MU-NLPC/Calc-aqua_rat huggingface dataset:
Working at their respective constant rates, machine A makes 100 copies in 20 minutes and machine B makes 150 copies in 10 minutes. If these machines work simultaneously at their respective rates for 30 minutes, what is the total number of copies that they will produce?	Pick
A) 250 B) 425 C) 675 D) 700 E) 600

Solution: Machine A can produce 100 *30/20= 
100 *30/20 = 150
150 copies   And, Machine B can produce   150* 30/10= 
  150* 30/10 = 450
450 Copies   Total producing 600 Copies.   600 is the answer
Answer: E
By approximately what percent is x greater than 4/7 if (1/7)(x) = 1?	Choose one:
A) 1125%
B) 956%
C) 417%
D) 3788%
E) 219%

Solution: what percent is x greater than 4/7 if (1/7)(x) = 1?   => x = 7   % change =[(7 -4/7) /(4/7) ] * 100   = (49/4 - 1) *100   = 45 * 25= 
45 * 25 = 1_125
1125%   1125%ns ,1125%
Answer: A
6 people meet for a business dinner. Each person shakes hands once with each other person present. How many handshakes take place?
Pick one:
A) 30  B) 21  C) 18  D) 15  E) 10

Solution: Let's look at the logic.   Every person shakes hand with other '5'. So, 6 people shake hands with 6X5= 30 people   But in this 30 we have counted two times the total handshakes (x shakes hand with y and y shakes hand with x)   So just divide 30/2= 
30/2 = 15
15 total handshakes   Answer is 15
Answer: D
A number is doubled and 11 is added. If resultant is doubled, it becomes 74. What is that number	Choose the correct choice from the following options.
A) 18 B) 10 C) 13 D) 14 E) 16

Solution: Explanation:   => 2(2x+11) = 74   => 4x + 22 = 74   => 4x=52   => x = 13   Option 13
Answer: C
P can do the work in 12 days and Q can do the same work in 20 days. If they work together for 4 days, what is the fraction of work that is left?	Pick one.
A) 7/15  B) 8/15  C) 11/15  D) 23/30  E) 41/60

Solution: 4/12 + 4/20 = 1/3 + 1/5 = 8/15 (completed work)   The work that is left is 1 - 8/15 = 7/15   The answer is 7/15.
Answer: A
If a particular player is never chosen, in how many ways can 11 cricket players be chosen out of 18 players?	Choose the correct choice from the following:
A) 12145  B) 12156  C) 12376  D) 12380  E) 12390

Solution: A particular players is never chosen, it means that 11 players are selected out of 17 players.   => Required number of ways = 171237611   = 12376   12376
Answer: C
The speed of a boat in upstream is 100 kmph and the speed of the boat downstream is 130 kmph. Find the speed of the boat in still water and the speed of the stream?  Pick one: A) 10 kmph B) 15 kmph C) 19 kmph D) 17 kmph E) 29 kmph

Solution: Speed of the boat in still water   = (100+130)/2= 
(100+130)/2 = 115
115 kmph. Speed of the stream= (130-100)/2= 
(130-100)/2 = 15
15 kmph.   Answer: 15 kmph
Answer: B
Sarah, Fatima, Salma, and Lina all got scholarship packages to the college they applied to. The average of Sarah, Fatima, and Salma's scholarships was $20000. The average of Fatima, Salma, and Lina's tips was $17000. If Lina earned $15000, what was Sarah awarded?  Select.
A) $24000 B) $25000 C) $27000 D) $30000 E) $32000

