MU-NLPC/Calc-aqua_rat huggingface dataset:
In a certain game, you perform three tasks. You flip a quarter, and success would be tails. You roll a single die, and success would be a six. You pick a card from a full playing-card deck, and success would be picking a spades card. If any of these task are successful, then you win the game. What is the probability of winning? Choose the correct choice from the following:
A) 1/48 B) 11/16 C) 11/12 D) 5/16 E) 23/48

Solution: First lets get the overview   Event 1(A) = Flipping the quarter( Probability of both winning/loosing = 1/2)   Event 2(B) = Rolling a dice( Probability of winning = 1/6 ;Probability of loosing= 1 - 1\6 =5\6)   Event 3(C) = Drawing a card( SPADES) Probability of winning = 13/52=3/4 ;Probability of loosing= 1 - 3/4 =1/4)   So now as above we have three events A,BC.   1st method(This is lengthy method)   Possible cases in which it's a win( the highlighted green event is a win and red is loose.   1.A11/16C= 1/2*5/6*3/4   OR   2.A11/16C= 1/2*1/6*3/4   OR   3.A11/16C= 1/2*5/6*1/4   OR   4.A11/16C= 1/2*1/6*3/4   OR   5.A11/16C= 1/2*5/6*1/4   OR   6.A11/16C= 1/2*5/6*1/4   OR   7.A11/16C= 1/2*1/6*1/4   As we now OR means add   Adding up all of them we'll get the probability of winning ie 11/16   Answer : 11/16
Answer: B
If a code word is defined to be a sequence of different letters chosen from the 8 letters A, B, C, D, E, F, G, AND H, what is the ratio of the number of 5-letter code words to the number of 4-letter code words?
Pick.
A) 4 B) 8 C) 5 D) 10 E) 12

Solution: Method #1: Using the permutation formula   # of 5 letter code words:   nPr = n! / (n – r)! = 8! / (8 – 5)! = 8*7*6*5*4   # of 4 letter code words:   nPr = 8! / (8 – 4)! = 8*7*6*5   # of 5 words / # of 4 words = (8*7*6*5*4)/(8*7*6*5)= 
(8*7*6*5*4)/(8*7*6*5) = 4
4= 4   4
Answer: A
A can do a certain work in the same time in which B and C together can do it. If A and B together could do it in 10 days and C alone in 50 days,then B alone could do it in :  Pick one.
A) 15 days  B) 20 days  C) 25 days  D) 30 days  E) None of these

Solution: Solution   (A +B)’s 1 day’s work =1/50; C's 1 day's work = 1/50   (A+B+C)’s 1 day’s work = (1/10+1/50)=6/50=3/25…..(i)   Also,A’s 1 day’s work =(B +C)’s 1 day’s work ……(ii)   From (i) and (ii),we get : 2 × (A’s 1 day’s work) =3/25   ⇒ A’s 1 day’s work = 3/50   ∴ B’s 1 day’s work = (1/10-3/50)=2/50=1/50   So, B alone could do the work in 25 days.   Answer 25 days
Answer: C
How many days are there in x weeks x days
Choose the correct choice:  A) 14x  B) 8x  C) 7x2  D) 7  E) 8

Solution: Explanation :   x weeks x days = (7 × x) + x = 7x + x = 8x days .Answer : Option 8x
Answer: B
In how many T ways can the letters of the word JUPITER be arranged in a row so that the vowels appear in alphabetic order?	Choose the correct choice from the following options:
A) 736 B) 768 C) 792 D) 840 E) 876

Solution: three letters can be arranged in 3! ways.   only one combination EIU is required.   7 letters can be arranged in 7! ways.   thus T=7!/ 3! * 1 = 840.   840
Answer: D
There are 8436 steel balls, each with a radius of 1 cm, stacked in a pile, with 1 ball on top, 3 balls in the second layer, 6 in the third layer, 10 in the fourth and so on. the number of horizontal layer on the pile is Choose the correct choice from the following:
A) 34	B) 38	C) 36	D) 32	E) None

