MU-NLPC/Calc-aqua_rat huggingface dataset:
How many Numbers can be formed with digits 2,4,6,8 without repetition?	Options:
A) 124
B) 256
C) 64
D) 84
E) 94

Solution: Number of one digit numbers = 4   Number of two digit numbers = 4 P 2 = 12   Number of Three digit numbers = 4 P 3 = 24   Number of four digit numbers = 4 P 4 = 24   So, total = 24 + 24 + 12 + 4= 
24 + 24 + 12 + 4 = 64
64   ANSWER:64
Answer: C
The ratio of two numbers is 4 : 7 and their H.C.F. is 4. Their L.C.M. is Choose the correct answer
A) 112
B) 22
C) 56
D) 27
E) 35

Solution: Explanation:   Let the numbers be 4x and 7x. Then, their H.C.F. = x. So, x = 4.   So, the numbers 16 and 28.   L.C.M. of 16 and 28 = 112.   112nswer: Option 112
Answer: A
The list price of an article is Rs.65. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is? Choose the correct choice from the following answers
A) 3%
B) 4%
C) 7%
D) 8%
E) 9%

Solution: Explanation:   65*(90/100)*((100-x)/100) = 56.16   x = 4%   Answer: Option 4%
Answer: B
How many five letter words are formed using the letters of the word BRINJAL? Choose the correct choice from the following answers:  A) 2800  B) 2640  C) 2400  D) 2500  E) 2520

Solution: The number of letters in the given word is seven.   The number of five letter words that can be formed using these seven letters is 7P5   = 7 * 6 * 5 * 4 * 3= 
7 * 6 * 5 * 4 * 3 = 2_520
2520.   Answer: 2520
Answer: E
Two whole numbers whose sum is 42 cannot be in the ratio  Pick
A) 2:5  B) 1:6  C) 2:4  D) 3:8  E) 2:40

Solution: 3:8) 3:8
Answer: D
If |r+s|=|r-s|, then r*s must be equal to:	Choose the correct answer
A) -2  B) 2  C) 0  D) -3  E) 3

Solution: Solution 1: Distance perspective   |r-s| = |r+s| ==> The distance of r and s is equal to the distance of r and -s.   <=======(-s)=======0=======(s)======>   Only 0 is the value that has a distance equal to s and -s.   Solution 2:   |r-s| = |r+s| (square both)   r^2 -2rs + s^2 = r^2 + 2rs + s^2   4rs = 0   rs = 0   Answer: 0
Answer: C
105,100,...,90,85,80,75
Insert the missing number
Pick:
A) 95	B) 78	C) 83	D) 84	E) none of the above

Solution: Missing number : 95   95nswer : 95
Answer: A
One paper sheet can be used to create 8 paper boats or 6 paper planes. If total exact 80 paper toys are to be made, minimum how many sheets need to be used to make paper boats?	Choose the correct choice from the following answers.
A) 5  B) 4  C) 3  D) 2  E) 1

Solution: Let us say x sheets are used to create paper boats and y sheets are used to create paper planes. Since total 80 paper toys are to be created, 8x + 6y = 80.   => 8x = 80 - 6y   => x = 10 - (6/8)y   => x = 10 - (3/4)y   To minimize x, we need to maximize y. And y needs to be multiple of 4.   y = 4, x = 10 - (3/4)4 = 7   y = 8, x = 10 - (3/4)8 = 4   y = 12, x = 10 - (3/4)12 = 1   Beyond this, x will become negative for greater values of y. So, minimum 1 sheet is required to be used for creating paper boats.   Answer: 1
Answer: E
A person travels equal distances with speeds of 3 km/hr, 4 km/hr and 5 km/hr and takes a total time of 40 minutes. The total distance is?	Choose the correct answer:
A) 1 km	B) 2 km	C) 3 km	D) 4 km	E) 2.55 km

