MU-NLPC/Calc-aqua_rat huggingface dataset:
Number of students in institutes A and B were in the ratio of 7 : 15 respectively in 2012. In 2013, the number of students in institute A increased by 25% and number of students in institutes B increased by 26%, then what was the respective ratio between number of students in institutes A and B? Choose the correct answer
A) 25 : 56 B) 24 : 55 C) 24 : 53 D) 25 : 53 E) 25 : 54

Solution: Solution:   Ratio of students in 2012 in institutes A and B,   = 7 : 15.   Let number of students in institute A in 2012 = 700.   And Number of students in institutes B in 2012 = 1500.   25% increase in the number of students in 2013,   Now, number of students in Institute A,   = 700 + 25% of 700. = 875.   Number of students in B in 2013 as 26% students increased in B,   = 1500 + 26% of 1500 = 1890.   Current Ratio of the students,   = 875 /1890 = 25 : 54.   Answer: Option 25 : 54
Answer: E
A and B start a business, with A investing the total capital of Rs.5000, on the condition that B pays A interest @ 10% per annum on his half of the capital. A is a working partner and receives Rs.500 per month from the total profit and any profit remaining is equally shared by both of them. At the end of the year, it was found that the income of A is twice that of B. Find the total profit for the year?	Options.
A) A)2500
B) B)3500
C) C)5000
D) D)6000
E) E)8000

Solution: Interest received by A from B = 10% of half of Rs.5000 = 10% * 2500 = 250.   Amount received by A per annum for being a working partner = 500 * 12 = Rs.1000.   Let 'P' be the part of the remaining profit that A receives as his share. Total income of A = (250 + 1000 + P)   Total income of B = only his share from the remaining profit = 'P', as A and B share the remaining profit equally.   Income of A = Twice the income of 3500   (250 + 1000 + P) = 2(P)   P = 1250   Total profit = 2P + 1000   = 2*1250+ 1000= 
2*1250+ 1000 = 3_500
3500   Answer:3500
Answer: B
In three annual examinations, of which the aggregate marks of each was 500, a student secured
average marks 45% and 55% in the first and the second yearly examinations respectively. To secure 60% average total marks, it is necessary for him in third yearly examination to secure marks :	Choose the most appropriate option:  A) 300  B) 350  C) 400  D) 450  E) 500

Solution: total marks:1500 for three exams   60% of 1500=900   first exam marks=45% of 500=225   second exam marks=55% of 500=275   let X be the third exam marks   225 + 275 + X =900   X=400   ANSWER:400
Answer: C
If 1/a + 3/a + 4/a is an integer, which of the following must also be an integer? Choose the correct choice from the following answers
A) 12/a
B) 3/a
C) 8/a
D) 9/a
E) 15/a

Solution: 1/a + 3/a + 4/a   =8/a   Answer 8/a
Answer: C
How long does a train 110 m long running at the speed of 36 km/hr takes to cross a bridge 132 m length?  Choose the correct choice from the following options.
A) 82.1 sec B) 12.1 sec C) 24.2 sec D) 13.1 sec E) 12.15sec

Solution: Speed = 36 * 5/18= 
36 * 5/18 = 10
10 m/sec   Total distance covered= 110 + 132= 
110 + 132 = 242
242 m.   Required time= 242/10= 
242/10 = 121/5 = around 24.2
24.2 sec.   Answer:24.2 sec
Answer: C
What is the greatest number of three digits which is divisible by 5, 10, 15 ?
Choose the correct choice from the following answers: A) 985 B) 970 C) 955 D) 990 E) 999

Solution: Greatest number of 3 digits = 999   LCM of 5, 10, 15 = 30   999 ÷ 30= 33, remainder = 9   Hence, greatest number of four digits which is divisible by 5,10,15   = 999 - 9= 
999 - 9 = 990
990   answer : 990
Answer: D
In a race with 30 runners where 6 trophies will be given to the top 6 runners (the trophies are distinct: first place, second place, etc), how many ways can this be done?	Choices
A) 6^6 ways
B) 8^9 ways
C) 7^8 ways
D) 8^7 ways
E) 8^6 ways

Solution: 6 people can be prized with distinct prizes in 6^6 ways   6^6 waysNSWER:6^6 ways
Answer: A
At what time between 6 and 7 are the hands of the clock coincide?  Pick one
A) 6:39 B) 6:37 C) 6:31 D) 6:32 E) 6:313

