MU-NLPC/Calc-aqua_rat huggingface dataset:
How many positive integers arethere from 0 to 1000 that leave a remainder of 3 on division by 7 & a remainder of 2 on division by 4?
Answers
A) 30  B) 36  C) 38  D) 42  E) 46

Solution: Number should be of the form 7n + 3 and 4m + 2.   The LCM of 7 and 4 is 28. So, let us see what are the possible remainders when we divide this number by 28.   A number of the form 7n + 3 can be written as 28K + 3 or 28k + 10 or 28 + 17 or 28k + 24.   A number of the form 4m + 2 can be written as 28l + 2, 28l + 6, 28l + 10, 28l + 14, 28l + 18, 28l + 22, 28l + 26.   For a detailed discussion on how we get to this, look at this post.   Within these, the only common term is 28K + 10.   The numbers in this sequence are 10, 38, 66.....990.   We still need to figure out how many numbers are there in this sequence. We are going in steps of 28, so let us see if we can write these numbers in terms of 28p + r.   10 = 28 * 0 + 10   38 = 28 * 1 + 10   66 = 28 * 2 + 10   94 = 28 * 3 + 10   ...........................   990 = 28 * 35 + 10   There are 36 numbers in this sequence.   Correct Answer: 36   36
Answer: B
Three 6 faced dice are thrown together. The probability that no two dice show the same number on them is ? Choose the correct answer.
A) 5/6	B) 5/9	C) 2/9	D) 5/7	E) 1/9

Solution: No two dice show same number would mean all the three faces should show different numbers. The first can fall in any one of the six ways. The second die can show a different number in five ways. The third should show a number that is different from the first and second. This can happen in four ways.   Thus   6 * 5 * 4= 
  6 * 5 * 4 = 120
120 favourable cases.   The total cases are   6 * 6 * 6= 
  6 * 6 * 6 = 216
216.   The probability= 120/216 =5/9.   Answer:5/9
Answer: B
A rectangular circuit board is designed to have a width of W inches, a length of L inches, a perimeter of P inches, and an area of C square inches. Which of the following equations must be true?  Choose the correct choice from the following:
A) 2W^2 + PW + 2C = 0
B) 2W^2 − PW + 2C = 0
C) 2W^2 − PW − 2C = 0
D) W^2 + PW + C = 0
E) W^2 − PW + 2C = 0

Solution: P = 2(L+W)-----------------1)   C= LW------------------------2)   option A is not possible why ?? because all the terms are positive.   lets try option B , put value of P and A from 1 and 2 we have,   2W^2-2(L+W)W + 2(LW)   2W^2 - 2LW - 2W^2 + 2LW=0.   hence answer is 2W^2 − PW + 2C = 0.
Answer: B
If the average of a sequence of consecutive multiple of 18 is 153, and the greatest term is 270, how many terms R in the sequence are smaller than the average  Pick
A) 5
B) 6
C) 7
D) 8
E) 9

Solution: Let the sequence have N terms starting 18*K   --> 18K, 18(K+1), 18(K+2), .... , 18(K+N-1) is the sequence.   The sum of the sequence is   ---> 18K + 18(K+1) + 18(K+2) + .... + 18(K+N-1) =18*(K+(K+1)+...+(K+N-1)) = 18*(N*(2K+N-1)/2).   So the average is   153=[18*(N*(2K+N-1)/2)]/N = 18*(2K+N-1)/2 = 9 *(2K+N-1) ---> by cancelling 9 we get 2K+N-118*(2 + -1)/2= 
18*(2 + -1)/2 = 9
9 *(2K+N-1) ---> by cancelling 9 we get 2K+N-1=17 --> 2K+N=18 ---*).   On the other hand, since the greatest term is 270, 18(K+N-1)=270 --> by cancelling 18 we get K+N-1=15 --> K+N=16 ---**).   By *), **) we have K=2, N=14.   Since 153/18= 
153/18 = 17/2 = around 8.5
8.5, 18*8<153<18*9. So the number of terms R which are smaller than the average is 18*2, 18*3, ..... ,18*8 ---> 7. The answer is 7.
Answer: C
The cost of an article is decreased by 10%. If the original cost is $60, find the decrease cost.
Choose the correct option:
A) 33
B) 12
C) 68
D) 36
E) 54

