MU-NLPC/Calc-aqua_rat huggingface dataset:
Jerry and john play a card game. In the beginning of the game they have an equal number of cards. Each player, at her turn, gives the other a third of her cards. john plays first, giving Jerry a third of her cards. Jerry plays next, and john follows. Then the game ends. jerry ended up with 14 more cards than Michelle. How many cards did each player have originally?	Select the correct option: A) 28 B) 27 C) 29 D) 30 E) 31

Solution: Game john jerry   Initially2727   After game 1 1836   After game 2 3024   After game 3 2034   Now Merry has 14 cards more than Michelle. This option gives us exactly what number of cards they had initially.   So the answer is 27
Answer: B
The ratio of two numbers is 5 to 1. The sum is 18. What are the two numbers?  Answers.
A) 17 B) 18 C) 19 D) 20 E) 21

Solution: Solution   Let x be the first number. Let y be the second number   x / y = 5 / 1   x + y = 18   Using x / y = 5 / 1, we get x = 5y after doing cross multiplication   Replacing x = 5y into x + y = 18, we get 5y + y = 18   6y = 18   y = 3   x = 5y = 5 × 3 = 15   As you can see, 15/3 = 5, so ratio is correct and  3 + 15= 
 3 + 15 = 18
18, so the sum is correct.   Answer 18
Answer: B
A drawer holds 5 red hats and 5 blue hats. What is the probability of getting exactly three red hats or exactly three blue hats when taking out 5 hats randomly out of the drawer and returning each hat before taking out the next one?	Choose the correct option:
A) 1/8  B) 1/4  C) 1/2  D) 5/8  E) 7/12

Solution: Let's find the probability of getting exactly 3 red hats.   One possible case is red-red-red-blue-blue.   The probability of this is 1/2*1/2*1/2*1/2*1/2 = 1/32   There are 5C3 = 10 such cases so we need to multiply this by 10.   P(exactly 3 red hats) = 10*1/32 = 5/16   Clearly the probability of getting exactly 3 blue hats will also be 5/16.   The sum of the probabilities is 5/16+5/16 = 5/8   The answer is 5/8.
Answer: D
From group of 15 cricket players a team of 11 players is to be chosen. How many ways this can be done?	Choose one:
A) 3252
B) 1365
C) 5325
D) 1432
E) 1324

Solution: 11 players are to be chosen from 15 players. This can be done in 15C11 ways. ie) 15!/11!x4! = 1365 ways. Ans: 1365
Answer: B
How many 3/4 foot pieces of cable can be cut out of a piece that is 30 feet long? Pick one.
A) a.30	B) b.36	C) c.37	D) d.38	E) e. 40

Solution: Pretty Simple..the answer is choice (E) 40.   All that one has to do is :   1: Convert 3/4 into an improper fraction (3/4) or a decimal (0.75)   2: Divide 30 by 3/4 (or 0.75)   Answer =40 (e. 40)
Answer: E
The ratio of the area of a square mirror to its frame is 16 to 33. If the frame has a uniform width (s) around the mirror, which of the following could be the value, in inches, of s ?
I. 2
II. 3 1/2
III. 5	Choose the correct option.
A) I only B) III only C) I and II only D) I and III only E) I, II, and III

Solution: Area of picture = 16x Area of frame = 33x   Area of picture / (Area of picture + area of frame) = 16x / 49x = 4x/7x.   This results in s value to be a multiple of 1.5 = multiple of 3/2 and since s is not constrained to be only integer all the three choices are possible   For i) the multiple of s is 4/3   For ii) the multiple of s is 7/3   For iii) the multiple of s is 10/3   The key is s can be any real positive number... very tricky problem.. took me > 15 minutes.   Answer is I, II, and III
Answer: E
The diagonals of a rhombus are 22 cm and 30 cm. Find its area?	Options.
A) 358 B) 329 C) 350 D) 330 E) 317

Solution: 1/2 * 22 * 30= 
1/2 * 22 * 30 = 330
330   Answer:330
Answer: D
Two women can do a work in 4 days. Six men can complete the same work in 3 days. What is the ratio between the capacity of a man and a woman? Choose the correct choice from the following options.
A) 1:2	B) 2:1	C) 4:9	D) 3:2	E) None of these

