) 8  C) 7  D) 6  E) 5

Solution: 20*3= 
20*3 = 60
60   6*2= 
6*2 = 12
12   9*2= 
9*2 = 18
18   9*1= 
9*1 = 9
9   9 notes   9NSWER:9
Answer: A
It is known that no more than 6 children will be attending a party. What is the smallest number of cookies that must be brought to the party so that each child receives the same number of cookies?	Choose the correct choice from the following options.
A) 35
B) 105
C) 60
D) 210
E) 420

Solution: The question states that there are no more than 6 children in the party. Thus, the possibility is that there could be 1, 2, 3, 4, 5 or 6 children.   If you assume answer as 35 and there are 3 children, you may not distribute be able to distribute cookies equally.   similarly if there were 105 cookies, and 2 children, cookies cannot be distributed equally.   or if there were 210 cookies, and 4 children, cookies cannot be distributed equally.   Thus, the question asks for a number of cookies which can be distributed to any number of children (from 1 to 6).   And therefore the smallest number of cookies would be lcm of (1, 2, 3, 4, 5, 6), i.e., 60.   Answer (60)
Answer: C
If the tens digit x and the units digit y of a positive integer n are reversed, the resulting integer is 18 more than n. What is y in terms of x ?	Choose the correct choice from the following answers:	A) x+2	B) x-2	C) x+5	D) x+6	E) x+3

Solution: Original Digits=xy i.e. Number=10x+y   After reversing the digits:   Digits=yx i.e. Number=10y+x   10y+x is 18 more than 10x+y   10x+y+18=10y+x   10x-x+18=10y-y   9x+18=9y   x+2=y   OR   y=x+2   x+2nswer : x+2
Answer: A
As a treat for her two crying children, a mother runs to the freezer in which she has two cherry ice pops, three orange ice pops, and four lemon-lime ice pops. If she chooses two at random to bring outside to the children, but realizes as she runs out the door that she cannot bring them different flavors without one invariably being jealous of the other and getting even more upset, what is the probability that she has to return to the freezer to make sure that they each receive the same flavor?  Choose the correct choice from the following choices.
A) 1/9	B) 1/6	C) 5/18	D) 13/18	E) 5/6

Solution: Probability of not getting the same flavor ->   Favorable -> Cherry - orange [ 2C1 * 3C1 [or simply 2*3 ] or Cherry - lemon [ 2*4] or orange - lemon [3*4]   Prob = (2*3 + 2*4 + 3*4 ) / 9C2 = 26/36 = 13/18   Answer -> 13/18
Answer: D
In a class, 30% of the students offered English, 20% offered Hindi and 10% offered both. If a student is selected at random, what is the probability that he has offered English and Hindi?	Choose the correct choice from the following choices:
A) 2/10 B) 1/10 C) 3/10 D) 2/5 E) 3/5

Solution: P(E)=30/100,   P(H)=20/100   P(E and H)=10/100   P(E or H)=3/10+2/10-1/10   =2/5   ANSWER 2/5 2/5
Answer: D
The length of a rectangular field is 7/5 its width. If the perimeter of the field is 336 meters, what is the width of the field?	Pick:  A) 50  B) 60  C) 70  D) 80  E) 90

Solution: Let L be the length and W be the width. L = (7/5)W   Perimeter: 2L + 2W = 336, 2(7/5)W + 2W = 336   Solve the above equation to find: W = 70 m and L = 98 m.   correct answer 70)70
Answer: C