Solution: Original cost = $60   Decrease in it = 10% of $60   = 10/100 Ã— 60   = 600/100= 
600/100 = 6
$6   Therefore, decrease cost= $60 - $6 = $54   Answer:5460 -  6= 
60 -  6 = 54
$54   Answer:54
Answer: E
A and B started a business with their capitals Rs. 36,000 and 12,000 respectively. Annual profit will be distributed between them in the ratio  Choose the correct choice from the following choices:  A) 2:5  B) 1:5  C) 2:3  D) 1:3  E) 3:1

Solution: 36,000:12,000   Ans. 3:1   ANSW3:1R:3:1
Answer: E
The ratio of spinsters to cats is 2 to 9. If there are 63 more cats than spinsters, how many spinsters are there?
Choose the correct choice from the following choices:
A) 10 B) 12 C) 14 D) 16 E) 18

Solution: Let 2x be the number of spinsters. Then 9x is the number of cats.   9x-2x=63   x=9 and the number of spinsters is 2(9)=18.   The answer is 18.
Answer: E
If the mode of Set D is equal to the median of Set D, Set D could be Choose one:
A) [0, 1, 2, 2, 3, 4, 5, 6]
B) [2, 2, 5, 7, 9]
C) [x, x+1, x+2, x+2, x+3, x+3]
D) [10, 102, 105, 105]
E) [4, 7, 10, 11, 25/2, 13, 13, 17, 29, 51, 51, 51]

Solution: Correct Answer: (C)   Set D could be The mode is the most common number; the median is the middle number when the numbers are arranged from least to greatest. Any number plus an integer value is greater than the original number, so x + 1 is greater than x, x + 2 is greater than x + 1, etc., so set (C) is arranged from least to greatest. Its median is the average of (x+2) and (x+2), which must be (x+2). (x+2) is also the most common number, so the mode of set [x, x+1, x+2, x+2, x+3, x+3] is equal to the median of set [x, x+1, x+2, x+2, x+3, x+3].
Answer: C
The weight of every type A widget is the same, the weight of every type B widget is the same, and the weight of every type C widget is the same. If the weight of 7 type A widgets is equal to the weight of 2 type B widgets, and the weight of 5 type B widgets is equal to the weight of 7 type C widgets. What is the ratio of the total weight of 1 type A widget and 1 type B widget, to the total weight of 1 type B widget and 1 type C widget? Choose the most appropriate option.
A) 1:2	B) 2:3	C) 3:4	D) 4:5	E) 5:6

Solution: 5B = 73:4 and so B = 73:4/5   7A = 2B and so A = 2B/7 = 23:4/5   A+B = 23:4/5 + 73:4/5 = 93:4/5   B+3:4 = 73:4/5 + 3:4 = 123:4/5   The ratio of A+B:B+3:4 = 9:12 = 3:4   The answer is 3:4.
Answer: C
If x and y are different integers and x^2 = xy, which of the following must be true ?
I. y = 0
II. x = 0
III. x = -y Choose the most appropriate option
A) I only	B) II only	C) III only	D) I and III only	E) I, II, and III

Solution: Answer choice A is correct.   The question gives you x^2=xy   you can simplify that as x^2-xy=0   x(x-y)=0 the solution will be either x=0 or x=y, since x and y are different integers x cannot equal y, that leaves you x=0 to be the only answer.   Answer II only
Answer: B
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?	Select.
A) 50	B) 23	C) 26	D) 28	E) 27

