MU-NLPC/Calc-aqua_rat huggingface dataset:
Sara bought both German chocolate and Swiss chocolate for some cakes she was baking. The Swiss chocolate cost $2.5 per pound, and German chocolate cost $1.5 per pound. if the total the she spent on chocolate was $15 and both types of chocolate were purchased in whole number of pounds, how many total pounds of chocolate she purchased?	Pick one:	A) 9	B) 8	C) 10	D) 12	E) 15

Solution: If there were all the expensive ones 2.5....   There would be 15/2.5 or 6 of them but since 1.5$ ones are also there, answer has to be >6....   If all were 1.5$ ones, there will be 15/1.5 or 10...   So ONLY 8 is left   Ans 8..
Answer: B
In an electric circuit, two resistors with resistances 8 ohms and 9 ohms are connected in parallel. In this case, if R is the combined resistance of these two resistors, then the reciprocal of R is equal to the sum of the reciprocals of two resistors. What is R value ?
Answers:
A) 17 B) 45/78 C) 72/17 D) 17/72 E) 72

Solution: The wording is a bit confusing, though basically we are told that 1/R = 1/8 + 1/9, from which it follows that R=72/17.   Answer: 72/17.
Answer: C
The sum of first n odd numbers (i.e., 1 + 3 + 5 + 7 + ...+ 2n – 1) is divisible by 11111 then the value of n is	Choose the correct choice from the following answers
A) 12345 B) 11111 C) can't be determined D) None of these E) 22222

Solution: Solution   Go through option Sn = 1 + 3 + 5 + 7 +...+ 22221   S11111 = (11111)2   Hence it is divisible by 11111.   Thus Answer 11111
Answer: B
What is the probability for a family with four children to have a boy and three girls (assuming the probability of having a boy or a girl is equal)?  Choose one.
A) 1/2	B) 1/3	C) 1/4	D) 1/8	E) 1/16

Solution: One possible case is: girl - girl - girl - boy   The probability of this is 1/2*1/2*1/2*1/2 = 1/16   There are 4C3 = 4 such cases so we should multiply by 4.   P(one boy and three girls) = 4/16 = 1/4   The answer is 1/4.
Answer: C
A train 120 m long crosses a platform with a speed of 60 kmph in 15 sec; find the length of the platform?	Choose the correct choice from the following answers
A) 110	B) 130	C) 120	D) 125	E) 135

Solution: D = 120 + x   T = 15   S = 120+x/15 * 18/5 = 60 kmph.   => (120+x) * 18 = 4500   => 120 + x = 250 => x= 130 m   Answer: 130
Answer: B
What is the next number of the following sequence
8,8,15,23,39.....  Pick:
A) 44	B) 54	C) 64	D) 74	E) 68

Solution: 8,8,15,23,39, x     8 + 8= 
  8 + 8 = 16
16==> 16 - 1= 
16 - 1 = 15
15   8 + 15= 
8 + 15 = 23
23==> 23 + 0= 
23 + 0 = 23
23   15 + 23= 
15 + 23 = 38
38=> 38 + 1= 
38 + 1 = 39
39   23 + 39= 
23 + 39 = 62
62=> 62 + 2= 
62 + 2 = 64
64   ANSWER:64
Answer: C
A recycling facility is staffed by 9 floor workers and one manager. All of the floor workers are paid equal wages, but the manager is paid n times as much as a floor worker. If the manager’s wages account for 1/9 of all wages paid at the facility, what is the value of n? Pick one
A) 8/7 B) 8 C) 9/8 D) 7 E) 5

Solution: Say each floor worker is paid $x, then the manager is paid $xn.   Total salary would be 9x+xn and we are told that it equals to 9xn:   9x+xn=9xn --> reduce by x: 9+n=9n -->8n=9   n = 9/8   Answer: 9/8
Answer: C
In how many ways a team of 11 must be selected from 5 men and 11 women such that the team must comprise of not more than 3 men?
Choose the correct choice from the following options:  A) 2256  B) 2377  C) 2797  D) 2672  E) 1991