Solution: E   3 km   Let the total distance be 3x km.   Then, x/3 + x/4 + x/5 = 40/60   47x/60 = 40/60 => x = 0.85.   Total distance = 3 * 0.85= 
3 * 0.85 = 2.55
2.55 km.
Answer: E
Mr. Thomas invested an amount of Rs. 13,900 divided in two different schemes A and B at the simple interest rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in 2 years be Rs. 3508, what was the amount invested in scheme B? Choose the correct choice from the following:
A) 6400	B) 6408	C) 6406	D) 6405	E) 6402

Solution: Let the sum invested in scheme A be Rs. x and that in scheme B be Rs. (13900 - x). Then,   (x * 14 * 2)/100 + [(13900 - x) * 11 * 2]/100 = 3508   28x - 22x = 350800 - (13900 * 22)   6x = 45000 => x = 7500   So, sum invested in scheme B = (13900 - 7500) = Rs. 6400.   6400nswer: 6400
Answer: A
A passenger sitting near the window in a train moving at 40 km/h, noticed that it took 3 sec. for the oncoming train to pass by. What was the speed of the oncoming train if the length of the oncoming train was 69 metres?  Choices:
A) a)50km/h	B) b)42.8km/h	C) c)56km/h	D) d)60km/h	E) e)70km/h

Solution: im getting A   3 secs to pass a 75 mts train , therefore speed = 23 meters/sec   to convert m/s to km/hrs multiply by 3.6   23*3.6 = 90   so its  82.8-40= 
 82.8-40 = 42.8
42.8 .   b)42.8km/h
Answer: B
There is a sequence such that each term is positive integer and each digit of the terms in the sequence has 3 to be ordered, what is the value Q of 100th term?
Choose the correct option:
A) 126
B) 192
C) 232
D) 252
E) 342

Solution: (1~99) 19, (100~199)  19, (200~299) 19. The 100th term should be 100-(19+19+19)= 
100-(19+19+19) = 43
43th number. Hence, the correct answer Q is 342. The correct answer is 342.
Answer: E
The ratio, by weight, of coffee to sugar to water in a pot of coffee is 4:1:15. The ratio is then altered so that the ratio of coffee to sugar is halved while the ratio of coffee to water is doubled. If the altered pot of coffee contains 16 grams of sugar, how many grams of water does it contain after alteration?	Pick:
A) 64 B) 60 C) 56 D) 52 E) 48

Solution: The new ratio of coffee to sugar is 2:1   The new ratio of coffee to water is 8:15.   The new ratio of coffee to sugar to water is 8:4:15.   If there are 16 grams of sugar, then there are  (15/4)*16= 
 (15/4)*16 = 60
60 grams of water.   The answer is 60.
Answer: B
If T = 5/9 * (K - 32), and if T = 105, then what is the value of K?
Choose the most appropriate option:
A) 209
B) 212
C) 215
D) 218
E) 221

Solution: K-32=9T/5   K=9T/5 + 32   K=9(105)/5 + 32 = 221   The answer is 221.
Answer: E
A person covered one-fourth of the total distance at 25 kmph and remaining distance at 24 kmph. What is the average speed for the total distance?	Choose the correct choice from the following answers:
A) 21 (1/8)	B) 21 (1/33)	C) 24 (8/33)	D) 29 (1/33)	E) 21 (4/33)

Solution: Let the total distance be x km   total time taken = (x/4)/25 + (3x/4)/24 = x/100+ x/32 = 33x/800   Average speed = x/(33x/800) = 24 8/33 kmph.   Answer: 24 (8/33)
Answer: C
The cost per liter of petrol during a 4 year period is as follows:
Year 1, $1 per liter ;
Year 2, $1.5 per liter ;
Year 3, $1.2 per liter ;
Year 4, $2 per liter .
If a factory spent equal dollars on petrol each year, what was the average cost of a liter of petrol during the 4 year period?
Choose the correct choice from the following choices.
A) $1.22  B) $1.333  C) $1.425  D) $1.175  E) $1.500