Solution: Explanation:   (2 Ã— 4 ) women can complete the work in 1 day.   âˆ´ 1 woman's 1 day's work = 1/8   (6 Ã— 3) men can complete the work in 1 day.   âˆ´ 1 man's 1 day's work = 1/18   so, required ratio =1/8 : 1/18= 4:9   Answer: 4:9
Answer: C
85% of a number is added to 24, the result is the same number. Find the number?
Pick.
A) 13√5 B) 13√2 C) 13√9 D) 12√9 E) 13√1

Solution: 4a = 48 4a = 20   a = 12 a = 5   a2 = 144 a2 = 25   Combined area = a2 = 169 => a = 13   d = 13√2   Answer:13√2
Answer: B
Kamal obtained 96, 65, 82, 67 and 85 marks(out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks?	Answers.
A) 65  B) 69  C) 72  D) 79  E) NOne

Solution: Sol.   Average   = 96 + 65 + 82 + 67 + 85 / 5)   = (395 / 5)= 
(395 / 5) = 79
79.   Answer 79
Answer: D
The sum of two numbers is 25 and their difference is 13. Find their product. Answers
A) 104 B) 108 C) 114 D) 325 E) None

Solution: Sol.   Let the numbers be x and y.   Then, x + y = 25 and x - y = 13.   4xy = (x+y)2 - (x-y)2   = (25)2 - (13)2 = 625 - 169= 
625 - 169 = 456
456   ⇒ xy= 114.   Answer 114
Answer: C
For each of her sales, a saleswoman receives a commission equal to 20 percent of the first $500 of the total amount of the sale, plus 35 percent of the total amount in excess of $500. If the total amount of one of her sales was $800, the saleswoman’s commission was approximately what percent of the total amount of the sale?
Pick:
A) 22% B) 24% C) 25% D) 26% E) 28%

Solution: Total sales =800   Comission = (20/100)*500+ (35/100)*300   =100 + 105= 
100 + 105 = 205
205   %Comission=(205/800)*100=25.6~ 26%   Answer is 26%
Answer: D
A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 50 years now, the son's age five years back was?
Choose the correct choice from the following options.
A) 18years  B) 19years  C) 20years  D) 21years  E) 22years

Solution: Let the son's present age be x years. Then, (50 - x) = x   2x = 50.   x = 25.   Son's age 5 years back (25 - 5)= 
(25 - 5) = 20
20 years.   20years)
Answer: C
A shipment of 1500 heads of cabbage, each of which was approximately the same size was purchased for $600.The day the shipment arrived 2/3 of the heads were sold, each at 25% above the cost per head.The following day the rest were sold at a price per head equal to 12% less than the price each head sold for the day before.what was the gross profit on this shipment?  Choose the correct choice
A) $100 B) $115 C) $120 D) $130 E) $135

Solution: Sol:   1500 heads -> $600   1 head -> $600/1500   1 head -> $(2/5)   25% more of (2/5) -> 125/100 * 2/5 = $(1/2)   He sold   2/3*1500= 
  2/3*1500 = 1_000
1000 heads for $(1/2) per head   Total revenue by selling 1000 heads= 1000 * 1/2= 
1000 * 1/2 = 500
$500   Heads left: 500   $120ost per head: 88% of the previous price: 88/100 * 1/2= $(11/25)   Total revenue by selling 500 heads = 11/25 * 500= 
11/25 * 500 = 220
220   Total revenue after selling 1500 cabbage heads - 220+500= $720   Money spent on the purchase: $600   Profit = 720-600= 
720-600 = 120
$120   Ans: "$120
Answer: C
A train running at the speed of 60 km/hr crosses a pole in 15 sec. What is the length of the train?  Choose the correct choice
A) 250  B) 279  C) 277  D) 272  E) 150