Solution: Ans: C   Explanation;   The team may consist of 0 men + 11 women, 1 men + 10 women, 2 men + 9 women, or 3 men + 8 women.   So Number of ways are = 11C11+5C1×11C10+5C2×11C9+11C11+5C1×11C10+5C2×11C9+5C3×11C85C3×11C8   = 2256   2256nswer:2256
Answer: A
A man walking at the rate of 5 km/hr crosses a bridge in 15 minutes. The length of the bridge (in metres) is  Pick:
A) 600  B) 750  C) 1000  D) 1250  E) None of these

Solution: Explanation:   speed = (5 × 5/18)m/sec   = 25/18 m/sec.   Distance covered in 15 minutes = (25/18 × 15 × 60)m   = 1250 m.   Answer: 1250
Answer: D
A division of a company consists of three men and four women. If two of these employees are randomly selected as representatives of the division, what is the probability that both representatives will be female?
Choose the correct choice from the following answers.
A) 1/4 B) 2/7 C) 3/11 D) 4/15 E) 5/21

Solution: Total number of ways to select 2 members = 7C2 = 21   Total number of ways to select 2 females = 4C2 = 6   P(two females) = 6/21 = 2/7   The answer is 2/7.
Answer: B
Sophia finished 2/3 of a book. She calculated that she finished 90 more pages than she has yet to read. How long is her book?	Choose the correct choice from the following options
A) 140
B) 330
C) 460
D) 590
E) 270

Solution: Let x be the total number of pages in the book, then she finished 2/3⋅x pages.   Then she has x−2/3⋅x=1/3⋅x pages left.   2/3⋅x−1/3⋅x=90   1/3⋅x=90   x=270   So the book is 270 pages long   correct answer 270
Answer: E
The average marks obtained by 120 cndidates in a certainexaminationis 35.if the average marks of passed candidate is 39 and that ofthe failed candidates is 15,what is the no. of candidates who passed the examination Choose the most appropriate option:  A) 14 years  B) 14 years 3 month  C) 14 years 8 month  D) 15 years 8 month  E) 16 years 2 month

Solution: (d) Let No. of passed candidates are x   So, x * 39 + (120 – x) 15= 120 * 35   x = 100   2.(a) Total increase = 8 * 2= 
8 * 2 = 16
16 years   So, total age of two women= 35 + 45 +16= 
35 + 45 +16 = 96
96   Average age of two women=96/2= 
96/2 = 48
48 years   3(d) Total decrease= 20 * 2= 
20 * 2 = 40
40 month= 3 years 4 month   So, age of new boy = 18 years – 3 years 4 month   = 14 years 8 month   14 years 8 month
Answer: C
A clock shows the time as 8 a.m. If the minute hand gains 5 minutes every hour, how many minutes will the clock gain by 6 p.m.?  Choose the correct answer
A) 45 minutes	B) 55 minutes	C) 35 minutes	D) 25 minutes	E) 50 minutes

Solution: there are 10 hours in between 8 a.m. to 6 p.m.   10*5= 
10*5 = 50
50 minutes.   ANSW50 minutesR:50 minutes
Answer: E
Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 16 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is?  Choose the correct choice from the following answers:  A) 277  B) 444  C) 128  D) 127  E) 109

Solution: 1h ----- 5   ? ------ 60   12 h   RS = 16 + 21= 
16 + 21 = 37
37   T= 12   D = 37 * 12= 
37 * 12 = 444
444   Answer:444
Answer: B
Find the odd man out. 742, 743, 633, 853, 871, 616, 532	Pick: A) 616 B) 990 C) 633 D) 743 E) None of these

Solution: Explanation :   In all numbers except 616, the difference of third and first digit is the middle digit. 616nswer : Option 616
Answer: A
For any a and b that satisfy |a – b| = b – a and a > 0, then |a + 6| + |-b| + |b – a| + |ab| = Choose the most appropriate option
A) ab + 2b + 6
B) a-b-6
C) a+b+6
D) 2a+2b-6
E) 2a+b+6