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.   50nswer: 50
Answer: A
A man can row with a speed of 40 kmph in still water. If the stream flows at 8 kmph, then the speed in downstream is?	Answers:
A) 48	B) 28	C) 32	D) 82	E) 34

Solution: M = 40   S = 8   DS = 40 + 8= 
40 + 8 = 48
48 .48nswer:48
Answer: A
In a race, Mohan beats Sohan by 40m and Sohan beats Rohan by 80m. Mohan beats Rohan by 104m. Find the length of the race (in m).
Pick one.
A) 50 B) 100 C) 150 D) 200 E) 250

Solution: length of race = 200 mtrs   length of race = 40*80/(40+80-104) = 40*80/16= 
40*80/16 = 200
200 m   ANSWER:200
Answer: D
Increasing the original price of a certain item by 15 percent and then increasing the new price by 15 percent is equivalent to increasing the original price by what percent?  Pick:
A) 31.25  B) 37.5  C) 30.0  D) 32.75  E) 32.25

Solution: We're told that the original price of an item is increased by 15% and then THAT price is increased by 15%....   IF....   Starting value = $100   + 15% = 100 + .15(100) = 115   + 15% = 115 + .15(115) = 115 + 17.25= 
115 + 17.25 = 132.25
132.25   The question asks how the final price relates to the original price. This is essentially about Percentage Change, which means we should use the Percentage Change Formula:   Percentage Change= (New - Old)/Old = Difference/Original   Doing either calculation will yield the same result:   32.25/100 = 32.25%   Final Answer:   32.25
Answer: E
In a business, A and C invested amounts in the ratio 2 : 1, and B also invest some amount . If Rs 180000 was their profit, B receive 48000, what was the investment ratio between A and B?  Choose the correct choice from the following.
A) 4 : 9  B) 5 : 8  C) 7 : 11  D) 4 : 7  E) None of these

Solution: Explanation :   4 : 9ssume that investment of C = x   Then, investment of 4 : 9 =2x   4 : 9 receive 48000   Then C will receive = 48000/2= 
48000/2 = 24_000
24000   4 : 9nd B receive= 180000 - (24000+48000)= 
180000 - (24000+48000) = 108_000
108000   Ratio of investment between 4 : 9 and B= 48000 : 108000 = 4 : 9   4 : 9nswer : Option 4 : 9
Answer: A
If (1/2)^16 (1/81)^k = 1/18^16, then k =
Choose one.
A) 8 B) 12 C) 16 D) 24 E) 36

Solution: I'm going to focus on denominator only..   (2^16) . ((3^4)^k = 18^16   (2^16) . ((3^4k) = (2. 3^2)^16   (2^16) . ((3^4k) = (2^24) . (3^2)^16   hence   4k =32   k = 8   answer 8   I hope it's quite clear
Answer: A
If log	a/b	+	log	b/a= log (a + b), then:	Choose the correct option:
A) a + b = 1  B) a - b = 1  C) a = b  D) a2 - b2 = 1  E) None of these

Solution: Explanation:   log	a/b	+ log	b/a= log (a + b)   =>log (a + b) = log a/b	x	b/a = log 1.   So, a + b = 1.   a + b = 1NSWER IS a + b = 1
Answer: A
Rectangle A has sides a and b, and rectangle B has sides c and d. If a/c=b/d=2/3, what is the ratio of rectangle A’s area to rectangle B’s area?
Choose the correct choice from the following options
A) 4/9	B) 2/3	C) 3/2	D) 9/2	E) 9/4

Solution: The area of rectangle A is ab.   c=3a/2 and d=3b/2.   The area of rectangle B is cd=9ab/4.   The ratio of rectangle A's area to rectangle B's area is ab / (9ab/4) = 4/9.   The answer is 4/9.
Answer: A
21 ball numbered 1 to 21. A ballis drawn and then another ball is drawn without replacement.
Choose the correct choice from the following choices:
A) 9/41
B) 3/42
C) 9/42
D) 7/41
E) 7/40