Solution: Explanation :   Assume the number of layers in horizontal pile is n.   So, Σn(n+1)/2 = 8436.   => (1/2) [ Σn2 + Σn ] = 8436.   => n(n+1)(n+2)/12 +n(n+1)/4 = 8436.   => n(n +1) [(2n + 4) / 12 ] = 8436.   => n(n +1)(n+2) / 6 = 8436.   => n(n +1)(n+2) = 36 x 37 x 38.   So, n=36.   Answer : 36
Answer: C
A shopkeeper loses 15%,if an article is sold for Rs. 119. What should be the selling price of the article to gain 20%? Choose the correct choice from the following answers:
A) s.177 B) s.168 C) s.144 D) s.129 E) s.112

Solution: Given that SP = Rs. 119 and loss = 15%   CP = [100(SP)]/(100 - l%) = (100 * 119)/85 = Rs. 140.   To get 20% profit, New SP = [(100 + p%)CP]/100   = (140 * 120)/100   = Rs.168   Answer:s.168
Answer: B
The time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 48 kmph, find the speed of the stream? Choose one.
A) 16 kmph B) 19 kmph C) 14 kmph D) 11 kmph E) 13 kmph

Solution: The ratio of the times taken is 2:1.   The ratio of the speed of the boat in still water to the speed of the stream   = (2+1)/(2-1)= 
(2+1)/(2-1) = 3
3/1= 
3/1 = 3
3:1   Speed of the stream= 48/3= 
48/3 = 16
16 kmph.   16 kmphnswer: 16 kmph
Answer: A
0.1+0.1^2+ 0.1^3=  Pick.
A) 0.1	B) 0.111	C) 0.1221	D) 0.2341	E) 0.3

Solution: You have a mistake in your question. Choice B should be (.111) and not (.11).   The equation in the solution can be simplified to (.1 + .01 + .001).   Adding those together you get:   .100   .010   .001   ------   .111 - Which is answer choice (0.111)
Answer: B
All of the stocks on the over-the-counter market are designated by either a 6-letter or a 5-letter code that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different stocks that can be designated with these codes?
Choose the most appropriate option:  A) a. 2(26^5)  B) b. 26(26^4)  C) c. 27(26^4)  D) d. 26(26^5)  E) e. 27(26^5)

Solution: no of different stocks for 6-letter code = 26^6   no of different stocks for 5-letter code = 26^5   total = 26^6 + 26^5 = 26^5(26+1) = 27(26^5)   [Reveal]Spoiler:   Option e. 27(26^5)
Answer: E
A Bus running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the Bus?	Pick one
A) 160 metres B) 150 metres C) 130 metres D) 120 metres E) 110 metres

Solution: B   150 metres   Speed= 60 x 5/18 m/sec = 50/3 m/sec.   Length of the Bus = (Speed x Time).   Length of the 150 metresus = 50/3 x 9 m = 150 m.
Answer: B
A train 200 m long crosses a platform 150 m long in 20 sec; find the speed of the train?	Choose the correct choice from the following options:
A) 73  B) 63  C) 65  D) 70  E) 83

Solution: D = 200 + 150= 
200 + 150 = 350
350   T= 20   S = 350/20 * 18/5= 
350/20 * 18/5 = 63
63 kmph.   Answer: 63
Answer: B
Income and expenditure of a person are in the ratio 3 : 2. If the income of the person is Rs. 21000, then find his savings?  Choices
A) 6000  B) 7000  C) 8000  D) 9000  E) 10000

Solution: Let the income and the expenditure of the person be Rs. 3x and Rs. 2x respectively.   Income, 3x = 21000   => x = 7000   Savings = Income - expenditure   = 3x - 2x = x   So, savings =Rs.7000.   Answer: 7000
Answer: B
72 men working 8 hours per day dig 30 m deep. How many extra men should be put to dig to a depth of 50 m working 6 hours per day?	Choose the correct answer
A) A)77	B) B)99	C) C)66	D) D)55	E) E)88