Solution: For hour = 360/12 = 300300/hr   For Minute = full rotation = 36003600/hr   Let the line is 't' , for 6 = 6*30=18001800   then   30 t + 180=360 t   330t = 180   t = 180/330   t = 6/11 hr 6/11*60=360/11=32611611   Ans. 6:32
Answer: D
A fair coin with sides marked heads and tails is to be tossed eight times. What is the probability that the coin will land tails side up more than five times?
Pick.
A) 37/256  B) 56/256  C) 65/256  D) 70/256  E) 81/256

Solution: More than 5 times tails = 6times +7times  +8= 
  +8 = 8
8C6 + 8C7 + 8C8= 37   - - - - - - - -   2 2 2 2 2 2 2 2   2^8 times total events and 37 events where tails side up .   So probability = 37/2^8 = 37/256 (37/256nswer 37/256)
Answer: A
A certain bakery baked a batch of 450 cookies one day. Of those, 320 contained nuts, 230 contained chocolate chips, and 85 contained neither nuts nor chocolate chips. What is the fewest possible number of cookies with both chocolate chips and nuts that would need to be added to that batch so that cookies with both nuts and chocolate chips represented more than 3/5 of all the cookies in the batch?	Options.
A) 166	B) 213	C) 413	D) 438	E) 511

Solution: Cookies which have both nuts and chocolate chips = 185   Let fewest possible number of cookies with both chocolate chips and nuts that would need to be added to that   batch so that cookies with both nuts and chocolate chips represented more than 3/5 of all the cookies in the batch = x   (185+x)/(450+x) = 6/10   =>1850 + 10x = 2700 + 6x   => 4x = 850   => x = 212.5   Therefore x = 213   Answer 213
Answer: B
The avg. age ofa group of 12 students is 20yers.If 4 more students join the group,the avg age increases by 1 year.The avg age of the new student is? Select the correct option:
A) 22 years  B) 23 years  C) 24 years  D) 25 years  E) 26 years

Solution: Total age of 12 students=12*20= 
12*20 = 240
240   If total age of 4 students=x   Then, (240+x)/(12+4) =(20+1), x=96   So average age of new students=96/4= 
96/4 = 24
24 years   ANSWER:24 years
Answer: C
A room has equal number of men and women. Eight women left the room, leaving twice as many men as women in the room . What was the total number of men and women present in the room initially?	Options
A) 28  B) 30  C) 31  D) 32  E) 27

Solution: Assume that initial number of men = initial number of women = x   2(x-8) = x   => 2x - 16 = x   => x = 16   Total number of men and women = 2x = 2 × 16 = 32   Answer is 32.
Answer: D
In how many ways can you seat 4 people on a bench if one of them, Rohit, does not want to sit on the middle seat or at either end? Choose the correct choice from the following.
A) 720 B) 6 C) 2880 D) 5040 E) 10080

Solution: Since Rohit does not want to sit on the middle seat or at either end (3 chairs), then he can choose 1 chairs to sit. The remaining 3 people can sit in 3! ways. Thus the # of arrangements is 1*3! = 6.   Answer: 6.
Answer: B
The annual cost of owning and operating a car, C dollars, is a linear function of the distance, d kilometers, it is driven.  Choose the correct choice from the following choices
A) 0.3d + 1609 B) 0.3d + 16089 C) 0.3d + 1600 D) 0.3d + 1602 E) 0.3d + 1601

Solution: c = md + b   The cost is $ 4600 for 10 000 km   4600 = m (10 000) + b   10 000 m + b = 4600   b = -10 000 m + 4600 ------- (i)   The cost is $ 9100 for 25 000 km   9100 = m (25 000) + b   9100 = 25 000 m + b   25 000 m + b = 9100   b = -25 000 m + 9100 --------- (ii)   From equation (i) and (ii) we get;   -10 000 m + 4600 = -25 000 m + 9100   -10 000 m + 25 000 m = 9100 – 4600   15 000 m = 4500   m = 4500/15 000   m = 3/10= 
3/10 = 3/10 = around 0.3
0.3   Now, put the value of m= 0.3 in equation (i) we get;   b = -10 000 (0.3) + 4600   b = -3000 + 4600= 
-3000 + 4600 = 1_600
1600   Answer: m= 0.3 and b = 1600   (b) c = md + b   m = 0.3   b = 1600   c = 0.3d + 1600   Answer: 0.3d + 1600 = 0.3d + 1600
Answer: C
Linda and Angela contract to paint a neighbor's house. Even though Linda spends 80% more time painting the house than Angela, each receives a payment of m dollars when the work is completed. If Angela decides to pay Linda n dollars so that they would have received the same compensation per hour worked, what is n in terms of m ?
Choose the correct choice from the following answers.
A) 1/2 m	B) 1/3 m	C) 1/4 m	D) 1/5 m	E) 1/6 m