Solution: Observation-1: |a – b| = b – a   which is possible only when signs of a and b are Same   Since Given a > 0   so we figure out that a and b are both positive   Observation-2: |a – b| must be Non-Negative and so should be the value of b-a which is possible only when absolute value of b is greater than or equal to absolute value of a   Now you may choose the values of a and b based on above observations   e.g. b = 6 and a=1 and check the value of given functions and options   |a + 6| + |-b| + |b – a| + |ab| = |1 + 6| + |-6| + |6 – 1| + |1*6| = 24   ab + 2b + 6= 1*6+12+6= 
1*6+12+6 = 24
24   all other options are not equal to 24   ab + 2b + 6nswer : ab + 2b + 6
Answer: A
In how many different number of ways 5 men and 2 women can sit on a shopa which can accommodate persons?  Options:
A) 209 B) 210 C) 230 D) 235 E) 240

Solution: Option '210'   7p3 = 7 × 6 × 5 = 210
Answer: B
If s and t are positive integers such that s/t = 64.18, which of the following could be the remainder when s is divided by t ? Options
A) 2	B) 4	C) 8	D) 20	E) 45

Solution: The remainder is 0.18 or 18/100. You can go one step further and say that X/Y=18/100, where X and Y are whole numbers. Plug in all the answer choices for X and see which one makes Y a whole number.   One thing that jumps out at me is that A, B, C, and D are all even. E on the other hand is odd. Why? Maybe I'll start plugging in here first.   45/Y=18/100   18Y=4500   Y=250   Answer: 45.
Answer: E
In a party men drink only beer, women drink only wine , sons drink only orange juice and daughters drink only apple juice. There are 1.05L of beers, 1.05L of wine 3.5L of orange juice and 4.9L of apple juice. If every one has the same drinking capacity then what can be the minimum number of people present at the party?	Choose the correct choice from the following options:
A) 20 B) 30 C) 40 D) 50 E) 60

Solution: Take HCF of 1.05,1.05,3.5,4.9.   which is 0.35.   Then divide each quantity by HCF to get the number people drinking that particular beverage.   i.e 3+3+10+14=30.   ANSWER:30
Answer: B
Which is a better investment 6% stock at of 220 or 5 1/2 stock at 200?
Choose the correct answer.
A) 6% stock at of 220  B) Cannot be compared, as the total amount of investment is not given  C) Both are equally good  D) None  E) 5 1/2 stock at 200

Solution: Let investment in each case be Rs. (220 x 200).   Income in 1st case = Rs.6 x 220 x 200/220	= Rs. 1200.   Income in 2nd case = Rs.11 x 220 x 200/(2*200)= Rs. 1210   Clearly, 5 1/2 stock at 200 is better.   ANSW5 1/2 stock at 200R:5 1/2 stock at 200
Answer: E
A train moves fast a telegraph post and a bridge 264 m long in 8 sec and 30 sec respectively. What is the speed of the train?	Choose the correct choice:
A) 89
B) 23
C) 56
D) 43.2
E) 67

Solution: Let the length of the train be x m and its speed be y m/sec.   Then, x/y = 8 => x = 8y   (x + 264)/30 = y   y = 12   Speed = 12 m/sec = 12 * 18/5= 
12 * 18/5 = 216/5 = around 43.2
43.2 km/hr.   Answer: Option 43.2
Answer: D
The price of 2 sarees and 4 shirts is Rs. 1600. With the same money one can buy 1 saree and 6 shirts. If one wants to buy 12 shirts, how much shall he have to pay ?	Pick one:  A) 4800  B) none of these  C) 3600  D) 1200  E) 2400