Solution: Solution: $24000verage scholarships for Sarah, Fatima and Sarah = $20000   Total scholarship = 3*20000= 
3*20000 = 60_000
$60000   $24000verage scholarship for Fatima, Salma, and Lina= $17000   Total scholarship = 3*17000= 
3*17000 = 51_000
$51000   Lina's scholarship award= $15000   Now,   (Sarah+Fatima+Salma) - (Fatima+Salma+Lina) = $60000-$51000 = $9000   Sarah-Lina 60000- 51000= 
60000- 51000 = 9_000
$9000   Sarah-Lina= $9000   Sarah = Lina +$9000 = $24000   $24000nswer: Option $24000
Answer: A
Company Z has 53 employees. If the number of employees having birthdays on Wednesday is more than the number of employees having birthdays on any other day of the week, each of which have same number of birth-days, what is the minimum number of employees having birthdays on Wednesday.
Choose the correct choice from the following
A) 6 B) 7 C) 8 D) 11 E) 12

Solution: Say the number of people having birthdays on Wednesday is x and the number of people having birthdays on each of the other 6 days is y. then x + 6y = 53.   Now, plug options for x. D x > y as needed.   Answer: 11.
Answer: D
Out of 11 persons working on a project, 4 are graduates. If 3 are selected, what is the probability that there is at least one graduate among them?	Choose the correct choice from the following answers
A) 5/17
B) 26/13
C) 26/31
D) 26/33
E) 5/33

Solution: P(at least one graduate) = 1 - P(no graduates)   = 1 - 7C₃/11C₃ = 1 - (7 * 6 * 5 )/(11* 10 * 9 )   = 26/33   Answer: 26/33
Answer: D
Priya covers journey from kavali to nellore by car at average speed of 60 Km/hr. She returns back by scooty with an average speed of 40 Km/hr. Find her average speed during the whole journey?
Choose one: A) 20Km/hr B) 48Km/hr C) 50Km/hr D) 52Km/hr E) 53km/hr

Solution: Explanation:   Average speed = 2 xy/x+y   = 2*60*40/100= 
2*60*40/100 = 48
48 Km/hr   Answer: Option 48Km/hr
Answer: B
Find the 10th and 12th term of the series 1, 3.5, 6, 8.5,...? And their ratio is?
Select the correct option
A) .98  B) 2.5  C) 1.21  D) 3.4  E) 2

Solution: common difference = d = 3.5 - 1= 
3.5 - 1 = 2.5
2.5 ,, n= 10, a = first term = 1-----   By using arithmetic progression , t10 = a + (n-1)*d = 1 + (10-1)*2.5 = 1+22.5= 
1+22.5 = 23.5
23.5 Also 12th term , t12= a + (n-1)*d = 1 + (12-1) * 2.5= 
1 + (12-1) * 2.5 = 28.5
28.5   Ratio= t12/t10 = 28.5/23.5 = 1.21..... Ans - 1.21
Answer: C
4 dice are thrown simultaneously on the board. Find the probability show the same face.  Answers
A) 2/215  B) 3/155  C) 1/216  D) 2/213  E) 3/212

Solution: The total number of elementary events associated to the random experiments of throwing four dice simultaneously is:   =6×6×6×6=64=6×6×6×6=64   n(S)=64n(S)=64   Let XX be the event that all dice show the same face.   X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}   n(X)=6n(X)=6   Hence required probability,   =n(X)n(S)=664=n(X)n(S)=664   =1/216   1/216
Answer: C
Some persons can do a piece of work in 32 days. Two times the number of these people will do half of that work in?	Choose the correct choice from the following
A) 3	B) 4	C) 5	D) 6	E) 8

Solution: 32/ (2 * 2)= 
32/ (2 * 2) = 8
8 days   Answer:8
Answer: E
Starting with 0, a mathematician labels every non-negative integer as one of five types: alpha, beta, gamma, delta, or epsilon, in that repeating order as the integers increase. For instance, the integer 8 is labeled delta. What is the label on an integer that is the sum of an alpha raised to the seventh power and a gamma raised to the seventh power?
Choose the correct option: A) alpha B) beta C) gamma D) delta E) epsilon

Solution: Let the alpha be 5k and let the gamma be 5j+2.   (5k)^7 + (5j+2)^7 which has the form 5k+3, which is a gamma.   The answer is gamma.
Answer: C
How many words, meaningful or meaningless, can be formed by shuffling the letters of the word INFORMATION?  Answers.
A) 11!  B) 11!/2!  C) 11!/(2!^3)  D) 11!/{(3!)(2!^3)}  E) 6!