Solution: Speed = 60 * 5/18 = 50/3 m/sec   Length of the train = speed * time = 50/3 * 15= 
50/3 * 15 = 250
250 m   250nswer: 250
Answer: A
An escalator moves towards the top level at the rate of 10 ft.sec and its length is 112 feet. If a person walks on the moving escalator at the rate of 4 feet per second towards the top level, how much time does he take to cover the entire length.  Select.
A) 14 sec
B) 10 sec
C) 12 sec
D) 8 sec
E) 9 sec

Solution: Time taken to cover the entire length = tot.dist/resultant speed   = 112/ (10+4)= 
112/ (10+4) = 8
8 sec   ANSWER:8 sec
Answer: D
If FRIEND is coded as HUMJTK, how is CANDLE written in that code ?  Pick:	A) EDRIRL	B) FFIIIUU	C) WDFDD	D) DRFED	E) E8U8W

Solution: Explanation:   The first, second, third, fourth, fifth and sixth letters of th word are respectively moved two, three, four, five, six and seven steps forward to obtain the corresponding letters of the code.   EDRIRLnswer: EDRIRL
Answer: A
The average of 10 numbers is calculated as 16. It is discovered later on that while calculating the average, the number 35 was incorrectly read as 25, and this incorrect number was used in the calculation. What is the correct average?  Choose the correct choice from the following:
A) 16 B) 17 C) 19 D) 22 E) 26

Solution: The total sum of the numbers should be increased by 10.   Then the average will increase by  10/10= 
 10/10 = 1
1.   The correct average is 17.   The answer is 17.
Answer: B
After 10% of the inhabitants of a village disappeared, a panic set in during which 25% of the remaining inhabitants left the village. At that time, the population was reduced to 5265. What was the number of original inhabitants?	Select the correct option:	A) 7500	B) 7800	C) 8100	D) 8400	E) 8700

Solution: Let the total number of original inhabitants be x.   (75/100) * (90/100) * x = 5265   (27/40) * x = 5265   x = 5265 * 40 / 27= 
5265 * 40 / 27 = 7_800
7800   The answer is 7800.
Answer: B
A BAG CONTAINS 6 WHITE AND 4 BLACK BALLS .2 BALLS ARE DRAWN AT RANDOM. FIND THE PROBABILITY THAT THEY ARE OF SAME COLOUR.  Choose the correct choice from the following answers
A) 8/9
B) 75/4
C) 7/15
D) 3/7
E) 4/3

Solution: LET S BE THE SAMPLE SPA7/15E   THEN N(S)=NO OF WAYS OF DRAWING 2 BALLS OUT OF (6+4)=107/152=(10*9)/(2*1)= 
(10*9)/(2*1) = 45
45   LET E=EVENT OF GETTING BOTH BALLS OF SAME 7/15OLOUR   THEN N(E)=NO OF WAYS(2 BALLS OUT OF SIX) OR(2 BALLS OUT OF 4)   =(67/152+47/152)=(6*5)/(2*1)+(4*3)/(2*1)=15+6= 
15+6 = 21
21   P(E)=N(E)/N(S)=21/45=7/15   Ans: 7/15
Answer: C
A certain company had a total annual expenditure of 1.47∗10^7 on employee salaries last year. If the company employed 420 people, what was the average employee salary? Choose the correct choice from the following:
A) $20,000 B) $25,000 C) $35,000 D) $40,000 E) $45,000

Solution: Given: Total annual expenditure of 1.47∗10^7 on employee salaries   Total employees = 420   Observe that  420*3.5= 
 420*3.5 = 1_470
1470   Therefore try to bring the numerator in terms of 1470   Average salary= (1470*10^4) /420 = 3.5*10^4 = 35,000   Option $35,000
Answer: C
which number need to add to 859622 to get a number exactly divisible by 456? Choices
A) 544365	B) 465674	C) 345465	D) 675644	E) 859622

Solution: Dividend = Quotient * Divisor + Reminder   859622 / 456 gives quotient = 1885 and reminder = 62.   So, the next number divisible by 456 is 456 places infront of 456 * 1885   Which means 456 – 62 = 394 should be added to 859622.   859622
Answer: E
A rectangular with dimensions 16 inches by 20 inches is to be divided into squares of equal size. Which of the following could be a length of a side of the squares?
Choose the correct choice:  A) a) 4 inches  B) b) 6 inches  C) c) 7 inches  D) d) 8 inches  E) e) 10 inches