Solution: Let the price of a saree and a shirt be Rs. x and Rs. y respectively.   Then, 2x + 4y = 1600 .... (i)   and x + 6y = 1600 .... (ii)   Divide equation (i) by 2, we get the below equation.   => x + 2y = 800. --- (iii)   Now subtract (iii) from (ii)   x + 6y = 1600 (-)   x + 2y = 800   ----------------   4y = 800   ----------------   Therefore, y = 200.   Now apply value of y in (iii)   => x + 2 x 200 = 800   => x + 400 = 800   Therefore x = 400   Solving (i) and (ii) we get x = 400, y = 200.   Cost of 12 shirts = Rs. (12 x 200) = Rs. 2400.   Answer is 2400.
Answer: E
Sushil got thrice as many marks in English as in Science. His total marks in English, Science and Maths are 162. If the ratio of his marks in English and Maths is 3:5, find his marks in Science?	Pick:
A) 24
B) 18
C) 20
D) 25
E) 16

Solution: S:E = 1:3   E:M = 3:5   ------------   S:E:M = 3:9:15   3/27 * 162= 
3/27 * 162 = 18
18   ANSWER 18
Answer: B
Amol was asked to calculate Arithmetic mean of 10 positive integers, each of which had 2 digits. By mistake, he interchanged the 2 digits, say a and b,in one of these 10 integers. As a result, his answer for the Arithmetic mean was 1.8 more than what it should have been. Then b - a equals	Choose the correct choice from the following answers
A) 1 B) 2 C) 3 D) 4 E) None of these

Solution: Explanation :   Arithmetic mean is more by 1.8 means sum is more by 18.   So, ba – ab = 18.   b > a because sum has gone up, e.g. 31 – 13 = 18.   Hence, b – a = 2.   Answer : 2
Answer: B
A, B and C enter into partnership. A invests some money at the beginning, B invests double the amount after 6 months, and C invests thrice the amount after 8 months. If the annual gain be Rs.24000. A's share is?	Choose the correct choice from the following answers
A) 2999 B) 8000 C) 6000 D) 2889 E) 6612

Solution: x* 12 : 2x* 6: 3x* 4   1:1:1   1/3 * 24000= 
1/3 * 24000 = 8_000
8000   Answer:8000
Answer: B
From the beginning to the end of 2007, the price of a stock rose 20 percent. In 2008, it dropped 25 percent. In 2009, it rose 15 percent. What percent of the stockâ€™s 2007 starting price was the price of the stock at the end of 2009? Choose the correct option:
A) 80
B) 103.5
C) 95
D) 100
E) 108

Solution: Assume a value at the beginning of 2007. As this is a % question, assume P=100.   At the end of 2007 it becmae = 1.2*100= 
1.2*100 = 120
120   At the end of 2008 it decreased by 25%= 120*.75= 
120*.75 = 90
90   At the end of 2009 it increased by 20%= 90*1.15= 
90*1.15 = 103.5
103.5   Thus ratio= 103.5/100 = 1.03 (in % terms = 103%). Thus 103.5 is the correct answer.
Answer: B
A man’s speed with the current is 16 km/hr and the speed of the current is 2.5 km/hr. the man’s speed against the current is : Choices.
A) 8.5 km/hr
B) 9.5 km/hr
C) 11 km/hr
D) 12.5 km/hr
E) None of these

Solution: Solution   Man's rate in still water = (16-2.5) km/hr = 13.5 km/hr.   Man's rate against the current = (13.5-2.5) km/hr = 11 km/hr Answer 11 km/hr
Answer: C
A large box contains 18 small boxes and each small box contains 25 chocolate bars. How many chocolate bars are in the large box? Choose the correct option
A) 250  B) 350  C) 450  D) 550  E) 650

Solution: The number of chocolate bars is equal to   18 * 25= 
18 * 25 = 450
450   correct answer 450
Answer: C
A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is? Choose the correct choice from the following:  A) 11  B) 50  C) 99  D) 77  E) 55

Solution: Speed of the train relative to man = 125/10 = 25/2 m/sec.   = 25/2 * 18/5= 
25/2 * 18/5 = 45
45 km/hr   Let the speed of the train be x km/hr. Then, relative speed= (x - 5) km/hr.   x - 5 = 45 => x = 50 km/hr.   Answer: 50
Answer: B
A boy has 10 trousers and 12 shirts. In how many different ways can he select a trouser and a shirt?  Choose the correct answer:
A) 120ways  B) 110ways  C) 125ways  D) 130ways  E) 145ways

