MU-NLPC/Calc-aqua_rat huggingface dataset:
A sock drawer contains seven socks, each one a different solid color. The colors of the socks are black,red, orange, yellow, green, blue, indigo, and violet. A person reaches into the drawer, pulls out two socks, and puts a single sock on each foot. If each sock can fit either the left or the right foot, and if it matters whether a particular sock is on the left or the right foot, how many different sock fashion combinations could the person make from the eight socks? Choose the correct option:
A) 12
B) 15
C) 21
D) 36
E) 56

Solution: It's a question of permutation since order matters here ....   It can be deduced to-   8P2 = 8!/6! = 8*7= 
8*7 = 56
56 .........Answer is - 56
Answer: E
Aman started a business investing Rs. 70,000. Rakhi joined him after six months with an amount of Rs. 1,05,000 and Sagar joined them with Rs. 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Aman, Rakhi and Sagar respectively, 3 years after Aman started the business?
Options: A) 2:35:16 B) 2:15:16 C) 2:15:77 D) 2:15:98 E) 2:15:23

Solution: Aman : Rakhi : Sagar = (70000 * 36) : (105000 * 30) : (140000 * 24)   = 12:15:16   Answer: 2:15:16
Answer: B
If a man can cover 16 metres in one second, how many kilometres can he cover in 3 hours 45 minutes?  Choose the correct answer:
A) 180km  B) 190km  C) 200km  D) 210km  E) 216km

Solution: 16 m/s = 16 * 18/5 kmph   3 hours 45 minutes = 3 3/4 hours = 15/4 hours   Distance = speed * time = 16 * 18/5 * 15/4= 
16 * 18/5 * 15/4 = 216
216 km.   Answer:216km
Answer: E
Rs.590 is divided amongst A, B, C so that 5 times A's share, six times B's share and eight times C's share are all equal. Find C's share?	Choose the correct choice:
A) Rs.157
B) Rs.150
C) Rs.176
D) Rs.165
E) Rs.156

Solution: A+Rs.150+C = 590   5A = 6Rs.150 = 8C = x   A:Rs.150:C = 1/5:1/6:1/8   = 24:20:15   15/59 * 590 = Rs.150   Answer:Rs.150
Answer: B
The remainder when E=1+3+3^2+3^3+..........+3^200 is divided 13.	Choose the correct answer.
A) 12  B) 7  C) 0  D) 5  E) 3

Solution: E=1+3+3^2+3^3+..................+3^200   Is a Geometric progression having common ratio as '3' and number of terms as '201'.   Since Sum to n terms in GP = a(r^n-1)/(r-1)   where a=First term and r =common ration   Hence,   1*(3^201 -1 )/(3-1)   Rem of (3^201-1)/2 divided by 13   3^201 -1 /26   WKT, 3^3 = 27 = 26+1   {(26+1)^67 - 1}/26   {1-1}/26   =>0.0
Answer: C
Cara leaves her home and walks toward Don's house. Two hours later, Don leaves his home and walks toward Cara's house. The distance between their homes is 45 kilometers, Cara's walking speed is 6 km/h, and Don's walking speed is 5 km/h. How many kilometers will Cara walk before she meets Don?  Choose the correct choice from the following answers
A) 26	B) 27	C) 28	D) 29	E) 30

Solution: Cara walks 12 km in the first two hours so there are 33 km remaining.   When Don starts walking, they complete a total of 11 km per hour.   They will meet three hours after Don starts walking.   Since Cara walks for 5 hours, she walks 30 km.   The answer is 30.
Answer: E
If a, b and c are even integers, which of the following could be the value of a^2 + b^2 + c^2?  Choose the most appropriate option.
A) a)36  B) b)38  C) c)42  D) d)46  E) e)50

Solution: a, b and c are even integers which means that, supposing that x, y and z are integers, then a=2x, b=2y and c=2z   Therefore we have: a^2+b^2+c^2=2^2*x^2+2^2*y+2^2*z=4x^2+4y^2+4z^2=4(x^2+y^2+z^2).   Which means that the total a^2+b^2+c^2 must be divisible by 4.   The only choice which is divisible by 4 is: a)36)   36=4^2+4^2+2^2   a)36nswer: a)36.
Answer: A
If 6000209× 6111209× K^20 is divisible by 3, which of the following could be the value of K? Options.
A) 6000209 B) 6111209 C) 6123309 D) 6111109 E) 6111309