Solution: you need to divide the width and length of the rectangular to equal pieces where L = W   you can solve this using GCF   16=2*2*2*2   20=2*2*5   GCF = 2*2= 
2*2 = 4
4   P.S you can make squares with side of 2,4 and we choose 4 because 2 is not in the answers   a) 4 inchesnswer : a) 4 inches
Answer: A
A woman invested $1,000, part at 5% and the rest at 6%. Her total investment with interest at the end of the year was $1,054. How much did she invest at 5%?	Choose the correct choice from the following choices.
A) $500	B) $600	C) $700	D) $900	E) $950

Solution: et x be the portion invested at 5% and   Let (1-x) be the rest which is invested at 6%   The question states that the return after 1 year is (1054/1000)-1= 
(1054/1000)-1 = 27/500 = around 0.054
0.054= 5.4%   We want to find the dollar amount invested in X   Using our defined variables, put together the equation and solve for x (the percentage of 1000 invested at 5%)   0.05x+0.06(1-x)= 0.054   (0.05)x +0.06 - (0.06)x = 0.054   -0.01x = -0.006   x= -0.006/-0.01 = 6/10 = 60%   So X = 60% of the 1000 which is 600   ANSWER:$600
Answer: B
CX, EV, GT, IR, ?
Choose one:
A) JH	B) UU	C) KP	D) UY	E) IS

Solution: ANSWER:KP
Answer: C
The figure shown can be folded into the shape of a cube. In the resulting cube, which of the lettered faces is opposite the face marked x?
Answers.
A) D	B) H	C) J	D) H	E) W

Solution: Explanation: If you fold the above picture at the dotted lines, X and C are opposite to each other.   Dnswer:D
Answer: A
A cylinder and a cone have the same height and same radius of base. The ratio between the volumes of the cylinder and the cone is: Choose the correct choice from the following choices.
A) 4:1 B) 2:1 C) 7:1 D) 5:1 E) 3:1

Solution: Volume of the cylinder = πr(power2)h   Volume of the cone = 1/3 πr(power2)h   (πr(power2)h)/(1/3 πr(power2)h) = 3/1= 
3/1 = 3
3 : 1   Answer is 3:1.
Answer: E
A 10-by-5 inch piece of paper is used to form the lateral surface of a cylinder. If the entire piece of paper is used to make the lateral surface, which of the following must be true of the two possible cylinders that can be formed? Choose one
A) The volume of the cylinder with height 10 is 50/pi cubic inches greater than the volume of the cylinder with height 6.  B) The volume of the cylinder with height 5 is 50/pi cubic inches greater than the volume of the cylinder with height 10.  C) The volume of the cylinder with height 10 is 50pi cubic inches greater than the volume of the cylinder with height 6.  D) The volume of the cylinder with height 5 is 50pi cubic inches greater than the volume of the cylinder with height 10.  E) The volume of the cylinder with height 5 is 250/pi cubic inches greater than the volume of the cylinder with height 10.

Solution: Pretty straightforward. Plug in the values to compute the volume of the cylinder. Keep in mind 5 and 10 are the circumference of the base and not the radius. The volume of the cylinder with height 5 is 50/pi cubic inches greater than the volume of the cylinder with height 10. is the right answer.
Answer: B
A BUS is running at a speed of 40 km/hr and it crosses a post in 18 seconds. What is the length of the BUS ? Choose the correct choice from the following answers:
A) metres  B) metres  C) metres  D) metres  E) metres

Solution: Explanation:   Speed of the BUS, v = 40 km/hr = 40000/3600 m/s = 400/36 m/s   Time taken to cross, t = 18 s   Distance metresovered, d = vt = (400/36)× 18 = 200 m   Distance covered is equal to the length of the BUS= 200 m   Answer: Option metres
Answer: C
The average age of the mother and her six children is 8 years which is reduced by 5 years if the age of the mother is excluded. How old is the mother?  Pick:
A) 38 B) 41 C) 42 D) 43 E) 44