Solution: The probability that first toy shows the even number,   =1021=1021   Since, the toy is not replaced there are now 9 even numbered toys and total 20 toys left.   Hence, probability that second toy shows the even number,   =920=920   Required probability,   =(1021)×(920)=(1021)×(920)   =9/42   9/42
Answer: C
Seven carpenters can individually complete a particular task in 3, 4, 5, and 7 hours, respectively. What is the maximum fraction of the task that can be completed in forty-five minutes if six of the carpenters work together at their respective rates ?  Select the correct option.
A) 11/15	B) 3/5	C) 11/30	D) 47/70	E) 5/9

Solution: Farmer A, B, C, and D   A's rate: 1/3 job/hour   B's rate: 1/4 job/hour   C's rate: 1/5 job/hour   D's rate: 1/7 job/hour   By intuition we know that the three fastest farmers are A B and C.   As such   (1/3 + 1/4 + 1/5)*(6/7) = ?   47/70 or (47/70)
Answer: D
If f(a)=6a+6, what is the value of (f(2a)+f(a)) ? Choose the correct choice from the following choices: A) 2a-4 B) 8a-7 C) 10a+12 D) 12a+12 E) 3a+5

Solution: f(a)=6a+6   f(2a)= 8a+6   (f(2a)+f(a)) = 8a+6+2a+6 = 10a+12   Answer is 10a+12
Answer: C
Ted’s score was in the 80th percentile out of 200 students in one class. In another class of 100 students there were 15 scores higher than ted’s. If nobody had Ted’s score, then Ted’s was what percentile of the two classes combined?  Choose the correct choice from the following.
A) 86  B) 84  C) 82  D) 80  E) 78

Solution: Being in 80% percentile out of 200 grades means Ted was 161st (from the least scores) in the class (as long as nobody had Ted’s grades), he outscored 160.   In another class his score would rank him 76 (from the least grade out of 101, 100+Ted), 75 had the grades higher than Ted.   So in combined classes he outscored 160+75= 
160+75 = 235
235. There are 300 students 235/300=0.78   Answer: E (78%)   Generally being in x% means that x% has the grades less than you.   Ted in 80% --> he outscored 80% of of 200=160 (Joseph is 161st).   Of the 100 scores from another class, 15 were higher than Ted 's, and the rest were lower --> rest is 75, hence Ted outscored 75.   So out of total  200+100= 
 200+100 = 300
300, Ted outscored 160+75= 
160+75 = 235
235. Hence he is in 235/300=78%.
Answer: E
Twenty people at a meeting were born during the month of September, which has 30 days. The probability that at least two of the people in the room share the same birthday is closest to which of the following?  Choose the correct choice from the following choices.
A) 10%
B) 33%
C) 67%
D) 90%
E) 99%

Solution: The probability that at least two people sharing the same birthday = 1 - the probability that none of them sharing the same birthday   A = The number of ways of none of them sharing the same birthday = 30P20 = 30!/(30-20)! = 30!/10! = 11*12*...*29*30   B = The total number of possible ways of 20 people born in September = 20*20*....*20*20 = 20^30 ( each day has 20 options)   A/B = the probability that none of them sharing the same birthday   since B is much greater than A, A/B may equal 1%   --> The probability that at least two people sharing the same birthday = 1 - 1% = 99%   Answer 99%
Answer: E
An aeroplane covers a certain distance at a speed of 120 kmph in 5 hours. To cover the same distance in 1 2/3 hours, it must travel at a speed of: Choose the correct choice from the following answers.
A) 520	B) 620	C) 820	D) 740	E) 720