Solution: Let money spent each year = $6   liters bought first year = 6   liters bought second year = 4   liters bought third year = 5   liters bought fourth year = 3   Total number of liters = 18   Total money spent = 6*4= 
6*4 = 24
24   Average= 24/18 = 4/3 = 1.33   Answer is $1.333
Answer: B
If n denotes a number to the left of 0 on the number line such that the square of n is less than 1/36, then the reciprocal of n must be  Select:
A) Less than -6
B) Between -1 and -1/6
C) Between -1/6 and 0
D) Between 0 and 1/6
E) Greater than 6

Solution: n^2 < 1/36   abs(n) < 1/6   Since n<0, then 0 > n > -1/6   1/n < -6   The answer is Less than -6.
Answer: A
Everyone shakes hands with everyone else in a room. Total number of handshakes is 105. Number of persons=?	Choose the correct choice from the following options:
A) 14 B) 12 C) 11 D) 15 E) 16

Solution: In a room of n people, the number of possible handshakes is C(n,2) or n(n-1)/2   So n(n-1)/2 = 105 OR n(n-1)=210 OR n=15   Answer is (15)
Answer: D
Average score in 10 matches is 32, How many runs one should should score to increase his average by 4
runs.	Choose the correct choice from the following answers: A) 70 B) 76 C) 78 D) 80 E) 82

Solution: Average after 11 innings should be 36   So, required score = (11 * 36) - (10 * 32)   = 396 - 320= 
396 - 320 = 76
76   Answer: Option 76
Answer: B
The simple interest accrued on an amount of Rs.49500 at he end of three is Rs.17820. What would be the compound interest accured on the same amount at teh same rate in the same period? (Round off your answer to two decimal places)	Choose the most appropriate option
A) Rs.20043.94 B) Rs.20043.97 C) Rs.20043.96 D) Rs.20043.16 E) Rs.20043.17

Solution: Let the rate of interest be R% p.a.   (49500)(3)(R)/100 = 17820   495R = 5940   R = 12   CI on Rs.49500 at 12% p.a. for three years   = 49500{[1 + 12/100]3 - 1} = 69543.936 - 49500 = Rs.20043.94   when rounded off to two decimal places.   Rs.20043.94nswer:Rs.20043.94
Answer: A
Rahim bought 42 books for Rs.520 from one shop and 22 books for Rs.248 from another. What is the average price he paid per book ? Choose the correct choice from the following: A) s.17 B) s.18 C) s.12 D) s.11 E) s.10

Solution: Average price per book   = (520 + 248) / (42 + 22) = 768/ 64   = Rs.12   Answer:s.12
Answer: C
In a class total 34 students, 16 are have a brother, 15 are have sisters, 9 students don't have either brothers or sisters.Find the number of students having both brother and sisters.
Choose the correct choice:
A) 4  B) 5  C) 6  D) 7  E) 8

Solution: Total Number of students = 34   Let A be the Number of students have a brothers.   Let B be the number of students have a sisters.   AUB = Number of students have either brothers or sisters=34-9= 
34-9 = 25
25   n(AUB)= n(A)+n(B)-n(AnB)   25=16+15-n(AnB)   n(AnB)=31-25   n(AnB)=6   The number of students having both brother and sisters = 6   ANSWER:6
Answer: C
What is the greatest 5-digit number when divided by 6, 7 ,8 , 9, and 10 leaves a remainder of 4, 5, 6, 7, and 9 respectively?  Choose the correct answer.
A) 56780	B) 78910	C) 97479	D) 97918	E) 97920

Solution: When you divide a positive integer by 10, the remainder will just be the units digit. We know the remainder is 9 when we divide by 10, so 97479 is the only possible answer.
Answer: C
The inverse ratio of 6: 2: 1 is?  Choose the most appropriate option:  A) 2:3:7  B) 2:3:9  C) 2:3:2  D) 1:3:6  E) 2:3:1

Solution: 1/6: 1/2: 1/1 = 1:3:6   Answer:1:3:6
Answer: D
If f(x) = ax^5 – 3x^2 + ax^2 – x, then f(b) – f(-b) will equal:	Choices.
A) 0  B) 2ab  C) 2ab^4 – 6  D) 2ab^5-2b  E) ab^5