Solution: Total age of mother and 6 children = avg x n = 8 x (6+1)= 56   If mother is excluded new average is  (8 - 5)= 
 (8 - 5) = 3
3   so for 6 children= 6 x 3 =18   so mother's age is  56 - 18= 
 56 - 18 = 38
38   38nswer: Option 38
Answer: A
If a and b are positive real numbers, and a^3 + b^3 = 25, then the greatest possible value of a is between:
Choose the correct option:
A) 0 and 3	B) 3 and 4	C) 4 and 5	D) 5 and 7	E) 7 and 9

Solution: If a > 3, then a^3 + b^3 > 25.   The answer is 0 and 3.
Answer: A
The “length of integer x” refers to the number of prime factors, not necessarily distinct, that x has. (If x = 60, the length of x would be 4 because 60 = 2 × 2 × 3 × 5.) What is the greatest possible length of integer z if z < 1,080?  Select the correct option:
A) 13 B) 10 C) 9 D) 7 E) 6

Solution: To maximize the length of z we should minimize its prime base. The smallest prime is 2 and since 2^10=1,024<1,080 then the greatest possible length of integer z is 10.   Answer: 10.
Answer: B
How many distinct integer values of n satisfy the inequality||n-3| + 2| ≤ 12?  Choose the correct choice from the following answers.
A) 15	B) 16	C) 12	D) 18	E) 19

Solution: so i can write this as In-3I+2<=12   or In-3I<=10   so n can have -7 to 13 = 12 true values....   12
Answer: C
There are 1200 jelly beans divided between two jars, Jar X and Jar Y. If there are 400 fewer jelly beans in jar X than three times the number of beans in jar Y, how many beans are in jar X?
Options:
A) 650
B) 700
C) 750
D) 800
E) 850

Solution: X+Y=1200 so Y=1200-X   X=3Y-400   X=3(1200-X)-400   4X=3200   X=800   The answer is 800.
Answer: D
The banker's discount on a bill due 4 months hence at 15% is $6.20. The true discount is:
Pick one: A) $5.90 B) $6.80 C) $6.60 D) $6.70 E) $6.10

Solution: T.D.	=	B.D. x 100/100 + (R x T)   = $ [6.20 x 100/100 +15 x 1/3]   = $	[6.20 x 100/105]   = $ 5.90   $5.90NSWER:$5.90
Answer: A
Find the area of the quadrilateral of one of its diagonals is 10 cm and its off sets 7 cm and 3 cm?  Choose the correct choice from the following answers
A) 50 cm2	B) 100 cm2	C) 150 cm2	D) 200 cm2	E) 250 cm2

Solution: 1/2 * 10(7 + 3)   = 50 cm2   50 cm2nswer: 50 cm2
Answer: A
If ab > 0, which of the following must be negative? Choose one: A) a + b B) |a| + b C) b - a D) a/b E) -a/b

Solution: If ab > 0 the we Infer that a and b both have same sign i.e. either both a and b are Positive or Both a and b are Negative   Now Checking Options:   (A) a + b will be positive for both a and b to be positive hence INCORRECT OPTION   (B) |a| + b will be positive for both a and b to be positive hence INCORRECT OPTION   (C) b - a May be positive for both a and b to be positive (e.g. b=3 and a=2) henceINCORR-a/bCT OPTION   (D) a/b will be positive for both a and b to be positive or Negative hence INCORR-a/bCT OPTION   (-a/b) -a/b will always be Negative because an and b have same sign so a/b will be positive therefore -a/b will be Negative hence CORR-a/bCT   Answer: Option -a/b
Answer: E
Anand and Deepak started a business investing Rs. 22,500 and Rs. 35,000 respectively. Out of a total profit of Rs. 13,800, Deepak's share is : Choose the correct choice from the following choices
A) Rs. 5400
B) Rs. 700
C) Rs. 8400
D) 2Rs. 9600
E) Rs. 8000