Solution: The total number of ways in which a total N items, out of which p are identical of one type, q are identical of another type and rest are different, can be arranged in a line is N!/{p!q!}   In the given problem, we have 11 letters out of which 2 are I's (identical), 2 are N's (identical), 2 are F's (identical) and rest all are different.   Hence the number of words that can be formed is 11!/{2!2!2!}   Ans 11!/(2!^3)
Answer: C
A right triangle AQC has to be constructed in the xy-plane so that the right angle is at A and AQ is parallel to x axis. The coordinates of A, Q and C are integers and satisfy the inequalities -1 ≤ x ≤ 7 and 1 ≤ y ≤ 7. How many different triangles can be constructed with these properties?  Select the correct option:
A) 63
B) 336
C) 567
D) 3024
E) 5040

Solution: All the cordinates are integer hence,   possible AQ values are   {-1,0}, {-1,1} ....{-1,7}: 8 ways   ....   {7,-1}, {7,0} ......{7,6}: 8 ways     9*8= 
  9*8 = 72
72   for AC values can be   {1,2}, {1,3} .... {1,7} : 6ways   ......   {7,1}, {7,2} ..... {7,6} : 6 ways     7*6= 
  7*6 = 42
42   Total= 72 * 42= 
72 * 42 = 3_024
3024 hence 3024
Answer: D
A club wants to mix 20 pounds of candy worth $10.00 per pound with candy worth $5.00 per pound to reduce the cost of the mixture to $6.00 per pound. How many pounds of the $5.00 per pound candy should be used?	Answers:  A) 40  B) 50  C) 60  D) 70  E) 80

Solution: Let number of pounds of 5$ candy to be used be w   6 = (20*10 + 5*w)/(20 +w)   =>120 + 6w = 200 + 5w   => w = 80   Answer 80
Answer: E
If all of the telephone extensions in a certain company must be even numbers, and if each of the extensions uses all four of the digits 1, 2, 5, and 6, what is the greatest number of four-digit extensions that the company can have?	Choose the correct choice from the following answers.
A) 4  B) 6  C) 11  D) 12  E) 24

Solution: Since the phone number must be even, the unit's digit can be either 2 or 6.   When the unit's digit is 2 --> number of possibilities is 3! = 6   When the unit's digit is 6 --> number of possibilities is 3! = 6   Largest number of extensions = 6 + 6= 
6 + 6 = 12
12   Answer:12
Answer: D
Two trains start at same time from two stations and proceed towards each other at the rate of 20 km/hr and 25 km/hr respectively. When they meet, it is found that one train has traveled 70 km more than the other. What is the distance between the two stations? Pick one
A) 630 km B) 540 km C) 276 km D) 178 km E) 176 km

Solution: Explanation:   Let us assume that trains meet after 'x' hours   Distance = speed * Time   Distance traveled by two trains = 20x km and 25x km resp.   As one train travels 70 km more than the other,   25x â€“ 20x = 70   5x = 70   x = 14 hours   As the two trains are moving towards each other, relative speed = 20 + 25= 
20 + 25 = 45
45 km/hr   Therefore, total distance= 45*14= 
45*14 = 630
630 km.   630 kmNSWER: 630 km
Answer: A
If the sides of a triangle are 28 cm, 26 cm and 10 cm, what is its area?
Answers
A) 120 cm2 B) 112 cm2 C) 776 cm2 D) 130 cm2 E) 886 cm2

Solution: The triangle with sides 28 cm, 26 cm and 10 cm is right angled, where the hypotenuse is 28 cm.   Area of the triangle = 1/2 * 26 * 10= 
1/2 * 26 * 10 = 130
130 cm2   Answer: 130 cm2
Answer: D
The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 180 resolutions?
Pick.
A) 724 m  B) 704 m  C) 287 m  D) 278 m  E) 253.4 m