Solution: Distance = (120 x 5) = 600 km.   Speed = Distance/Time   Speed = 600/(5/3) km/hr. [We can write 1 2/3 hours as 5/3 hours]   Required speed = (600 x 3/5) km/hr = 360 km/hr   520nswer 520) 360 Km/hr
Answer: A
A person was asked to state his age in years. His reply was , "Take my age 5 years hence, multiply it by 3 and subtract 3 times my age 5 years ago and you will know how old I am." What was the age of the person ? Choose the correct choice.
A) 18  B) 92  C) 27  D) 26  E) 30

Solution: Explanation:   Let the present age of person be x years.   Then, 3(x + 5) - 3(x - 5) = x <=> (3x + 15) - (3x - 15) = x <=> x = 30..   Answer: 30
Answer: E
A boy needs to deliver three different newspaper to three different house. The problem is that he doesn't know which newspaper belong to which house. Find the probability that the boy only got one house with the wrong newspaper.
Choose the correct option:
A) 0	B) 1/3	C) 2/3	D) 4/27	E) 1/27

Solution: This one is a trick question. There are three house and three different newspapers. If he only got one wrong delivery, it means that he got the other two house correct. This is not possible because there are only three newspaper. If there are two correct delivery made the remaining one must also be correct. So the possibility of getting o my one of the delivery made wrong is impossible ore 0   0nswer: 0
Answer: A
Find the total number of prime factors in the expression (4)^11 x (7)^7 x (11)^2	Choose the correct choice.
A) 31
B) 22
C) 25
D) 27
E) 29

Solution: (4)^11x (7)^7 x (11)^2   = (2 x 2)^11 x (7)^7 x (11)^2   = 2^11 x 2^11 x7^7x 11^2   = 2^22 x 7^7 x11^2   Total number of prime factors = (22 + 7 + 2)= 
(22 + 7 + 2) = 31
31.   31nswer is 31.
Answer: A
If ‘n‘ integers taken at random and multiplied together, then what is the probability that the last digit of the product is 1, 3, 7 or 9 ?  Choose the correct answer:	A) (2/5)^n	B) (1/5)^n	C) (3/5)^n	D) (4/5)^n	E) (6/5)^n

Solution: Last digit may be 0,1,2,3,4,5,6,7,8,9 = 10   condition is 1,3,7,9 = 4   and n random no. so   probability is 4^n/10^n=(4/10)^n=(2/5)^n   (2/5)^nNSWER:(2/5)^n
Answer: A
A man sold 18 toys for Rs. 18900, gaining thereby the cost price of 3 toy find the cost price of a toy  Choose one:  A) s. 600  B) s. 800  C) s.500  D) s.900  E) s. 990

Solution: Let the cost of one toy = X.   Then, cost of 18 toys = 18X.   Gain = 3X.   SP of 18 toys = Rs. 18900.   Gain = SP â€“ CP   3X = 18900 â€“ 18X   21X = 18900   X = Rs. 900.   ANSWER : OPTION s.900
Answer: D
the sum of the ages of 5 children born at the intervals of 3 year each is 40 year. what is the age of the eldest child ?	Choose one:  A) 14 year  B) 8 year  C) 10 year  D) None of these  E) 9 year

Solution: Solution   let the ages of the children be x,(x + 3),(x + 6),(x + 9) and (x + 12) year.   then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 40 â‡” 5 x = 10 â‡” x= 2.   âˆ´ Age of the youngest child = x + 12= 2 + 12= 
2 + 12 = 14
14 years. 14 yearnswer 14 year
Answer: A
Joan took out a mortgage from hel local bank. Each monthly mortgage payment she makes must be triple the amount of the previous month's payment. If her first payment is $100, and the total amount she must pay back is $914800, how many months will it take Joan to pay back her mortgage?
Choose the correct answer.
A) 6
B) 8
C) 10
D) 9
E) 13