Solution: After the final transaction:   Angela received $(m-n) for t hours;   Linda received $(m+n) for 1.5t hours;   We are told that after that transaction they received the same compensation per hour: (m-n)/t=(m+n)/1.5t --> 1.5m-1.5n=m+n -->m=5n --> n=m/2.   1/2 mnswer: 1/2 m.
Answer: A
The toll for crossing a certain bridge is $0.65 each crossing. Drivers who frequently use the bridge may instead purchase a sticker each month for $13.00 and then pay only $0.30 each crossing during that month. If a particular driver will cross the bridge twice on each of x days next month and will not cross the bridge on any other day, what is the least value of x for which this driver can save money by using the sticker? Choose one.
A) 14  B) 15  C) 16  D) 28  E) 29

Solution: Option #1: $0.75/crossing....Cross twice a day = $1.5/day   Option #2: $0.30/crossing....Cross twice a day = $0.6/day + $13 one time charge.   If we go down the list of possible answers, you can quickly see that 14 days will not be worth purchasing the sticker. 1.5x14 (21) is cheaper than 0.6x14 +13 (21.4)...it's pretty close so let's see if one more day will make it worth it... If we raise the number of days to 15, the sticker option looks like a better deal...1.5x15 (22.5) vs 0.6x15 + 13 (22). Answer: 16
Answer: C
How many 4-letter word with or without meaning can be formed out of the letters of the word 'LOGARITHMS' if repetition of letters is not allowed
Choose the correct choice from the following options
A) 5040	B) 1254	C) 4510	D) 1203	E) 4510

Solution: 'LOG5040RITHMS' contains 10 different letters   Required number of words   = Number of arrangements of 100 letters taking   4 at a time   = 10P4   = 10 * 9 * 8 * 7= 
10 * 9 * 8 * 7 = 5_040
5040   5040ns: 5040
Answer: A
If n is a 9-digit positive integer, all of whose digits are the same, which of the following must be true?
I. n is divisible by 3
II. n is divisible by 9
III. n is divisible by 10 Choose the correct answer:  A) I and II only  B) I only  C) I and III only  D) II and III only  E) I, II and III

Solution: Rule for divisibility by 3: The sum of the digits of the number should be multiple of 3   Rule for divisibility by 9: The sum of the nos digits of the number should be divisible by 9 or the number should be divisible by 3 two times.   Rules for divisibility by 9: The sum of the digits should a multiple of 9   Consider no 11111111...9 times = The sum 9*1=27----> divisbible by 3,9   consider number to be 222....9 times, then sum of the no. 9*2=18 divisible by 3,9   So why so because when you sum the numbers either you can add the digits 9 times or multiply the digit *9..   Note that since 9 is divisble by 9 and 3 and thus the sum of the nos will be divisible by all the nos.   I and II only
Answer: A
Bill made a profit of 10% by selling a product. If he had purchased that product for 10% less and sold it at a profit of 30%, he would have received $28 more. What was his original selling price?	Select
A) $200
B) $260
C) $320
D) $380
E) $440

Solution: Let P be the original purchase price of the product.   Bill originally sold the product for 1.1*P.   In the second scenario, the purchase price is 0.9*P.   A 30% profit means the selling price would be 1.3*0.9*P = 1.17*P   Thus, according to the information in the question, 1.17P - 1.1P = 28   0.07 = 28   P = 400   The original selling price was  400*1.1= 
 400*1.1 = 440
440.   The correct answer is $440.
Answer: E
In a diving competition, each diver has a 25% chance of a perfect dive. The first perfect dive of the competition, but no subsequent dives, will receive a perfect score. If Janet is the third diver to dive, what is her chance of receiving a perfect score? (Assume that each diver can perform only one dive per turn.) Choose the correct choice from the following choices:
A) 1/5
B) 1/15
C) 4/25
D) 9/64
E) 61/125

Solution: Probability = Favourable Outcomes / Total Outcomes = 1 - (Unfavourable Outcomes / Total Outcomes)   Given:Probability of Perfect dive = 0.25 = 25/100 = 1/4   i.e. Probability of Non-Perfect dive = 0.75 = 75/100 =3/4   The probability of Janet to dive and get a perfect score depends on that other other previous two dives must be Imperfect   Method-1:   i.e. Probability of First two being Imperfect and Third being Perfect dive = (3/4)*(3/4)*(1/4) =9/64   9/64
Answer: D
If 40 men take 15 days to to complete a job, in how many days can 25 men finish that work? Choose the correct choice from the following options
A) 24
B) 25
C) 26
D) 27
E) 28