Solution: f(x)=ax^5 – 3x^2 + ax^2 – x   f(b) = ab^5 – 3b^2 + ab^2 – b   f(-b) = -ab^5 – 3b^2 + ab^2 + b   f(b) - f(-b) = ab^5 – 3b^2 + ab^2 – b + ab^5 + 3b^2 - ab^2 – b   =2ab^5-2b   Answer 2ab^5-2b
Answer: D
For the set { 3, 3, 4, 4, 5, 5, x}, which of the following values of x will most increase the standard deviation? Select:
A) (-3)^2	B) 2	C) 3	D) 4	E) 5

Solution: Standard Deviation Step 1, as pointed out by others, is to find out the mean = 4   Step 2, For each number: subtract the Mean and square the result =   (1-4)^2=(-3)^2   (2-4)^2=(-2)^2   (3-4)^2 =(-1)^2   (4-4)^2=(.0)^2   (5-4)^2=(1)^2   Clearly (1-4)^2=(-3)^2 will give you the greatest value among all the other options.   Hence (-3)^2
Answer: A
Gold is 10 times as heavy as water and copper is 5 times as heavy as water. In what ratio should these be mixed to get an alloy 9 times as heavy as water?	Pick
A) 3:2	B) 1:2	C) 4:1	D) 5:2	E) 4:3

Solution: G = 10W   4:1 = 5W   Let 1gm of gold mixed with x gm of copper to get 1+x gm of the alloy   1gm gold + x gm copper = x+1 gm of alloy   10W+5Wx = x+1 * 9W   10+5x = 9(x+1)   x = 1/4   Ratio of gold with copper = 1:1/4 = 4:1   Answer is 4:1
Answer: C
Media companies sell their magazine through a distributor, which take a commission of 3% of the price set by the media company. The distributor obtains the magazines through each company at the price of $12 per subscription. What is the price that the buyer observers if the distributor wants to maintain a 3% profit on the cost of a subscription?	Choose the correct option:
A) 11.13
B) 11.72
C) 11.74
D) 12.72
E) 12.74

Solution: Magazine price = $12;The distributor wants to maintain a 3% profit on the cost of each magazine subscription, thus he must get $ 12*1.03= 
 12*1.03 = 12.36
$12.36 after the distributor takes a commission of 3% of the final price --> (final price)*0.97= $12.36 --> (final price) = $12.74Answer: 12.74.
Answer: E
How many 6 digit telephone numbers can be formed if each number starts with 35 and no digit appears more than once?
Choose one:  A) 720  B) 360  C) 1420  D) 1680  E) 1780

Solution: 6 digit number where first 2 digit are fixed .   1*1*8*7*6*5= 
1*1*8*7*6*5 = 1_680
1680   ANSWER:1680
Answer: D
The number of arrangement of letters of the word BANANA in which the two N's do not appear adjacently is:	Choose the correct choice from the following answers:
A) 40
B) 50
C) . 60
D) 80
E) 100

Solution: Total # of arrangements of BANANA is 6!/(3!2!) = 60 (arrangement of 6 letters {B}, {A}, {N}, {A}, {N}, {A}, where 3 A's and 2 N's are identical).   The # of arrangements in which the two N's ARE together is 5!/3!=20 (arrangement of 5 units letters {B}, {A}, {A}, {A}, {NN}, where 3 A's are identical)..   The # of arrangements in which the two N's do not appear adjacently is {total} - {restriction} = 60 - 20= 
60 - 20 = 40
40.   40nswer: 40.
Answer: A
Bill has a small deck of 14 playing cards made up of only 2 suits of 7 cards each. Each of the 7 cards within a suit has a different value from 1 to 7; thus, there are 2 cards in the deck that have the same value. Bill likes to play a game in which he shuffles the deck, turns over 4 cards, and looks for pairs of cards that have the same value. What is the chance that Bill finds at least one pair of cards that have the same value?  Choices:
A) 8/67
B) 61/130
C) 17/33
D) 63/143
E) 25/88