Solution: The boy can select one trouser in 10 ways.   The boy can select one shirt in 12 ways.   The number of ways in which he can select one trouser and one shirt is   10 * 12= 
  10 * 12 = 120
120 ways.   120waysnswer: 120ways
Answer: A
A bag contains 6 red, 4 blue and 2 green balls. If 2 ballsare picked at random, what is the probability that both are red?
Choose the correct choice from the following choices:
A) 1/13	B) 2/23	C) 5/26	D) 5/22	E) 3/23

Solution: P(Both are red),   =6C212C2=6C212C2   =15/66=5/22   5/22
Answer: D
The length of a rectangle is increased by 25% and its breadth is decreased by 20%. What is the effect on its area? Choose the correct choice from the following answers:	A) Remains same	B) 5% decrease	C) 5% increase	D) 10% increase	E) 20% increase

Solution: 100 * 100= 
100 * 100 = 10_000
10000   125 * 80= 
125 * 80 = 10_000
10000   No change   Remains sameNSWER:Remains same
Answer: A
From the word 'ASTOUNDER', how many independent words can be made with-out changing the order of the letters and using each letter only once ? Choose the correct option:
A) 5	B) 8	C) 3	D) 2	E) 9

Solution: Explanation:   The words formed are   AT and UN2ER, AS and UN2ER (or) AT and SOUN2   Answer: 2) 2
Answer: D
If each side of a square is increased by 25%, find the percentage change in its area.	Choose the correct choice from the following options
A) 26.25%	B) 36.25%	C) 46.25%	D) 56.25%	E) 66.25%

Solution: Let each side of the square be a. Then, area = a2.   New side =(125a/100) =(5a/4). New area = (5a/4) 2=(25a2)/16.   Increase in area = ((25 a2)/16)-a2=(9a2)/16.   Increase% = [((9a2)/16)*(1/a2)*100] % = 56.25%.   Option 56.25%
Answer: D
Two persons starting from the same place walk at a rate of 10kmph and 14.5kmph respectively. What time will they take to be 18km apart, if they walk in the same direction?  Choose the correct choice from the following:
A) 4 hrs
B) 9 hrs
C) 5 hrs
D) 2 hrs
E) 6 hrs

Solution: The relative speed of the boys = 14.5kmph – 10kmph   = 4.5 kmph   Distance between them is 18 km   Time= 18km / 4.5 kmph = 4 hrs   4 hrsnswer : 4 hrs
Answer: A
Three partners A,B and C invest Rs.18000, Rs.22500 and Rs.27000 respectively in a business. If total profit is Rs.12000 then B's share is (in Rs.)  Choices.
A) 10000
B) 6500
C) 4000
D) 7500
E) 8500

Solution: 18000:22500:27000   4:5:6   B's share=12000*5/15= 
12000*5/15 = 4_000
4000   ANSWER:4000
Answer: C
The school soccer team looks at their record and finds that they win, lose, and tie games in a ratio of 4:3:1. How many games did they play if they lost 9 games?
Choose the most appropriate option:
A) 3
B) 9
C) 12
D) 18
E) 24

Solution: The ratio is 4 wins: 3 losses: 1 tie.   Think of ratio as "parts."   Divide 9 (total losses) by 3 (ratio losses) to find 1 "part" of the ratio.   9/3= 
9/3 = 3
3   This means the team tied 3 games.   Multiply 3 (1 "part" of ratio) by 4 (ratio wins) to find total wins.   3*4= 
3*4 = 12
12.   This mean the team won 12 games.   Add up wins, losses, and ties.   12+9+3= 
12+9+3 = 24
24   The answer is 24
Answer: E
A gardener wants to plant trees in his garden in rows in such a way that the number of trees in each row to be the same. If there are 24 rows the number of trees in each row is 42 if there are 12 more rows find the number of trees in each row?
Pick.
A) 63  B) 28  C) 48  D) 32  E) 33