Solution: The first two terms are not divisible by 3, so we need the third term to be divisible by 3. The only way that (k^2) is going to be a multiple of 3 is if k is a multiple of 3. Therefore, we need the single answer that is a multiple of 3.   Answer =(6111309)
Answer: E
A boy has nine trousers and 12 shirts. In how many different ways can he select a trouser and a shirt?	Pick one.
A) 189  B) 829  C) 108  D) 829  E) 823

Solution: The boy can select one trouser in nine ways.   The boy can select one shirt in 12 ways.   The number of ways in which he can select one trouser and one shirt is   9 * 12= 
  9 * 12 = 108
108 ways.   Answer:829
Answer: D
A customer pays 60 dollars for a coffee maker after a discount of 20 dollars
What is the original price of the coffe maker? Choose the correct choice:  A) A)$50  B) B)$60  C) C)$70  D) D)$80  E) E)$90

Solution: Let x be the original price.   x - 20 = 60   x - 20 + 20 = 60 + 20   x + 0 = 80   x = 80   correct answer is $80)$80
Answer: D
In a shop apple, orange, mango and pomegranate are sold. Average price of them is Rs.100 per kg. Apple, orange, mango are sold for Rs.100, Rs.90, Rs.80 per kg respectively. Therefore what is price of pomegranate? Choose the correct option:
A) Rs. 100 B) Rs. 90 C) Rs. 130 D) Rs. 120 E) Rs. 110

Solution: EXPLANATION   Total price for apple, orange & mango = Rs. (100 + 90 + 80) = Rs. 270.   Pomegranate price = Rs. [ (100 x 4) – 270 ]   = Rs. (400 – 270)   = Rs. 130.   Answer Rs. 130
Answer: C
If a 3-number code is formed of the integers from 1 to 15 inclusively, and each of the numbers in the code is different, how many possible codes are there?
Answers.
A) 2400
B) 2510
C) 2620
D) 2730
E) 2840

Solution: 15*14*13= 
15*14*13 = 2_730
2730   The answer is 2730.
Answer: D
If the compound interest on a certain sum of money for 6 years at 10% per annum be Rs. 993, what would be the simple interest?  Choose the correct answer
A) Rs. 880  B) Rs. 890  C) Rs. 1800  D) Rs. 900  E) None

Solution: Let P = Principal   A - Amount   We have a = P(1 + R/100)3 and Rs. 1800I = A - P   ATQ 993 = P(1 + R/100)3 - P   ? P = 3000/-   Now SI @ 10% on 3000/- for 6 yrs = (3000 x 10 x 6)/100   = 1800/-   Answer: Rs. 1800.
Answer: C
Which of the following is a possible length for side AB of triangle ABC if AC = 4 and BC = 10?
I. 6
II. 9 √3
III. 11.5
Choose the correct choice from the following:
A) I only
B) II only
C) III only
D) II and III
E) I, II, and III

Solution: (10-4) < AB < (10+4)   The answer is III only.
Answer: C
Two dice are rolled together. What is the probability of getting two numbers whose product is even?	Choose the correct choice from the following choices
A) 2 B) 3/4 C) 1/4 D) 7/4 E) 9/4

Solution: Total number of outcomes possible=36   probability of getting two numbers whose product is even=27   P(E) =27/36=3/4   ANSWER:3/4
Answer: B
John went to a shop and bought things worth Rs. 25, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?	Choices.
A) 17  B) 18  C) 19.7  D) 21  E) 27

Solution: Total cost of the items he purchased = Rs.25   Given that out of this Rs.25, 30 Paise is given as tax   => Total tax incurred = 30 Paise = Rs.30/100   Let the cost of the tax free items = x   Given that tax rate = 6%   ∴ (25−30/100−x)6/100 = 30/100   ⇒ 6(25 −0.3 −x) = 30   ⇒ (25 − 0.3 − x) = 5   ⇒ x = 25 − 0.3 − 5 = 19.7   19.7)
Answer: C
Simple interest on a certain sum is 22.5 over 10 of the sum. Find the rate per cent and time, if both are equal.	Choose the correct answer
A) 8% and 8 years	B) 15% and 15 years	C) 10% and 10 years	D) 12 % and 12 years	E) None of these