Solution: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 180 resolutions.   = 180 * 2 * 22/7 * 22.4= 
180 * 2 * 22/7 * 22.4 = 25_344
25344 cm= 253.4 m   Answer:253.4 m
Answer: E
What is the next number of the following sequence
123, 444, 888, 1776, 8547, . . . .
Select the correct option:  A) 38799  B) 16005  C) 27887  D) 27072  E) 27081

Solution: Explanation:   1) 123 + 321 = 444   2) 444 + 444 = 888   3) 888 + 888 = 1776   4) 1776 + 6771 = 8547   5) 8547 + 7458 = 16005   Answer: 16005
Answer: B
If a certain coin is flipped, the probability that the coin will land heads is 1/2. If the coin is flipped 5 times, what is the probability that it will land heads up on the first 3 flips and not on the last 2 flips?
Choose the correct answer:
A) 3/5  B) 1/2  C) 1/5  D) 1/8  E) 1/32

Solution: On the first three flips, you must get heads. Whats the probability of getting heads ? Its 1/2   So for the first three flips, your probability is (1/2)^3 = 1/8   Now for the last two, you want to get tails only. Whats the prob of getting tails ? Well, its the same as prob of getting a heads, namely, 1/2   For the last two flips, your probability is (1/2)^2 = 1/4   So your overall probability for the event in question is 1/8*1/4 = 1/32   Answer: 1/32
Answer: E
A man saves 20% of his monthly salary. If an account of dearness of things he is to increase his monthly expenses by 20%, he is only able to save Rs. 200 per month. What is his monthly salary? Choose one
A) 5000  B) 25000  C) 7500  D) 8500  E) 9000

Solution: Income = Rs. 100   Expenditure = Rs. 80   Savings = Rs. 20   Present Expenditure 80*(20/100) = Rs. 96   Present Savings = 100 â€“ 96 =Rs. 4   100 ------ 4   ? --------- 200 => 5000   5000NSWER 5000
Answer: A
A certain college's enrollment at the beginning of 1992 was 20 percent greater than it was at the beginning of 1991, and its enrollment at the beginning of 1993 was 5 percent greater than it was at the beginning of 1992. The college's enrollment at the beginning of 1993 was what percent greater than its enrollment at the beginning of 1991 ? Choose the correct choice from the following answers: A) 17.5% B) 26% C) 30% D) 35% E) 38%

Solution: Suppose enrollment in 1991 was 100   Then enrollment in 1992 will be 120   And enrollment in 1993 will be 120*1.05= 
120*1.05 = 126
126   Increase in 1993 from 1991= 126-100= 
126-100 = 26
26   Answer : 26%
Answer: B
In how many different ways can the letters of the word 'MATHEMATICS' be arranged such that the vowels must always come together?
Select the correct option.
A) 9800	B) 100020	C) 120960	D) 140020	E) 150000

Solution: Explanation:   The word 'MATHEMATICS' has 11 letters. It has the vowels 'A','E','A','I' in it and these 4 vowels must always come together. Hence these 4 vowels can be grouped and considered as a single letter. That is, MTHMTCS(AEAI).   Hence we can assume total letters as 8. But in these 8 letters, 'M' occurs 2 times, 'T' occurs 2 times but rest of the letters are different.   Hence,number of ways to arrange these letters   =8!(2!)(2!)=8!(2!)(2!) =8Ã—7Ã—6Ã—5Ã—4Ã—3Ã—2Ã—1(2Ã—1)(2Ã—1)=10080=8Ã—7Ã—6Ã—5Ã—4Ã—3Ã—2Ã—1(2Ã—1)(2Ã—1)=10080   In the 4 vowels (AEAI), 'A' occurs 2 times and rest of the vowels are different.   Number of ways to arrange these vowels among themselves =4!2!=4Ã—3Ã—2Ã—12Ã—1=12=4!2!=4Ã—3Ã—2Ã—12Ã—1=12   Hence, required number of ways   =10080Ã—12=120960   ANSWER IS 120960
Answer: C
The sum of ages of 5 girls born at the intervals of 3 years each is 60 years. What is the age of the youngest girl?
Choose the correct choice from the following answers:
A) years
B) years
C) years
D) years
E) years