Solution: (72 * 8)/30   = (x * 6)/50   => x =160   160 – 72   = 88   Answer:88
Answer: E
If q and r are both odd numbers M, which of the following must also be odd? Answers.
A) q – r  B) (q + r)^2  C) q(q + r)  D) (qr)^2  E) q/r

Solution: We're told that q and r are both ODD numbers M. We're asked which of the following must also be odd.   IF...   q = 1   r = 3   Answer A) q – r = 1-3 = -2 NOT odd   Answer B) (q + r)^2 = (1+3)^2 = 16 NOT odd   Answer C) q(q + r) = (1)(4) = 4 NOT odd   Answer (qr)^2) (qr)^2 = (3)^2 = 9 This IS O(qr)^2(qr)^2   Answer E) q/r = 1/3 NOT odd   Final Answer:   (qr)^2
Answer: D
If W is a positive integer, which of the following must be odd? Choose the correct choice from the following answers
A) x+1	B) W^2W	C) W^2+W+1	D) x^2−1	E) 3x^2−3

Solution: A. W+1 = can be odd or even. Since O + O =E or E + O = O   B. W^2 + W = W(W+1). Since from the above derivation we already know the term W+1 can be Odd or Even, directly substitute here. W(ODD) = Even (When W is Even) or W(EVEN) = EVEN [When W is ODD]   C. Here's the answer. Since we know the term W^2 + W can always take a EVEN number, EVEN + 1 = ODD   Hence W^2+W+1.
Answer: C
A can finish a work in 6 days and B can do the same work in 15 days. B worked for 10 days and left the job. In how many days, A alone can finish the remaining work?  Choose the correct choice from the following answers.
A) 6	B) 5	C) 5.5	D) 2	E) 8

Solution: B's 10 day's work = ( 1 x 10 ) = 2 .   15 3   Remaining work = ( 1 - 2 ) = 1 .   3 3   Now, 1 work is done by A in 1 day.   6   Therefore 1 work is done by A in ( 6 x 1 ) = 2 days.   2
Answer: D
A certain bacteria colony doubles in size every day for 10 days, a which point it reaches the limit of its habitat and can no longer grow. If two bacteria colonies start growing simultaneously, how many days will it take them to reach the habitat’s limit?
Answers
A) 6.33
B) 9
C) 10
D) 15
E) 19

Solution: Case 1: Consider the bacteria num to be B. As it doubles every day, number of bacteria at the end of each day would be   Day 1 – B   Day 2 – 2B   Day 3 – 4B   Day 4 – 8B   .   .   .   Day 10 – 2^19 B   It can be implied that the capacity of the habitat is 2^19 B.   Case 2: There are 2 bacteria which keep doubling every day. So, the count would be   Day 1 – 2B   Day 2 – 4B   Day 3 – 8B   .   .   .   Day 18 – 2^18 B   Day 19 – 2^19 B --> this is the point where the habitat is filled to its capacity.   Hence, 9 is the answer   9
Answer: B
How many terms are in the G.P. 3, 6, 12, 24, ......., 3072 ? Select.
A) 8
B) 9
C) 11
D) 5
E) 2

Solution: Explanation:   Here a = 3 and r = 6/3= 
6/3 = 2
2. Let the number of terms be n.   Then, t= 3072 => a * r^(n-1) = 3072   => 3 * 2^(n-1) = 3072 => 2^(n-1) = 1024 = 2^(10)   => n-1 = 10 => n = 11   Answer: 11
Answer: C
Convert 50miles into yards?	Answers.
A) 25630 yards B) 35200 yards C) 88000 yards D) 42560 yards E) 41520 yards

Solution: 1 mile = 1760 yards   50 miles = 50*1760= 
50*1760 = 88_000
88000 yards   Answer is 88000 yards
Answer: C
The length of a rectangular landscape is 4times its breadth. There is a playground in it whose area is 1200 square mtr & which is 1/3rd of the total landscape. What is the length of the landscape?  Pick:  A) 100  B) 140  C) 120  D) 160  E) 180