Solution: P(no pairs) = 12/13*10/12*8/11 = 80/143   P(at least one pair) = 1 - 80/143 = 63/143   The answer is 63/143.
Answer: D
In a theater, the first row has 15 seats and each row has 2 more seats than previous row. If the last row has 53 seats, what is the total number of seats in the theater? Choose the correct choice from the following answers:  A) 600  B) 640  C) 680  D) 720  E) 760

Solution: The number of seats in the theater is   15 + (15+2) + ...+ (15+38)=   20(15) + 2(1+2+...+19)=   20(15) + 2(19)(20)/2=   20(15+19) = 20(34) = 680   The answer is 680.
Answer: C
In an xy-coordinate plane, a line is defined by y = kx + 1. If (4, b), (a,3), and (a, b+1) are three points on the line, where a and b are unknown, then k = ?	Choose the correct choice from the following options
A) 1/2	B) 1/4	C) 3/2	D) 2	E) 5/2

Solution: b=4k+1...(1)   b+1=ak+1...(2)   3=ak+1...(3)   Taking (2) and (3)   3=b+1   b=2   Taking (1)   2=4k+1   k=1/4   Answer : 1/4
Answer: B
What is the greatest prime factor of 8^13 - 2^30?  Choose the correct option.
A) 23 B) 37 C) 59 D) 73 E) 107

Solution: 8^13 - 2^30   =(2^3)^13 - 2^30   = 2^39 - 2^30   = 2^30 (2^9 -1)   = 2^30 * (512-1)   = 2^30 * 511   = 2^30 * 7 * 73   The greatest prime factor is 73.   The answer is 73.
Answer: D
Ten identical machines, running continuously at the same constant rate, take 6 days to complete a shipment. How many additional machines, each running at the same constant rate, would be needed to reduce the time required to complete a shipment by four days?
Pick.
A) 25  B) 20  C) 14  D) 9  E) 5

Solution: From the question you know that 10R = 1/6. The question asks you (partially) to make the rate from 1/6 to 1/2 (drop from 6 day to 2). So the only thing that you need to do is to find the magic number than can convert 1/6 to 1/2.   So 1/6 * x = 1/2 (1 equation with one unknown). So by solving this you get x = 6/2 or 3/1. Thats it then! Take the magic number 3/1 and multiply 20OTH sides of the original equation and you have:   10*(3/1)*R = (3/1) * 1/6   10 * 3 * R = 1/2, Hence 30R = 1/2, therefore 20 more machines!   20
Answer: B
If S is the sum of the reciprocals of the consecutive integers from 91 to 100, inclusive, which of the following is less than S?
I. 1/8
II. 1/9
III. 1/10
Choices:
A) None	B) I only	C) III only	D) II and III only	E) I, II, and III

Solution: Since we summarize the reciprocals from 100 to 91, we can say also that we add ten numbers who are all (with one exception 1/100) greater than 1/100, so that the sum must be greater than 1/10.   On the other side we can say that we add the reciprocals from 91 to 100, so that the sum has to be less than the sum of ten times 1/91.   We can conclude that the sum has to be less than 1/9 but more than 1/10. That leaves us III only as the only possible answer.
Answer: C
A cistern 9m long and 4 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is: Choose the correct choice
A) 49 m2 B) 50 m2 C) 53.5 m2 D) 68.5 m2 E) 57 m2

Solution: Area of the wet surface	= [2(lb + bh + lh) - lb]   = 2(bh + lh) + lb   = [2 (4 x 1.25 + 9 x 1.25) + 9 x 4] m2   = 68.5 m2.   Answer: Option 68.5 m2
Answer: D
A delegation of 5 members has to be formed from 3 ladies and 5 gentlemen. In how many ways the delegation can be formed, if 2 particular ladies are always included in the delegation?  Select:
A) 20  B) 30  C) 37  D) 40  E) 39