Solution: Let the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years.   Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 60   5x = 30   x = 6.   Age of the youngest child = x = 6years.   years)
Answer: A
Laura took out a charge account at the General Store and agreed to pay 4% simple annual interest. If she charges $35 on her account in January, how much will she owe a year later, assuming she does not make any additional charges or payments?	Choices
A) $36.4 B) $37.10 C) $37.16 D) $38.10 E) $38.80

Solution: Principal that is amount taken by Laura at year beginning = 35$   Rate of interest = 4%   Interest = (4/100)*35= 
(4/100)*35 = 7/5 = around 1.4
1.4$   Total amount that Laura owes a year later= 35+1.4= 
35+1.4 = 36.4
36.4 $   $36.4nswer $36.4
Answer: A
A began business with Rs.45000 and was joined afterwards by B with Rs.5400. When did B join if the profits at the end of the year were divided in the ratio of 2:1?
Choose the correct choice from the following choices.
A) 2	B) 6	C) 7	D) 8	E) 2

Solution: 45*12 : 54*x = 2: 1   x = 5   12 -5= 
12 -5 = 7
7   Answer:7
Answer: C
In the faculty of Reverse-Engineering, 226 second year students study numeric methods, 423 second year students study automatic control of airborne vehicles and 134 second year students study them both. How many students are there in the faculty if the second year students are approximately 80% of the total? Choices
A) 515  B) 545  C) 618.  D) 644.  E) 666

Solution: Solution : Total number of students studying both are 423 + 226 - 134= 
423 + 226 - 134 = 515
515 (Subtracting the 134 since they were included in the both the other numbers already).   So 80% of total is 515, so 100% is approx. 644.   Answer is 644. :644
Answer: D
In a caravan, in addition to 50 hens, there are 45 goats and 8 camels with some keepers. If the total number of feet be 224 more than the number of heads in the caravan, the number of keepers is	Choose the correct answer
A) 5  B) 8  C) 10  D) 15  E) 20

Solution: Explanation:   Let number of keepers be x. Then,   Total number of feet = 2 x 50 + 4 x 45 + 4 x 8 + 2x = 2x + 312.   Total number of heads = 50 + 45 + 8 + x= 103 + x.   Therefore (2x + 312) = (103 + x) + 224 or x = 15.   Answer: 15
Answer: D
Three positive integers a, b, and c are such that their average is 20 and a ≤ b ≤ c. If the median is (a + 11), what is the least possible value of c?  Choose the correct choice from the following options.
A) 23	B) 21	C) 25	D) 26	E) 24

Solution: Solution   Given Data   3 positive integers   Average of a, b, and c = 20.   So, a+b+c3a+b+c3 = 20 or a + b + c = 60   a ≤ b ≤ c   Median = (a + 11)   Median of these 3 numbers a, b, and c is ‘b’ because a ≤ b ≤ c   Therefore, b = a + 11   Objective To find the least value of 'c'   Theoretically, the least value of c is when c = b.   Therefore, a + (a + 11) + (a + 11) = 60 (b and c are equal and b, the median, is a + 11)   Or 3a = 38 or a = 12.66   So, b = c = 12.66 + 11= 
12.66 + 11 = 23.66
23.66   However, we know that these numbers are all integers.   Therefore, a, b, and c cannot take these values.   So, the least value for c with this constraint is NOT likely to be when c= b   Let us increment c by 1. Let c = (b + 1)   In this scenario, a + (a + 11) + (a + 12) = 60   Or 3a = 37. The value of the numbers is not an integer in this scenario as well.   Let us increment c again by 1. i.e., c = b + 2   Now, a + (a + 11) + (a + 13) = 60   Or 3a = 36 or a = 12.   If a = 12, b = 23 and c = 25.   The least value for c that satisfies all these conditions is 25.   25orrect answer is choice 25.
Answer: C
Find the Missing Number 6, 24, 60,120, 210, ?
Answers: A) 331 B) 336 C) 333 D) 339 E) 332