Solution: Explanation:   Ratio of their shares = 22500 : 35000 = 9 : 14.   Deepak's share = Rs.   (13800âˆ—14/23)   = Rs. 8400.   ANSWER IS Rs. 8400
Answer: C
Some persons can do a piece of work in 12 days. Two times the number of these people will do half of that work in?	Select
A) 2 days
B) 3 days
C) 1 days
D) 5 days
E) 7 days

Solution: 3 days   3 days     12/ (2 * 2)= 
  12/ (2 * 2) = 3
3 days
Answer: B
Ram's age and Shyam's age are in the ratio 3:4. Seven years ago the ratio of their ages was 2:3. Find the ratio of their ages five years hence? Choose the correct choice from the following options.
A) 26/73
B) 26/39
C) 26/93
D) 26/33
E) 26/13

Solution: Let ages of Ramu and Shyam be x and y respectively.   x/y = 3/4 => x = 3/4 y   (x- 7)/(y - 7) = 2/3   => 3x - 21 = 2y - 14 => 3x = 2y + 7   But x = 3/4 y   3 * 3/4 y = 2y + 7   9y = 8y + 28 => y = 28years   => x = 21 years   Ratio of their ages five years hence, (21 + 5)/(28 + 5) = 26/33.   Answer: 26/33
Answer: D
A salesman`s commission is 5% on all sales upto Rs.10,000 and 4% on all sales exceeding this.He remits Rs.31,100 to his parent company after deducing his commission . Find the total sales.
Choose the correct option.
A) 32500 B) 33400 C) 44000 D) 40000 E) 45000

Solution: Let his total sales be Rs.x.Now(Total sales) – (Commission )=Rs.31,100   x-[(5% of 10000 + 4% of (x-10000)]=31,100   x-[((5/100)*10000 + (4/100)*(x-10000)]=31,100   x-500-((x-10000)/25)=31,100   x-(x/25)=31200  24x/25=31200x=[(31200*25)/24)=32,500.   Total sales=Rs.32,500   32500NSWER 32500
Answer: A
What is the remainder when 263251 is divided by 9? Pick
A) 8  B) 3  C) 6  D) 1  E) 9

Solution: If the sum of the digits of a number is divisible by 9, the number will be divisible by 9.   2 + 6 + 3 + 2 + 5 + 1= 
2 + 6 + 3 + 2 + 5 + 1 = 19
19   The nearest multiple of 9 is 18.   19 - 18= 
19 - 18 = 1
1.   ANSWER:1
Answer: D
A set of numbers has the property that for any number x in the set, x+4 is also in the set. If -4 is in the set, which of the following must also be in the set
1. 0
2. -8
3. 8 Options
A) 1 only  B) 2 only  C) 1 and 2 only  D) 2 and 3 only  E) 1,2 and 3

Solution: If X is in the set than X+ 4 is also in the set   If -4 in the set than    -4+4= 
 -4+4 = 0
0 is also in the set   Since + 4 is Present, 4 + 4= 8 Is also present in the set .   Therefore Ans 1 and 2 only
Answer: C
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?  Options:  A) 7  B) 8  C) 9  D) 6  E) 5

Solution: 45*12 : 54*x = 2: 1   x = 5   12 -5 = 7.7nswer: 7
Answer: A
If 40% of a number is greater than 80% of 5 by 2, what is the number? Choose the correct choice from the following answers.
A) 3  B) 15  C) 20  D) 2  E) 5

Solution: Explanation:   40/100 * x - 80/100 * 5 = 2   40/100 * x - 4 = 2   40/100 * x = 6   x = 6 * 100 / 40= 
6 * 100 / 40 = 15
15   Answer: Option 15
Answer: B
If a coin is flipped, the probability that the coin will land tails is 1/2. If the coin is flipped 5 times, what is the probability that it will land tails up on the first 2 flips and not on the last 3 flips?	Pick
A) 3/5 B) 1/32 C) 1/5 D) 1/4 E) 1/2