Solution: Ans. 24 days
Answer: A
Two trains of equal are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 sec. The length of each train is?	Choose the correct choice from the following choices:
A) 50 m	B) 72 m	C) 80 m	D) 82 m	E) 84 m

Solution: Let the length of each train be x m.   Then, distance covered = 2x m.   Relative speed = 46 - 36= 
46 - 36 = 10
10 km/hr.= 10 * 5/18 = 25/9 m/sec.   2x/36 = 25/9 => x = 50.   50 mNSWER:50 m
Answer: A
The banker's discount on Rs. 1600 at 15% per annum is the same as true discount on Rs. 1680 for the same time and at the same rate. The time is:
Choose the correct choice from the following:
A) 1 months B) 4 months C) 7 months D) 9 months E) 4 months

Solution: S.I. on Rs. 1600 = T.D. on Rs. 1680.   Rs. 1600 is the P.W. of Rs. 1680, i.e., Rs. 80 is on Rs. 1600 at 15%.   Time = 100 x 80	year	=	1	year = 4 months.   1600 x 15	3   View Answer Discuss in Forum Workspac   Answer:4 months
Answer: B
The average weight of D, E and F is 42 kg. If the average weight of D and E be 35 kg and that of E and F be 41 kg, what is the weight of E?	Choose the correct choice from the following answers.
A) 23 Kg  B) 24 Kg  C) 25 Kg  D) 26 Kg  E) 27 Kg

Solution: Let the weight of D, E and F are a,b and c respectively.   Average weight of 26 Kg,E and F = 42   a + b + c = 42 × 3 = 126 --- equation(1)   Average weight of 26 Kg and E = 35   a + b = 35 × 2 = 70 --- equation(2)   Average weight of E and F = 41   b + c = 41 × 2 = 82 --- equation(3)   equation(2) + equation(3) - equation(1)   => a + b + b + c - (a + b + c) = 70+82 - 126   => b = 152-126= 
152-126 = 26
26   Weight of B= 26 Kg   ANSWER:26 Kg
Answer: D
A clock is set right at 8 a.m. The clock gains 10 minutes in 24 hours will be the true time when the clock indicates 1 p.m. on the following day?  Choose the correct choice from the following answers
A) 48 min. past 19 B) 48 min. past 12 C) 48 min. past 10 D) 48 min. past 11 E) 48 min. past 14

Solution: Time from 8 a.m. on a day to 1 p.m. on the following day = 29 hours.   24 hours 10 min. of this clock = 24 hours of the correct clock.   hrs of this clock = 24 hours of the correct clock.   29 hours of this clock = hrs of the correct clock   = 28 hrs 48 min of the correct clock.   Therefore, the correct time is 28 hrs 48 min. after 8 a.m.   This is 48 min. past 12.   Answer: A) 48 min. past 12.
Answer: A
If the number 67925*4 is completely divisible by 8, then the smallest whole number in place of * will be?	Choose the correct choice from the following.
A) 1
B) 2
C) 0
D) 4
E) None of these

Solution: The number 5x4 must be divisible by 8.   x=0 as 504 is divisible by 8.   0orrect Option : 0
Answer: C
The first flight out of Phoenix airport had a late departure. If the next three flights departed on-time, how many subsequent flights need to depart from Phoenix on-time, for the airport's on-time departure rate to be higher than 40%?	Options.
A) 4	B) 6	C) 5	D) 2	E) 8

Solution: We need on-time departure rate to be higher than 4/10, so it should be at least 5/11, which means that 5 out of 11 flights must depart on time. Since for now 3 out of 4 flights departed on time then  5-3= 
 5-3 = 2
2 subsequent flights need to depart on-time.   Answer: 2
Answer: D
Pam and Stanley packed several boxes with reams of paper. While both packed, Pam packed 40% of the boxes. After Pam stopped, Stanley packed the same number of boxes that he had packed while working with Pam. What is the ratio of the number of boxes Pam packed to the number of boxes Stanley packed?
Select: A) 1 to 4 B) 1 to 3 C) 2 to 6 D) 3 to 4 E) 3 to 2