Solution: 22.5â„10 P = PÃ—RÃ—R/100   â‡’ R2 = 2250â„10 â‡’ 225 => R = 15%   Also, time = 15 years   Answer 15% and 15 years
Answer: B
What is the square root of 83,521?  Options.
A) 476	B) 489	C) 289	D) 511	E) 311

Solution: 1) Checking the last digits in the answer options A, C, E are out since last digit of the square is known to be 1.   2) C = 489^2 and E = 511^2   C = (300-11)^2 and E = (300 + 11)^2   Since we need the answer less than 90000 => E is out.   Thus we have 289 as the ans.
Answer: C
If (A+B) = 4, (B+C) = 5 and (C+D) = 3, what is the value of (A+D)? Answers:
A) 16.	B) 8.	C) 7.	D) 2.	E) -2.

Solution: Given A+B = 4   B+C = 5   C+D = 3   (A+B)-(B+C)+(C+D)=(A+D)   =>4 - 5+3= 
4 - 5+3 = 2
2.   Option 2....
Answer: D
Look at this series: 7, 10, 8, 11, 9, 12, 10, 13, ... What number should come next?	Select.
A) 10	B) 11	C) 12	D) 13	E) 14

Solution: This is a simple alternating addition and subtraction series. In the first pattern, 3 is added; in the second, 2 is subtracted.   The answer is 11.
Answer: B
Two pipes A and B can fill a tank in 20 and 30 minutes respectively. If both the pipes are used together, then how long it will take to fill the tank ? Choose the correct choice: A) 10 mins B) 12 mins C) 15 mins D) 20 mins E) 30 mins

Solution: Explanation:   In this type of questions we first get the filling in 1 minute for both pipes then we will add them to get the result, as   Part filled by A in 1 min = 1/20   Part filled by B in 1 min = 1/30   Part filled by (A+B) in 1 min = 1/20 + 1/30   = 1/12   So both pipes can fill the tank in 12 mins.   Answer: Option 12 mins
Answer: B
In a certain sequence of numbers, a1, a2, a3, ..., an, the average (arithmetic mean) of the first m consecutive terms starting with a1 is m, for any positive integer m. If a1=1, what is a15?
Choose the correct choice from the following answers.
A) 100 B) 55 C) 29 D) 19 E) 1

Solution: As stated above, (a1+a2+a3......+a15)/15=15   therefore a1+a2+a3.......a15=225 (1)   using the same logic, we got a1+a2+a3..........+a14=196 (2)   (2)-(1) we got a15=29   29
Answer: C
The bankers discount of a certain sum of money is Rs. 144 and the true discount on the same sum for the same time is Rs. 120. The sum due is:
Choose one
A) 715 B) 716 C) 718 D) 720 E) 722

Solution: Sum = (B.720*T.720)/(B.720-T.720)   (144*120)/144-120;   720   ANSWER: 720
Answer: D
If the length is increased by 25%, by what percent the width of a rectangle should be decreased so as to keep the area same. Choose the correct answer.
A) 25%
B) 20%
C) 30%
D) 10%
E) 15%

Solution: SOLUTION :   Let the original length be l and the width be b   Therefore, the area = l*b   Now, as the length is increased by 25%, the new length is (1.25*l) and let the new width be x.   As the area is same, 1.25*l*x = l*b   x = b/1.25 = 0.8b   Therefore, the width is to be decreased by 20%.   ANSWER IS 20%
Answer: B
A man can row 5 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. How far is the place? Select the correct option:
A) 2.25  B) 2.35  C) 2.45  D) 2.55  E) 2.65

Solution: M = 5   S = 1.2   DS = 5 + 1.2= 
5 + 1.2 = 6.2
6.2   US= 5 - 1.2= 
5 - 1.2 = 3.8
3.8   x/6.2 + x/3.8= 1   x = 2.35.Answer: 2.35
Answer: B
38 69 22 43 31 47 13 82
Which of the following numbers is greater than three fourths of the numbers but less than one fourth of the numbers in the list above? Options:
A) 56 B) 69 C) 70 D) 71 E) 73

Solution: Arrange the numbers in ascending order:   13, 22, 31, 38, 43, 47, 69, 82 (Just cross check the count to ensure that you didn't miss anything)   How many numbers do we see?   8, alright.   What's (1/4)8?   2.   What's (3/4)8?   6.   We're asked to find a number that are greater than 6 numbers in the list AND smaller than the remaining two.   13, 22, 31, 38, 43, 47, 69, 82   13, 22, 31, 38, 43, 47: Find a number greater than any of these numbers.   69, 82: Find a number smaller than any of these numbers.   Only 56 fits the description.   56ns:56
Answer: A
Arun and Tarun can do a work in 10 days.After 4 days tarun went to his village.How many days are required to complete the remaining work by Arun alone.Arun can do the work alone in 70 days. Choose one:	A) 16 days.	B) 17 days.	C) 18 days.	D) 19 days.	E) 42 days.