Solution: Sol. x * 4x = 3 * 1200   x = 30   Length = 4 * 30= 
4 * 30 = 120
120   120
Answer: C
Eshan and Mary each wrote two or three poem every day over a period of time eshan wrote 43 poems while Mary wrote 61. The number of days in this period is.....	Choose the correct choice from the following answers:
A) 19	B) 21	C) 20	D) 18	E) 17

Solution: suppose, Eshan writes 2poems in first 18days   18*2= 
  18*2 = 36
36.   2poems in next 2 days 2*2= 
2*2 = 4
4, 36+4=40   and 3poems in next 1day  1*3= 
 1*3 = 3
3, 40+3=43   So, Ultimately he takes (18+2+1)= 
(18+2+1) = 21
21days to write 43 poems.   now suppose, Marry writes 3poems in 1st 18days   18*3= 
  18*3 = 54
54   2poems in next 2days   2*2= 
  2*2 = 4
4, 54+4=58   3poems in next 1 day   1*3= 
  1*3 = 3
3, 58+3=61   So ultimately marry takes   (18+2+1)= 
  (18+2+1) = 21
21days to write 61poems.   ANSWER:21
Answer: B
What is the product of all positive factors of 25?  Pick one
A) 39
B) 324
C) 125
D) 150
E) 175

Solution: Positive factors of 25 are 1, 5, 25.   Product of positive factors:   25*5= 
  25*5 = 125
125   Answer: 125
Answer: C
A truck rental agency has the following terms. If a truck is rented for 8 hours or less the charge is RS.100 per hour or RS.8 per km whichever is more. On the other hand , if the truck is rented for more than 8 hours,the charge is RS.80 per hour or RS.6 per km whichever is more. A company rented a truck from the agency, and used it for 120 km and paid RS.800. For how many hours did the company rent the truck? Options:
A) 6  B) 8  C) 10  D) 12  E) 16

Solution: We can check each answer by substitution as it is fairly simple.   a) Cost = Max(960,600) = 960. Wrong   b) Cost = Max(960,800) = 960. Wrong   c) Cost = Max(720,800) = 800. Correct answer.   d) Cost = Max(720,960) = 960. Wrong   Answer is hence 10.
Answer: C
4 mat-weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 8 mat-weavers in 8 days?  Choices:  A) 4  B) 16  C) 8  D) 1  E) 2

Solution: Explanation:   Let the required number of mats be x   More mat-weavers, more mats (direct proportion)   More days, more mats (direct proportion)   Hence we can write as   (mat-weavers) 4:8   (days) 4:8}::4:x   ⇒4×4×x=8×8×4   ⇒x=2×2×4=16   Answer: Option 16
Answer: B
If f(x) + f(1 - x) + f(1 + x) + f(2 + x) = 2x for all real value of x. If f(0) = 1, then find the value of f(4)  Select the correct option:  A) 1  B) 2  C) 8  D) 7  E) 9

Solution: For x = 0, f(0) + f(1) + f(2) = 0 ............. (i)   For x = 1, f(1) + f(0) + f(3) = 2 ............. (ii)   subtracting (i) from (ii), we get f(3) - f(1) = 2 .......... (a)   For x (3) -  (1)= 
(3) -  (1) = 2
2 .......... (a)   For x= 2, f(2) + f(-1) + f(3) + f(4) = 4 ........ (iii)   For x = -1, f(-1) + f(2) + f(0) + f(1) = -2 ......... (iv)   subtracting from (iii) from (iv), we get   ⇒f(0)−f(4)−2=−6⇒f(0)−f(4)−2=−6 [ from (a) we know that f(3) - f(1) = 2]   Answer:2(3) -  (1)= 
(3) -  (1) = 2
2]   Answer:2
Answer: B
In a recent election, James received 2.1 percent of the 2,000 votes cast. To win the election, a candidate needed to receive more than 46 percent of the vote. How many additional votes would James have needed to win the election? Choose the correct choice from the following answers: A) 901 B) 879 C) 990 D) 991 E) 1,001