Solution: Correct Answer: C   Solution: C. We know that when Pam and Stanley were both working, the ratio was 2 boxes by Pam to 3 boxes by Stanley. We also know that Stanley continued working after Pam stopped. He packed as many boxes alone as he had packed whlie working with Pam, effectively doubling his number of boxes. Thus, the ratio of Pam's boxes to Stanley's boxes is 2 to 6. Answer 2 to 6 is correct.
Answer: C
If 85 percent of the test takers taking an old paper and pencil GMAT exam answered the first question on a given math section correctly, and 65 percent of the test takers answered the second question correctly, and 5 percent of the test takers answered neither question correctly, what percent answered both correctly? Pick one:
A) 60 %
B) 55 %
C) 70%
D) 75%
E) 80%

Solution: {Total} = {First correctly} + {Second correctly} - {Both correctly} + {Neither correctly}   100 = 85 + 65 - {Both correctly} + 5   {Both correctly} = 55.   Answer: 55 %.
Answer: B
If x and j are integers and 2x–j= 11, then 4x+ j CANNOT be  Choose the correct choice from the following.
A) –5
B) 1
C) 13
D) 17
E) 551

Solution: 2x-j=11....j=2x-11   4x+j=4x+2x-11=6x-11   6x-11=-5...x=1   6x-11=1... x=2   6x-11=13...x=4   6x-11=17..X is not integer   6x-11=551..X is not integer   I think the choice E is 55 not 551. Otherwise both 17E CANNOT be solution=17
Answer: D
x and y are positive integers. When x is divided by 9, the remainder is 2, and when x is divided by 7, the remainder is 4. When y is divided by 11, the remainder is 3, and when y is divided by 13, the remainder is 12. What is the least possible value of y - x? Pick:
A) 12
B) 13
C) 14
D) 15
E) 16

Solution: When x is divided by 9, the remainder is 2: So, the possible values of x are: 2, 11, 21, 29, etc.   When x is divided by 7, the remainder is 4: So, the possible values of x are: 4,11,18,... STOP. Since both lists include 11, the smallest possible value of x is 11.   When y is divided by 11, the remainder is 3: So, the possible values of y are: 3, 14, 25, etc.   When y is divided by 13, the remainder is 12: So, the possible values of y are: 12, 25, ...STOP. Since both lists include 25, the smallest possible value of y is 25   Since the smallest possible values of x and y are 11 and 25 respectively, the smallest possible value of y - x is 14. So,14 is the correct answer to the original question.
Answer: C
A necklace is made by stringing N individual beads together in the repeating pattern yellow bead, green bead, red bead, white bead, and blue bead. If the necklace design begins with a yellow bead and ends with a red bead, then N could equal	Pick:
A) 45 B) 55 C) 35 D) 65 E) 68

Solution: Recognize that we are going to have to look for an answer thats a multiple of 5, plus 3.   Mutliple of 5 because there are 5 beads in the pattern, and plus 3 because the bead ends on red, which is 3 into the pattern.   I just went through all the answer choices, and only E fits. 5x13 = 65, and   65+3= 
  65+3 = 68
68   Answer : 68
Answer: E
Aryan runs at a speed of 40 metre/minute. Rahul follows him after an interval of 5 minutes and runs at a speed of 50 metre/minute. Rahul's dog runs at a speed of 60 metre/minute and start along with Rahul. The dog reaches Aryan and then comes back to Rahul, and continues to do so till Rahul reaches Aryan. What is the total distance covered by the dog? Choose one:
A) 1100 meters
B) 1200 meters
C) 1250 meters
D) 1300 meters
E) 1400 meters

Solution: Let X = Minutes   And Y = Aryan runs speed = 40 meter per X   And Z = Rahul runs speed = 50 meter per X (i.e., 200 + 50x)   And D = Total distance covered by the dog = X* 60meters   Y = Z   40x = 200 + 50x   200 = 10x   x = 200/10= 
200/10 = 20
20   So, by 20minutes, both Aryan and Rahul meets.(Rahul reaches Aryan.)   So, dog covered distance, D= X * 60 meters = 20*60= 
20*60 = 1_200
1200 meters   ANSWER:1200 meters
Answer: B
Andrew purchased 11kg of grapes at the rate of 98 per kg and 7 kg of mangoes at the rate of 50 per kg. How much amount did he pay to the shopkeeper?
Choose one.
A) 1000 B) 1055 C) 1428 D) 1500 E) 1080