Solution: Required number of trees   = 24/36 * 42= 
24/36 * 42 = 28
28.   ANSWER:28
Answer: B
What is the average of xx, 2x2x, and 66? Choose the correct choice from the following choices
A) x+2x
B) 2x+2
C) x+2x+2
D) 2x
E) 2x+1

Solution: By the definition of an average, we get:   x+2x+63=3x+63x+2x+63=3x+63   =3(x+2)3=x+2.=3(x+2)3=x+2.   Hence, the answer is x+2x+2 or Option x+2x+2
Answer: C
Five fencers participate in a fencing championship. Assuming all competitors have an equal chance of winning, how many possibilities are there with respect to how a first-place and second-place medal can be awarded? Pick one
A) 6
B) 8
C) 12
D) 16
E) 20

Solution: 5*4= 
5*4 = 20
20   The answer is 20.
Answer: E
In the city of San Durango, 80 people own cats, dogs, or rabbits. If 50 people owned cats, 20 owned dogs, 30 owned rabbits, and 16 owned exactly two of the three types of pet, how many people owned all three? Pick: A) 1 B) 2 C) 4 D) 7 E) 9

Solution: Total = C + D + R - (CD + DR + CR) - 2CDR   80 = 50 + 20 + 30 - (16) - 2x   x = 2   So, answer will be 2
Answer: B
If 20% of a = b, then b% of 20 is the same as: Choose the correct answer
A) None of these
B) 10% of a
C) 4% of a
D) 20% of a
E) 30% of a

Solution: Explanation:   20% of a=b   b=20a/100=a/5   b% of 20=20 x b/100   =b/5=a/5x1/5=a/25   =4a/100=4% of a   ANSWER IS 4% of a
Answer: C
The cost price of 13 articles is equal to the selling price of 11 articles. Find the profit percent? Select the correct option:
A) 18 2/91%
B) 18 2/11%
C) 18 9/11%
D) 18 2/91%
E) 12 2/11%

Solution: 13 CP = 11 SP   11 --- 2 CP   100 --- ? =>18 2/11%   Answer:18 2/11%
Answer: B
The cost of 12 packets of sugar, each weighing 900 grams is Rs. 28. What will be the cost of 27 packets, if each packet weighs 1 kg?
Choose the correct choice from the following answers:
A) Rs 52.50
B) Rs 56
C) Rs 58.50
D) Rs 70
E) None of these

Solution: Explanation :   Let the required cost be Rs. x. Then,   More packets, More cost (Rs 70irect Proportion)   More weight, More cost (Rs 70irect Proportion)   Packets 12 : 27   Weight 900 : 1000 :: 28 : x   (12 x 900 x x) = (27 x 1000 x 28)   x = (27 x 1000 x 28) /12 x 900   =70   Answer Rs 70
Answer: D
A train 490 m long, running with a speed of 63 km/hr will pass a tree in?  Choices:	A) 15 sec	B) 16 sec	C) 28 sec	D) 20 sec	E) 25 sec

Solution: Speed = 63 * 5/18 = 35/2 m/sec   Time taken = 490 * 2/35= 
490 * 2/35 = 28
28 sec   ANSWER: 28 sec
Answer: C
Can you replace the question mark with the number to complete the series, provided the pair of numbers exhibits a similar relationship?
? : 4623 :: 9 : 647 Answers:	A) 17	B) 16	C) 14	D) 19	E) 20

Solution: 20   17   20xplanation :   The relationship holds for below formula :   pow(x,3) - pow(x,2) - 1   => 9*9*9 - 9*9 - 1   => 729 - 81 - 1= 
729 - 81 - 1 = 647
> 647   Similarly,   17*17*17 - 17*17 - 1=> 4913 - 289 - 1= 
4913 - 289 - 1 = 4_623
> 4623
Answer: E
A father said to his son, "I was as old as you are at present at the time of your birth." If the father's age is 60 years now, the son's age 10 years back was?
Select.
A) 12yr B) 15yr C) 14yr D) 10yr E) 20yr

Solution: Let the son's present age be x years   Then, 60-x = x   x = 30   Son's age 10 years back = 30-10= 
30-10 = 20
20years   Answer is 20yr
Answer: E
A coin is tossed 3 times. Find out the number of possible outcomes.
Choose the most appropriate option:
A) None of these
B) 8
C) 2
D) 1
E) 3