Solution: There are three ladies and five gentlemen and a committee of 5 members to be formed.   Number of ways such that two ladies are always included in the committee   = ⁶C₃ = (6 * 5 * 4)/6= 
(6 * 5 * 4)/6 = 20
20.   20nswer:20
Answer: A
A and B start a business jointly. A invests Rs.16000 for 8 months and B remains in the business for 4 months. Out of the total profit B claims 2/7th share. How much money is contributed by B?	Choose the correct choice from the following answers:
A) 12288	B) 12800	C) 27636	D) 19287	E) 19281

Solution: Explanation:   16*8: x*4 = 5:2   x = 12.8 => Rs.12800   Answer: 12800
Answer: B
In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the rate in the remaining 40 overs to reach the target of 252 runs?
Choose the correct choice from the following answers:
A) 6.25
B) 6.22
C) 5.5
D) 6.39
E) 6.13

Solution: Required run rate   = [252 - (3.2 * 10)]/40   = 220/40= 
220/40 = 11/2 = around 5.5
5.5   Answer: 5.5
Answer: C
A bag contains 14 wool scarves, exactly one of which is red and exactly one of which is green. If Deborah reaches in and draws three scarves, simultaneously and at random, what is the probability that she selects the red scarf but not the green scarf?
Choose the most appropriate option: A) 2/15 B) 11/23 C) 18/121 D) 33/182 E) 51/273

Solution: Total possible ways to choose three scarves is 14C3 = 364   We need to choose the red scarf and two of 12 other scarves (not the green scarf).   The number of successful possibilities is 12C2 = 66   P(red scarf but not green scarf) = 66/364 = 33/182   The answer is 33/182.
Answer: D
Rs.630/- distributed among A,B and C such that on increasing their shares by RS.10,RS.5 and RS.15 respectively, The balance money would be divided among them in the ratio 3:4:5. Then, A’s share is:?  Choices
A) Rs.155	B) Rs.145	C) Rs.150	D) Rs.140/-	E) Rs.160

Solution: A:B:C = 3:4:5   Total parts = 12   A's share is = 3 parts   12 -----> Rs.600/-   3 -----> Rs.150/-   A's total = 150 - 10 = Rs.140/-   Rs.140/-)
Answer: D
Five years ago the average of the ages of A and B was 40 years and now the average of the ages of B and C is 48 years. What will be the age of the B ten years hence?
Choose the correct choice
A) 22	B) 27	C) 96	D) 51	E) 2

Solution: Let the present ages of A, B and C be a, b and c respectively.   Given, [(a - 5) + (b - 5)] / 2 = 40 => a + b = 90 --- (1)   (b + c)/2 = 48 => b + c = 96 --- (2)   From (1) and (2), we cannot find b.   Answer:51
Answer: D
Two persons start running simultaneously around a circular track of length 200 m from the same point at speeds of 10 km/hr and 15 km/hr. When will they meet for the first time any where on the track if they are moving in opposite directions?	Select
A) 28 sec
B) 19.2 sec
C) 17 sec
D) 23 sec
E) 27 sec

Solution: Time taken to meet for the first time anywhere on the track   = length of the track / relative speed   = 200 / (10 + 15)5/18 = 300* 18 / 25 * 5 = 19.2 seconds.   Answer : 19.2 sec
Answer: B
A car covers a distance of 1728 km in 6 hours. Find its speed?  Choose the correct choice from the following answers.
A) 104
B) 288
C) 271
D) 276
E) 128

Solution: 1728/6= 
1728/6 = 288
288 kmph   Answer: 288
Answer: B
A certain candy manufacturer reduced the weight of Candy Bar M by 25 percent buy left the price unchanged. What was the resulting percent increase in the price per ounce of Candy Bar M?	Choices:	A) 20	B) 30	C) 34	D) 35	E) 33.33