Solution: Joan starts off with 100 $ .. which is to be tripled every month   Her monthly payments look like this :   100 , 300 , 900 , 2700 ......... Upto 914800   This can be re written as :   100 x 1 , 100 x 3 , 100 x 9 , 100 x 27 ...... 100 x 9148   So we have 1 , 3 , 9 , 27 ..... 914800 in GP   We know that a =1 , and r = 3 ( its easy to figure it out by looking at the question , but regardless of it being mentioned in the question we can still compute the value of r using the formula Tn = a3^n-1 ...)   Therefore to find the Sum of n terms of a GP we use this formula :   Sn = a (1-r^n) / 1 -r   Using this and plugging in the information we get ...   9148 = 1 - 3^n / 1-3 ; 1-3^n / -2   Cross multiplying we get   9148 x -2 = 1- 3^n   - 19682 = 1 - 3^n   - 19682 = - 3 ^n   19683 = 3 ^n (negatives cancel out)   19863 can also be re written as 3 ^ 9   Therefore ; 3 ^9 = 3 ^n   Thus n = 9 (9)
Answer: D
If A and B get profits of Rs.18,000 and Rs.15,000 respectively at the end of year then ratio of their investments are Answers: A) 6 : 5 B) 1:4 C) 3:2 D) 2:3 E) 2:5

Solution: Ratio = 18000/15000 = 6 : 5   6 : 5nswer : 6 : 5
Answer: A
The value of P, when 4864 x 9P2 is divisible by 12, is	Pick:	A) 2	B) 5	C) 8	D) NOne of these	E) Cannot be determined

Solution: Sol.   Since 4864 is divisible by 4, So 9P2 must be divisible by 3.   ∴ (11 + 9) must be divisible by 3.   ∴ Least value of P is 1.   Answer NOne of these
Answer: D
Nine men went to a theater. Eight of them spent Rs.3 each over their tickets and the ninth spent Rs.2 more than the average expenditure of all the nine. Determine the total money spent by them?
Pick one
A) 29
B) 29.25
C) 31
D) 31.23
E) 32

Solution: Average of 9 = x   9x = 8 * 3 + x * 2 x = 3.25   Total = 9 * 3.25= 
9 * 3.25 = 29.25
29.25   29.25
Answer: B
which of the following inequalities indicates the set of all values of d for which the lengths E of the three sides of a triangle can be 3,4, and d?  Choices.
A) 0<d<1  B) 0<d<5  C) 0<d<7  D) 1<d<5  E) 1<d<7

Solution: This question is a good way to apply one of the most basic relation between the 3 sides of a triangle. In a triangle (ANY TRIANGLE), any side MUST be greater than the positive difference of the other two sides and less than than the sum of the other 2 sides. Let the sides of a triangle be a,b,c .   Thus,   |a-b| < c < a+b   |b-c| < a < b+c   |c-a| < b < a+c   Thus, if the sides of the triangle are 3,4 and d,   4-3<d<4+3 ---=""> 1<d<7. Thus 1<d<7 is the correct answer.</d<4+3>
Answer: E
A family consists of two grandparents, two parents and three grandchildren. The average age of the grandparents is 67 years, that of the parents is 35 years and that of the grandchildren is 6 years. What is the average age of the family?
Choose the most appropriate option
A) 200/7years  B) 222/7years  C) 225/7years  D) 245/7years  E) None of these

Solution: Multiply avg age of grand parents, parents and grand childrens with respectively to the no of persons in the family.   i.e,   Total Age of the family => (67*2)+(35*2)+(3*6)= 
(67*2)+(35*2)+(3*6) = 222
222   Total no of persons in family= 7   Now the avg age of the family = 222/7 years   ANSWER:222/7years
Answer: B
Two fair die with sides numbered 1 to 6 are tossed. What is the probability that the sum of the exposed faces on the die is a prime number?	Choose the correct choice from the following answers.
A) 5/11!
B) 7/8!
C) 5/9!
D) 15/21!
E) 4/9!