Solution: 1*2*3= 
1*2*3 = 6
6   2*3*4= 
2*3*4 = 24
24   3*4*5= 
3*4*5 = 60
60   4*5*6= 
4*5*6 = 120
120   5*6*7= 
5*6*7 = 210
210   6*7*8= 
6*7*8 = 336
336   ANSWER:336
Answer: B
39! is divided by 41. Then what is the remainder?
Choose the correct choice from the following.
A) 1 B) 3 C) 4 D) 5 E) 6

Solution: Substituting p = 41 in the wilson's theorem, we get   40!+141=0   40×39!+141=0   −1×39!41=−1   Cancelling -1 on both sides,   39!41=1   1
Answer: A
A certain amount becomes Rs. 5760 in 2 years and Rs. 6912 in 3 years. What is the principal amount and the rate of interest?  Pick:
A) Rs. 3050
B) Rs. 3150
C) Rs. 3450
D) Rs. 4000
E) Rs. 3500

Solution: SI on Rs. 5760 for 1 year = 6912 – 5760 = Rs. 1152   Therefore, Rate of interest for 1 year = 100*1152/5760*1= 
100*1152/5760*1 = 20
20%   Let the principal be p.   Then, Principal= p[1+ 20/100]2 = 5760   Solving which gives Principal = Rs. 4000 ANSWER : Rs. 4000
Answer: D
X and Y start a business with Rs.2000 and Rs.12000 respectively. Hoe should they share their profits at the end of one year?  Select
A) 1:6 B) 6:1 C) 1:5 D) 5:1 E) 1:4

Solution: They should share the profits in the ratio of their investments.   The ratio of the investments made by X and Y =   2000 : 12000 => 1:6 .   1:6nswer: 1:6
Answer: A
In a office work is distribute between p persons. If 1/4 members are absent then work increased for each person is?
Pick.
A) 33.33%
B) 24.33%
C) 15.33%
D) 16.33%
E) 17.33%

Solution: let total % of work is 100%   total person=p   1/4 person are absent of total person . so absent person is 1/4p ie p/4.   left person is, p-p/4=3p/4.   p person do the work 100%   1 person do the work 100*p%   3p/4 person do the work (100*p*4)/3p%=133.33%   work increased for each person is=(133.33-100)= 
(133.33-100) = 33.33
33.33%   33.33%NSWER:33.33%
Answer: A
A jogger running at 9 km/hr along side a railway track is 270 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?	Pick: A) 67 sec B) 89 sec C) 39 sec D) 87 sec E) 45 sec

Solution: Speed of train relative to jogger = 45 - 9= 
45 - 9 = 36
36 km/hr.= 36 * 5/18= 
36 * 5/18 = 10
10 m/sec.   Distance to be covered= 270 + 120= 
270 + 120 = 390
390 m.   Time taken= 390/10= 
390/10 = 39
39 sec.   Answer: 39 sec
Answer: C
People standing in a straight line are wearing alternating colored shirts. The pattern of shirts begins with red, followed by green, blue, and yellow. This pattern continues (red, green, blue, and yellow) until it ends with a red shirt. If there are more than 4 people in line, which of the following cannot be the number of people in the line? Choose one.
A) 17 B) 37 C) 49 D) 61 E) 72

Solution: The correct answer should not take the form: 4x + 1. Hence, it is 72
Answer: E
At the end of the month, a certain ocean desalination plant’s reservoir contained 26 million gallons of water. This amount is eighth the normal level. If this amount represents 65% of the reservoir’s total capacity, how many million gallons short of total capacity is the normal level?  Choose the correct choice from the following.
A) 15	B) 25	C) 35	D) 45	E) 55