Solution: James = (2.1/100)*2000= 
(2.1/100)*2000 = 42
42   Votes to win= (46/100)*Total Votes +1 = (46/100)*2000 +1= 
(46/100)*2000 +1 = 921
921   Remaining Voted needed to win election= 921 - 42= 
921 - 42 = 879
879   Answer: option 879
Answer: B
Paul's income is 40% less than Rex's income, Quentin's income is 20% less than Paul's income, and Sam's income is 40% less than Paul's income. If Rex gave 60% of his income to Paul and 40% of his income to Quentin, Quentin's new income would be what fraction of Paul's new income?  Choose the correct choice from the following choices
A) 11/12	B) 13/17	C) 22/30	D) 12/19	E) 11/19

Solution: MAKE R = 10   P = 0.6R = 6   Q = 0.8P = 4.8   S= 0.6P = 3.6   FOR THAT WE GET P = 12   AND Q 8.8   SO 8.8/12 = = 2.2/ 3   Ans:22/30
Answer: C
The length of the bridge, which a train 140 metres long and travelling at 45 km/hr can cross in 30 seconds, is?	Choose the correct choice from the following
A) 245 B) 777 C) 282 D) 266 E) 235

Solution: Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (140 + x)/30 = 25/2 => 2(140 + x) = 750 => x = 235 m.   Answer: 235
Answer: E
Find the least number which when divided by 37 and 7 leaves a remainder of 2 in each case. Choose the correct option:
A) 259	B) 261	C) 263	D) 265	E) 267

Solution: The least number which when divided by different divisors leaving the same remainder in each case   = LCM(different divisors) + remainder left in each case.   Hence the required least number   = LCM(37, 7) + 2 = 261.   ANSWER:261
Answer: B
The circus sells two kinds of tickets: lower seats for $30 and upper seats for $20. On a certain night, the circus sells 80 tickets and gets $2100 in revenue from the sales. How many tickets for lower seats did they sell? Choose the most appropriate option
A) 40	B) 45	C) 50	D) 55	E) 60

Solution: Let L be the number of lower seat tickets.   Let U be the number of upper seat tickets.   L + U = 80 and U = 80-L.   30L+20U=2100.   30L+20(80-L)=2100   10L+1600=2100.   10L=500.   L=50.   The answer is 50.
Answer: C
The length of the room is 3m and width is 3m. Find the cost of paving the floor by slabs at the rate of Rs.300 per sq meter?	Answers:
A) 1800 B) 1500 C) 1700 D) 1600 E) 1540

Solution: l=3m w=3m   area of the floor = 3 x 3 = 9 sq m   cost of paving = 200 x 9 = Rs. 1800   1800nswer: 1800
Answer: A
If a farmer wants to plough a farm field on time, he must plough 90 hectares a day. For technical reasons he ploughed only 85 hectares a day, hence he had to plough 2 more days than he planned and he still has 40 hectares left. What is the area of the farm field and how many days the farmer planned to work initially?  Pick one:
A) 1600	B) 2490	C) 3780	D) 4235	E) 6179

Solution: Let x be the number of days in the initial plan. Therefore, the whole field is 90â‹…x hectares. The farmer had to work for x+2 days, and he ploughed 85(x+2) hectares, leaving 40 hectares unploughed. Then we have the equation:   90x=85(x+2)+40   5x=210   x=42   So the farmer planned to have the work done in 6 days, and the area of the farm field is 90(42)=3780 hectares   correct answer 3780
Answer: C
If A got 80 marks and B got 40 marks, then what percent of A's mark is B's mark?  Choices:
A) A)60%
B) B)80%
C) C)50%
D) D)75%
E) of these

Solution: A's marks = 80 ; B's marks = 40.   Let x% of A = B => x/100 * 80 = 40   => x = (40 * 100)/80= 
(40 * 100)/80 = 50
50   B's marks is 50% of A's marks.   ANSWER:50%
Answer: C
The numbers of pizza slices that are sold in Joey's Pizza are only in quantities of 4 and 6 slices per customer. How many slices cannot be bought?	Choose the most appropriate option
A) 42.
B) 38.
C) 54.
D) 33.
E) 18.