Solution: Explanation :   When a coin is tossed once, there are two possible outcomes - Head(H) and Tale(T)   Hence, when a coin is tossed 3 times, the number of possible outcomes   = 2 x 2 x 2 = 8   (The possible outcomes are HHH, HHT, HTH, HTT, THH, THT, TTH, TTT ) Answer : Option 8
Answer: B
Sam purchased 20 dozens of toys at the rate of Rs. 375 per dozen. He sold each one of them at the rate of Rs. 33. What was his percentage profit?
Choose the most appropriate option:
A) 3.5%
B) 4.5%
C) 5.6%
D) 6.5%
E) 2.5%

Solution: Cost Price of 1 toy = Rs.375/12= Rs. 31.25   Selling Price of 1 toy = Rs. 33   So, Gain = Rs. (33 - 31.25) = Rs. 1.75   Profit % =(1.75/31.25x 100)%	=28/5= 
28/5 = 28/5 = around 5.6
5.6%   Answer is 5.6%.
Answer: C
A box contains 2 white balls, 3 black ball and 4 red balls. In how many ways can 3 balls be drawn from the box, if at least one black ball is to be included in the draw? Answers
A) 74  B) 58  C) 12  D) 52  E) 64

Solution: We may have ( 1 black and 2 non black) or (2 black and 1 non black)or(3 black)   =3c1 x 6c2 + 3c2 x 6c1 +3c3   =64   ANS: 64
Answer: E
What is the remainder when 8^381 is divided by 5 ?
Select
A) 0 B) 1 C) 2 D) 3 E) 4

Solution: I also agree that the remainder is '3' (using the last digit of the powers of 7). Could we have the official answer please?3
Answer: D
The average of seven consecutive numbers A, B, C, D, E, F and G is 9. What percent of G is A? Choose the correct choice from the following:  A) 42.0  B) 48.0  C) 50.0  D) 52.2  E) 54.0

Solution: Explanation :   In such a case the middle number (D) is the average   ∴ D = 9 and A = 6 and G = 12   Required percentage = 6/12 x 100 = 50.0   Answer : Option 50.0
Answer: C
A baker charges N dollars for a birthday cake. Next week, she intends to earn 320 dollars selling cakes. If she were to reduce the price of the cake by 20 percent, she would have to sell two more cakes to earn the same amount of revenue. How many cakes does she intend to sell next week?	Choose the most appropriate option.
A) 2  B) 4  C) 6  D) 8  E) 10

Solution: We're told that by selling cakes at N dollars/cake, a baker will make $320.   Reducing the price by 20% and selling 2 MORE cakes will also make her $320.   We're asked for the original number of cakes that the baker intends to sell.   $320 is a rather interesting number. Based on the answer choices, we're almost certainly dealing with integer values for the number of cakes AND the price per cake. As such, 6 is probably NOT going to be part of the solution (either as 4 and 6 cakes or as 6 and 8 cakes). As such, we can avoid Answers B and C....   Let's TEST ANSWER D: 8 cakes   IF....   Original cakes = 8   8(N) = $320, so N = $40/cake   20% off = $8 off = 40-8= 
40-8 = 32
$32/cake   +2 more cakes= 8+2= 
8+2 = 10
10 cakes   10(32)= $320   This is an exact MATCH for what we were told, so this MUST be the answer.   Final Answer:   8
Answer: D
If the perimeter of ΔACD is 9+3√3, what is the perimeter of equilateral triangle ΔABC? Select the correct option:  A) 9  B) 18−3√3  C) 18  D) 18+3√3  E) 27

Solution: The altitude of an equilateral triangle is side*√3/2.   As perimeter of triangle ACD is 9+3√3, AC + CD + AD =   (side+side/2+side*√3/2) = 9 + 3√3 or side =6.   Perimeter of equilateral triangle, ABC is 3(side) or 18.   Answer:(Option18)
Answer: C