Solution: Cost of 11 kg grapes = 98 × 11 = 1078.   Cost of 7 kg of mangoes = 50 × 7 = 350.   Total cost he has to pay = 1078 + 350= 
1078 + 350 = 1_428
1428   1428
Answer: C
Amith was 3 times as old as Harsh 6 years back. Amith will be 5/3 times as old as Harsh 6 years hence. How much old is Harsh today?
Choose the correct choice from the following options
A) 12	B) 11	C) 15	D) 16	E) 18

Solution: A   12   Let Harsh’s age 6 years back = A   Then, Amith’s age 6 years back = 32.   Then 5/3 (12 + 6 + 6) = (312 + 6 + 6)   5(12 + 12) = 3 (312 + 12)   412 = 24   12 = 6   Harsh’s age today = (12 + 6) years   = 12 years.
Answer: A
If (x/y)=(9/5), find the value (x^2+y^2)/(x^2-y^2)	Choose the correct answer
A) 53/28
B) 59/11
C) 51/77
D) 41/11
E) None of them

Solution: = (x^2+y^2)/(x^2-y^2) = ( x^2 /y^2+ 1)/ ( x^2 /y^2-1) = [(9/5)^2+1] / [(9/5)^2-1]   = [(81/25)+1] / [(81/25)-1] = 53/28   53/28nswer is 53/28.
Answer: A
A motor pool has 300 vehicles of which 40 percent are trucks. 20 percent of all the vehicles in the motor pool are diesel, including 15 trucks. What percent of the motor pool is composed of vehicles that are neither trucks nor diesel? Choose the correct choice from the following answers
A) 45%	B) 90%	C) 65%	D) 55%	E) 10%

Solution: Trucks = 40% of 300 = 120   Other Vehicles (Excluding Trucks) = 300-120= 
300-120 = 180
180   Diesel Vehicle= 20% of 300 = 60 (Including 15 Trucks)   Other Diesel Vehicles (Excluding Trucks) = 60-15= 
60-15 = 45
45   Trucks that are NOT diesel= 120 - 15= 
120 - 15 = 105
105   Other Vehicles that are NOT diesel Vehicles= 180-45= 
180-45 = 135
135   Required %= (135/300)*100= 
(135/300)*100 = 45
45%   45%nswer: option 45%
Answer: A
P is three times as fast as Q and working together, they can complete a work in 9 days. In how many days can Q alone complete the work? Choose the correct choice from the following:
A) 16 days  B) 17 days  C) 19 days  D) 12 days  E) 10 days

Solution: P = 3Q   P + Q = 3Q + Q = 4Q   These 4Q people can do the work in 9 days, which means Q can do the work in 48 days.   Hence, P can do the work in 12 days.   Answer:12 days
Answer: D
A larger cube has 64 cubic inch as a volume and in the cube there are 64 smaller cubes such that their volume is 1 cubic inch. What is the difference between the surface areas’ sum of the 64 smaller cubes and the surface area of the larger cube, in square inch?	Choose the correct choice from the following
A) 54  B) 64  C) 81  D) 288  E) 120

Solution: Volume of larger cube = 64 = 4^3   Side of larger cube = 4   Volume of smaller cube = 1 --> Side of smaller cube = 1   Surface area of larger cube = 6 * 4^2 = 96   Surface area of 27 smaller cubes = 64 * 6 * 1= 
64 * 6 * 1 = 384
384   288ifference= 384 - 96= 
384 - 96 = 288
288   Answer: 288
Answer: D
Calculate the largest 5 digit number which is exactly divisible by 77?	Pick.
A) 99111  B) 99946  C) 99869  D) 99792  E) 99654

Solution: Largest 4 digit number is 99999   After doing 99999 ÷ 77 we get remainder 53   Hence largest 5 digit number exactly divisible by 77 = 99999 - 53= 
99999 - 53 = 99_946
99946   99946
Answer: B
There are some pigeons and hares in a zoo. If heads are counted, there are 200. If legs are counted, there are 580. The number of hares in the zoo is?  Choose the most appropriate option.
A) 17  B) 26  C) 90  D) 27  E) 21

Solution: 200*2= 
200*2 = 400
400   580   -----   180   1----2   ?----180= 90   Answer: 90
Answer: C
In a group of 5 boys and 3 girls, four children are to be selected. In how many different ways can they be selected such that at least one girl is included?  Choices.
A) 65	B) 50	C) 80	D) 35	E) 120

Solution: The total number of ways to choose 4 children is 8C4 = 70   The number of ways to choose only boys is 5C4 = 5   The number of groups which include at least one girl is 65.   The answer is 65.
Answer: A