Solution: Two dices are thrown ! So we may get 1+1 or 1+2 ... or 1+6.. or 2+6 or 3+6 etc   Therefore the total different sum values we can get are :2,3,4,5,6,7,8,9,10,11,12[Sample space] ----------------(1)   Out of these values, 5 numbers are primes i.e.2,3,5,7,11[Favorable events] --------------------(2)   From (1)(2)   The answer is5/11!!   5/11!ns: 5/11!
Answer: A
From (1, 2, 3, 4, 5, 6), one number is picked out and replaced and one number is picked out again. If the sum of the 2 numbers is 9, what is the probability that the 2 numbers included the number 5?	Select the correct option
A) 1/2	B) 2/5	C) 3/10	D) 3/5	E) 1/4

Solution: We know that the sum of two numbers picked was 9. So, there could be the following cases:   (3, 6);   (6, 3);   (4, 5);   (5, 4);   Total of 4 cases out of which 2 have 5, thus the probability is 2/4=1/2.   1/2ns 1/2
Answer: A
A can do a piece of work in 4 days. B can do it in 5 days. With the assistance of C they completed the work in 2 days. Find in how many days can C alone do it?  Choose the correct choice from the following.
A) 33
B) 20
C) 88
D) 77
E) 11

Solution: C = 1/2 - 1/4 - 1/5 = 1/20   => 20 days   Answer:20
Answer: B
Mike's age is 57 years. If he is 5 more than twice the age of his son, find the age of his son.
Choose the correct answer
A) 20 years B) 26 years C) 16 years D) 18 years E) 19 years

Solution: Let Mike's son age be x.   5 + 2 x = 57   x = 26   Hence Mike's son age is 26years   Answer : 26 years
Answer: B
Subtracting 2% of A from A is equivalent to multiplying A by how much ?
Choose the correct choice.
A) 0.98	B) 9.4	C) 0.094	D) 94	E) None

Solution: Answer   Let A - 2% of A = AB.   ⇒ (98 x 0.98) / 100 = 0.98B   ∴ B = 0.98   Correct Option: 0.98
Answer: A
P, Q, R, S and T are five speakers who have to speak on a particular day, not necessarily in the same order. R is neither the first nor the last speaker. There are three speakers after S and three speakers ahead of T. If P speaks after Q, then who is the last speaker to speak? Choose the correct choice from the following answers.
A) S	B) T	C) P	D) Q	E) Cannot be determined.

Solution: Explanation:   There are three speakers after S. So, S is the 2nd speaker.   There are three speakers before T. So, T is the 4th speaker.   R is neither the 1st nor the 5th. So, R is the 3rd speaker.   P speaks after Q, So P is the 5th and Q is the 1st speaker. So, P is the last speaker.   ANSWER IS P
Answer: C
A rectangular floor is covered by a rug except fo a strip p meters along each of the four edges. If the floor is m meters by e meteres, What is the area of the rug in square meters?  Choose the correct choice from the following answers: A) mn - p(m+n) B) mn – 2p(m+n) C) mn – p^2 D) (m - p)(n - p) E) (m - 2p)(e - 2p)

Solution: The answer must be E.   Plug in M 100   N 50   e 10.
Answer: E
Simple interest on a sum at 4% per annum for 2 years is Rs.80. The C.I. on the same sum for the same period is?	Select the correct option.
A) 81.6  B) 81.7  C) 81.2  D) 81.3  E) 81.1

Solution: SI = 40 + 40   CI = 40 + 40 + 1.6= 
40 + 40 + 1.6 = 81.6
81.6   81.6nswer: 81.6
Answer: A
A charity collected $4,199 from donors during the last month. If each donor gave at least $20, what is the greatest possible number of donors the charity could have? Choose the correct choice from the following:	A) 209	B) 205	C) 200	D) 250	E) 215

Solution: Min fund = 20   Total = 4199   The closest multiple of 20 to 4199 is : 208   Which implies 208 people gave 20 and 1 person gave 39   Ans. 209
Answer: A