Solution: Answer:	Let X pizzas of 4 slices and Y pizzas of 6 slices.   4X + 6Y.   Lets check options wise.   A. 42 => 4(3) + 6(5)   B. 38 => 4(5) + 6(3)   C. 33 = 3(4) + 6(7)   D. 54 => we can't write anything with 4 and 6 series..Lets try 4(5) + 6(2) = 32 , 4(4) + 6(3) = 34 , nothing works out.   E. 18 => 4(3) + 6(1)   Answer: correct option is 33.
Answer: D
A person takes 5 hrs 45 min in walking to a place and riding back. He would have gained 1 hour by riding both ways. The time he would take to walk both ways is?
Choices:
A) 5 hours 45 min	B) 5 hours 55 min	C) 6 hours 45 min	D) 7 hours 45 min	E) 8 hours

Solution: ----------------------------------------------------------------   Solution 1   ----------------------------------------------------------------   Given that time taken for riding both ways will be 1 hours lesser than   the time needed for waking one way and riding back   From this, we can understand that   time needed for riding one way = time needed for waking one way - 1 hours   Given that time taken in walking one way and riding back = 5 hours 45 min   Hence The time he would take to walk both ways = 5 hours 45 min + 1 hours = 6 hours 45 min   6 hours 45 min
Answer: C
if p is a positive integer greater than 8, which of the following must be divisible by 4?  Choose the correct choice from the following answers
A) p(p-1)(p+2)(p+3)	B) p(p-1)(p+3)(p+4)	C) p(p-3)(p+2)(p+4)	D) p(p-3)(p+2)(p+3)	E) p(p+1)(p+3)(p+4)

Solution: D.   For any integer p, D is the only answer choice which will always be divisible by 4.   A product of 4 consecutive integers will always be divisible by 4. Since, none of the answer choices are a product of 4 consecutive integers, we have to ensure at least one of the integers is always a multiple of 4. The best way to do that is to ensure the answer choice isp* [(p-1)OR(p+3)] * [(p-2)OR(p+2)] * [(p-3)OR(p+1)]. (answer p(p-3)(p+2)(p+3))
Answer: D
Sum of the numbers from 1 to 25 is	Options:	A) 210	B) 325	C) 320	D) 105	E) None of these

Solution: Explanation: Sum of first n natural numbers = 1 + 2 + 3 + ..... n = n(n+1)/2   Substitute n = 25.   So S20=25Ã—26/2=325   Correct Option: 325
Answer: B
Set S consists of integers {2,3,4,5}. If two numbers are chosen from set S at random, what is the probability that the product of 2 numbers is more than 10?
Choices:
A) 1/2
B) 1/4
C) 2/5
D) 3/7
E) 1/6

Solution: Number of ways you can choose 2 from 4 = 4C2 = 6   E = event of getting the 2 numbers product is more than 10 = (3,4),(3,5),(4,5) = 3   probability = 3/6 = 1/2   1/2nswer is 1/2
Answer: A
A boat sails 15 km of a river towards upstream in 5 hours. How long will it take to cover the same distance downstream, if the speed of current is one-fourth the speed of the boat in still water:	Options:
A) 2
B) 3
C) 4
D) 5
E) 6

Solution: Explanation:   Upstream speed = 3-S   Downstream speed = 3+s   3-S = 15/5= 
15/5 = 3
3 km/h   Again 3= 4S   Therefore 3-S = 3= 3S   => S = 1 and 3= 4 km/h   Therefore 3+S = 5km/h   Therefore, Time during downstream = 15/5= 
15/5 = 3
3h   Answer: 3) 3h
Answer: B
Express of the following as a fraction:
44%
Pick:
A) 11/25 B) 13/25 C) 11/25 D) 17/25 E) None of them