Solution: assume 1oz candy cost $1 before.   now price remain same $1 but weight of candy reduces to 0.75 oz   new price of candy = 1/0.75 =1.3333   price increase 33.33 %   33.33
Answer: E
a renowned battery sells six different-sized wedding cakes. Each cake costs x dollars more than the next one below it in size, and the price of the largest cake is $24.50. If the sum of the prices of the six different cakes is $109.50, what is the value of x?	Choose the correct choice:	A) 1.50	B) 1.75	C) 2.00	D) 2.50	E) 3.00

Solution: Since the price of the largest cake (6th) is $24.50, then the price of the smallest cake (1st) is $(24.50-5x). Now, the prices of the cakes are evenly spaced so the sum of the prices is (average price)*(# of cakes)=(first+last)/2*(# of cakes). So, (24.50-5x+24.50)/2*6=109.50 --> x=2.5.   Answer: 2.50.
Answer: D
Fifteen more than three times a number is the same as ten less than six times the
number. What is the number	Choose the correct choice
A) 20/2 B) 15/4 C) 30/5 D) 25/3 E) 9/6

Solution: 3x+15 First, addition is built backwards   6x−10 Then, subtraction is also built backwards   3x+15=6x−10 Is between the parts tells us theymust be equal   −3x −3x Subtract 3x so variable is all on one side   15=3x−10 Nowwe have a two−step equation   +10 +10 Add 10 to both sides   25=3x The variable ismultiplied by 3   3 3 25/3ivide both sides by 3   25/3=x Our number is   25/3   correct answer 25/3
Answer: D
Mandrake has to choose from 4 from 10 people. There are 3 girls, 5 boys , 2 children. What is total probability that he will choose 1G , 2B , 1C?	Choose the correct choice from the following answers:
A) 1/7 B) 2/7 C) 3/7 D) 4/7 E) 5//7

Solution: (3C1 * 5C2 * 2C1)/ 10C4 = 3*10*2/210 = 60/210=2/7   ANSWER:2/7
Answer: B
Maddie has 48 apples, if she give 22 to mike, how many does she have left? Choose the correct choice from the following options
A) 12  B) 21  C) 26  D) 22  E) 5

Solution: 48-22= 
48-22 = 26
26   C. 26
Answer: C
Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is? Choose the correct answer
A) 3/7
B) 3/2
C) 3/5
D) 3/1
E) 3/3

Solution: Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 27 x meters, and length of the second train = 17 y meters. (27 x + 17 y) / (x + y) = 23   ==> 27 x + 17 y = 23 x + 23 y ==> 4 x = 6 y ==> x/y   = 3/2.   Answer: 3/2
Answer: B
The sume of the ages of a father and his son is 45 years.Five years ago,the product of their ages was 34 .The ages of the son and the father are respectively :	Select the correct option:
A) 6 and 39
B) 7 and 38
C) 9 and 36
D) 11 and 34
E) 12 and 74

Solution: Solution   Let the ages of father and son be x and (45 - x) years respectively.   Then,(x - 5)(45 - x - 5)=34 ⇔ (x - 5) (40 - x)=34 ⇔x2 - 45x + 234 = 0   ⇔ (x - 39)(x - 6)= 0 ⇔ x = 39 or x =6.   ∴ Father's age = 39 years and son's age =6 years. 6 and 39nswer 6 and 39
Answer: A
Divide Rs. 5500 among A, B and C so that A receives 1/3 as much as B and C together and B receives 1/5 as A and C together. A's share is? Pick
A) 1227	B) 1268	C) 1375	D) 1200	E) 1210

Solution: A+B+1375 = 5500   A = 1/3(B+1375); B = 1/5(A+1375)   A/(B+1375) = 1/3   A = 1/4 * 5500= 
1/4 * 5500 = 1_375
> 1375   Answer: 1375
Answer: C
There are 2 sections with 4 questions each. If three questions are selected from each section, the chance of getting different questions is________  Pick one.
A) 10
B) 214
C) 300
D) 216
E) 245

Solution: we have to select three questions from each section so the chances are 4C2.4C2.4C2=216   ANSWER:216
Answer: D