Solution: (1/2) * (1/2) * (1/2) * (1/2) * (1/2) = 1/32 Answer: 1/32
Answer: B
If a is a positive integer then 4^(2a) + (64^a)/(2^(2a)) =  Choose the correct option:	A) 0	B) 16^16	C) 8^15	D) 2 × 16^a	E) 18^a

Solution: 4^(2a) + 64^a/ 2^(2a) = 16^a + 36^a/4^a = 16^a + (64/4)= 
+ (64/4) = 16
16^a + 16^a= 2 × 16^a   Answer : 2 × 16^a
Answer: D
There are 5 locks and 5 keys and each of the 5 keys matches each of the 5 locks. What is the minimum and the maximum trial numbers of attempts needed to confirm that each of the 5 keys matches each of the 5 locks? Answers:
A) 5,15
B) 4,15
C) 5,10
D) 4,10
E) 5,20

Solution: the actual number of tries that we need to "unlock" all the lockers, and got into the trap 5-15.   of course, if we do not need to unlock the lockers, but just simply to check..   minimum # of attempts is 4.   maximum is 10,   ANS:4,10
Answer: D
A and B starts a business with Rs.8000 each, and after 4 months, B withdraws half of his capital . How should they share the profits at the end of the 19 months?  Choose the correct choice from the following choices: A) 18:11 B) 18:15 C) 18:19 D) 18:121 E) 19:11

Solution: A invests Rs.8000 for 19 months, but B invests Rs.8000 for the first 4 months and then withdraws Rs.4000. So, the investment of B for remaining 14 months is Rs.4000 only.   A : B   8000*19 : (8000*4) + (4000*14)   152000 : 88000   A:B = 19:11.Answer:19:11
Answer: E
In the set of positive integers from 1 to 60, what is the sum of all the odd multiples of 5?  Select:
A) 180
B) 185
C) 190
D) 160
E) 165

Solution: 1 - 60   5 - 15 - 25 - 35 - 45 are valid multiples of 5. 180dd them    5+15+25+35+45+55= 
 5+15+25+35+45+55 = 180
180   180
Answer: A
Two bus tickets from city A to B and three tickets from city A to C cost Rs. 154 but three tickets from city A to B and two tickets from city A to C cost Rs. 146. What are the fares for cities B and C from A ?
Choose the correct choice from the following choices:
A) s. 4, Rs. 23
B) s. 13, Rs. 17
C) s. 15, Rs. 14
D) s. 17, Rs. 13
E) s. 26, Rs. 34

Solution: If fares for cities B and C from A are x and y respectively, then   2x+3y=154 or 6x+9y= 462   3x+2y =146 or 6x+4y= 292   subtracting   5y = 170   y= Rs 34   Hence E. Rs. 26, Rs. 34   ANSWs. 26, Rs. 34R:s. 26, Rs. 34
Answer: E
If the difference between the length and breadth of a rectangle is 23 m and its perimeter is 206 m, what is its area? Choose the correct choice from the following options:
A) 2520
B) 2510
C) 2525
D) 2025
E) 2020

Solution: l-b=23...(1)   perimeter = 206   2(l=b)= 206   l+b = 103...(2)   (1)+(2)   2l=23+103= 
23+103 = 126
126   l=126/2= 
126/2 = 63
63 metre   Substituting the value of l in (1), we get   63-b=23   b=63-23= 
63-23 = 40
40 metre   area=lb=63Ã—40 =2520 m2   2520NSWER:2520
Answer: A
If Yury has been writing programming code for 11 hours at a rate of 5 lines of code per 20 seconds, how many lines of code has he written?  Choose the correct option:
A) 126(10^2)
B) 126(10^3)
C) 12.6(10^5)
D) 1.26(10^7)
E) 99(10^2)

Solution: 5 LIN99(10^2)S IN 20 S99(10^2)CONDS   SO FOR 1 MINUT99(10^2) ( 5 X 3 = 15 LIN99(10^2)S )   I HOUR = 60 MINUT99(10^2)S   15 X 60 = 900 LIN99(10^2)S IN AN HOUR   11 HOURS = 900 X 11 = 99(10^2)   ANSW99(10^2)R 99(10^2)
Answer: E