Solution: 44% = 44/100= 11/25.   11/25nswer is 11/25.
Answer: A
What is the probability of getting a sum 9 from two throws of a dice?
Pick one:	A) 1/9	B) 1	C) 2/9	D) 2	E) 2/3

Solution: In two throws of a dice, n(S) = (6 x 6) = 36.   Let E = event of getting a sum ={(3, 6), (4, 5), (5, 4), (6, 3)}.   P(E) = n(E)/n(S) = 4/36	= 1/9   Hence answer is 1/9
Answer: A
How many multiples of 4 are there between 12 and 92, inclusive?	Pick
A) 21
B) 22
C) 23
D) 24
E) 25

Solution: The multiples of 4 are from 4*3 up to 4*23.   23-3+1= 
23-3+1 = 21
21.   The answer is 21.
Answer: A
A train passes a station platform in 45 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
Choose the correct answer
A) 177 m
B) 375 m
C) 240 m
D) 187 m
E) 186 m

Solution: Speed = [54 * 5/18] m/sec = 15 m/sec.   Length of the train = (15 * 20)= 
(15 * 20) = 300
300 m.   Let the length of the platform be x meters.   Then, x + 300 / 45= 15   x + 300 = 675   x = 375 m.   Answer: 375 m
Answer: B
A mailman puts .05% of letters in the wrong mailbox. How many deliveries must he make to misdeliver 2 items? Choose the correct choice from the following answers
A) 4000 B) 400 C) 40 D) 40000 E) 4500

Solution: Let the number of total deliveries be x   Then, .05% of x=2   (5/100)*(1/100)*x=2   x=4000   4000nswer is 4000
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 the correct answer.
A) 0.5908 B) 0.5904 C) 0.5901 D) 0.5916 E) 0.5925

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
In Company A, the total monthly payroll for the 12 factory workers is $18,000 and the total monthly payroll for the 40 office workers is $100,000. By how much does the average (arithmetic mean) monthly salary of an office worker exceed that of a factory worker in this company?  Choose the correct choice from the following answers.
A) $600 B) $700 C) $800 D) $900 E) $1000

Solution: The average monthly salary of a factory worker is: $18,000 / 12 = $1500.   The average monthly salary of an office worker is: $100,000 / 40 = $2500.   The difference in average salary is: $2500 - $1500 = $1000.   The answer is $1000.  2500 -  1500= 
  2500 -  1500 = 1_000
$1000.   The answer is $1000.
Answer: E
What is the place value of 4 in the numeral 57468?
Answers:	A) 400	B) 40	C) 4000	D) 4	E) 46

Solution: place value of 4 = 4 * 100= 
4 * 100 = 400
400   400nswer is 400
Answer: A
How many different subset of the set {I, II, III, IV, V, VI, VII, VIII, IX) do not contain V.	Choose the correct choice from the following choices:	A) 273	B) 282	C) 285	D) 283	E) 281

Solution: This is a combination solution   Since we have 8 different Roman Numerals other than the V we can take any Roman numeral from the set of 8 to make a subset.   8C1 +8C2 + 8C3 + 8C4 + 8C5 + 8C6 + 8C7 + 8 C8 = 282   Plus the one set that is null that is the Set having no element in it which is 8C0 =1   = 282 + 1 = 16   283 = 283
Answer: D
Java House charges $4.25 for a cup of coffee that costs a total of $3.85 to make. Cup'O'Joe charges $4.80 for a cup that costs $4.65 to make. If Java House sells 55,000 cups of coffee, how many must Cup'O'Joe sell to make at least as much in total gross profit as its competitor does? Choose the correct choice from the following answers:
A) 7,858  B) 8,301  C) 14,667  D) 63,840  E) 146,667

Solution: Java: Profit/Cup = 4.25-3.85= 
4.25-3.85 = 0.4
0.4   : No of Cups= 55,000   : Gross Profit = 55,000*0.4 = 22,000   Joe: Profit/Cup = 0.15   : Gross Profit = 22,000   : No of Cups = 22,000/0.15 = 220,000/1.5 (only closes is 146,667)   Answer 146,667
Answer: E