Solution: the Q talks of total capacity, normal level, present level, shortage etc..   so it is all about not going wrong in these terms   26 MG= 65% of Total..   total = 26/.65= 
26/.65 = 40
40 MG..   Normal level= 1/8 of 40=5MG..   shortage of normal level=40-5= 
40-5 = 35
35MG..   35
Answer: C
The ratio of sodium chloride to ammonium in 100 kg of mixed ammonium normally used by three chemists is 3: 13. The amount of sodium chloride to be added to 100 kg of mixed ammonium to make the ratio 9 :25 is  Choose the most appropriate option
A) 10.5 kg B) 6.625 kg C) 6.25 kg D) 6.35 kg E) 6.55 kg

Solution: sodium chloride in 100 kg = 3/16 x 100 = 18.75 kg   ammonium in 100 kg = 13/16 x 100 = 81.25 kg   Now 81.25 is 25 parts out of   (25 + 9)= 
  (25 + 9) = 34
34 parts.   Hence 9 parts= 9/25 x 81.25 = 29.25   10.5 kgmount to be added = 29.25 - 18.75= 
29.25 - 18.75 = 10.5
10.5 Kg   10.5 kgNSWER:10.5 kg
Answer: A
If taxi fares were $2.00 for the first 1/5 mile and $0.40 for each 1/5 mile there after, then the taxi fare for a 4-mile ride was  Select
A) $4.60
B) $9.80
C) $19.60
D) $9.60
E) $29.60

Solution: In 4 miles , initial 1/5 mile charge is $2   rest of the distance = 4 - (1/5) = 19/5   rest of the distance charge = 19(0.4) = $7.6 (as the charge is 0.4 for every 1/5 mile)   => total charge for 4 miles = 2+7.6= 
2+7.6 = 9.6
9.6   Answer is $9.60
Answer: D
The greatest number which can divide 1356,1868 and 2764 leaving the same remainder 12 in each case, is :	Answers: A) 64 B) 124 C) 156 D) 260 E) None of these

Solution: Solution   Required number = H.C.F. of (1356-12), (1868-12) and (2764-12)   = H.C.F of 1344,1856 and 2752 = 64. 64nswer 64
Answer: A
If X+Y = 2X-2Z, X+2Y = 4Z and X+Y+Z = 21, what is the value of Y/Z?
Choose the correct choice from the following:
A) -4.5.
B) 0.667.
C) 1.7.
D) 3.
E) 2.5.

Solution: X+Y = 2X-2Z   Y= X-2Z---------- 1   X+2Y = 4Z   -X+4Z= 2Y--------- 2   Adding equation 1 from equation 2   2Z = 3Y   Y/Z = 0.667   0.667. is the answer
Answer: B
Two children want to walk together to visit their aunt, who lives exactly 6 blocks north and 5 blocks east of their current location. If they travel only along streets and do not travel diagonally, the shortest possible route connecting the two points is exactly 11 blocks. How many different 11-block routes may they take to travel the shortest possible distance to their aunt’s house?	Choose the correct choice from the following answers
A) 11!/(6!*5!)  B) 11!/(6*5)  C) 11!*6!*5!  D) 6!*5!  E) 11*6*5

Solution: If they need to walk 6 blocks north and 5 blocks east, we can express this route as NNNNNNEEEEE. The question thus asks us how many ways we can arrange those letters.   The number of arrangements of 11 things is 11!   We then divide by the repetitions of N's and E's, which are 6! and 5! respectively.   The number of walking routes is 11!/(6!*5!).   The answer is 11!/(6!*5!).
Answer: A
On seven consecutive flips of a coin, what is the probability that all seven produce the same result?
Choose the correct choice: A) 1/64 B) 1/8 C) 1/4 D) 3/8 E) 1/2

Solution: TTTTTTT case --> P = (1/2)^7 = 1/128   HHHHHHH case --> P = (1/2)^7 = 1/128   P(TTTTTTT or HHHHHHH) = 1/8 + 1/8 = 1/64   1/64nswer: 1/64
Answer: A