Solution: They together completed 4/10 work in 4 days.   balance 6/10 work will be completed by Arun alone in   70*6/10= 
  70*6/10 = 42
42 days.   ANSW42 days.R:42 days.
Answer: E
A car gets 40 kilometers per gallon of gasoline. How many gallons of gasoline would the car need to travel 180 kilometers?	Select
A) 8.5 gallons	B) 7.5 gallons	C) 6.5 gallons	D) 5.5 gallons	E) 4.5 gallons

Solution: Each 40 kilometers, 1 gallon is needed. We need to know how many 40 kilometers are there in 180 kilometers?   180 / 40= 
180 / 40 = 9/2 = around 4.5
4.5 * 1= 
4.5 * 1 = 4.5
4.5 gallons correct answer 4.5 gallons
Answer: E
A lemonade stand sold only small and large cups of lemonade on Tuesday. 2/5 of the cups sold were small and the rest were large. If the large cups were sold for 7/6 as much as the small cups, what fraction of Tuesday's total revenue was from the sale of large cups? Pick.
A) 7/11  B) 7/15  C) 10/21  D) 17/35  E) 1/2

Solution: Let the total # of cups be 10.   # of small cups sold 2/5*10= 
2/5*10 = 4
4;   # of large cups sold  10-4= 
 10-4 = 6
6;   Let the price of small cup be $6, then the price of larges cup would be 7/6*6= 
7/6*6 = 7
$7;   Revenue from small cups: 4*$6=$24;   Revenue from large cups cups: 6*$7  4* 6= 
  4* 6 = 24
$24;   Revenue from large cups cups: 6*$7=$42;   Fraction of total revenue from large cups: 42/(42+24) 6* 7= 
 6* 7 = 42
$42;   Fraction of total revenue from large cups: 42/(42+24)=7/11.   7/11   7/11nswer: 7/11.
Answer: A
If Scott has earned y dollars by working 7 days a week at a constant daily rate for w weeks, which of the following represents his daily wage?	Choose the correct choice from the following answers.
A) 3yw B) 3w/y C) w/(7y) D) yw/7 E) y/(7w)

Solution: Scott total earning = y   No days he worked = 7   Rate = w   Daily wage = total / (Rate * days)   y/(7w) is correct answer...
Answer: E
A sum of money place at compound interest doubles itself in 4 years. In how many years will it amount to eight times itself?	Choose the most appropriate option:
A) 22	B) 18	C) 12	D) 88	E) 29

Solution: 100 ---- 200 ---- 4   400 ---- 4   800 ---- 4   ------   12 years   Answer: 12
Answer: C
7128+1252=1202+X
Choose the most appropriate option
A) 7158 B) 7149 C) 7145 D) 7128 E) 7178

Solution: X=1278+1252-1202   X=7128+50= 
7128+50 = 7_178
7178   CORR7178CT ANSW7178R : 7178
Answer: E
A room of 5m 44cm long and 3m 74cm broad is to be paved with squre tiles. Find the least number of squre tiles required to cover the floor? Pick one:
A) 178
B) 128
C) 127
D) 176
E) 171

Solution: area of the room = 544 * 374 sq cm   size of largest square tile = H.C.F of 544cm and 374cm= 34cm   area of 1 tile = 34*34 sq cm   no. of tiles required = (544*374) / (34 * 34)= 
(544*374) / (34 * 34) = 176
176   Answer: 176
Answer: D
The cost price of 30 articles is the same as the selling price of x articles. If the profit is 25%, what is x?	Choose the correct choice from the following options:
A) 18	B) 20	C) 22	D) 24	E) 26

Solution: Let the cost price = y   The cost price of 30 articles = 30y   The selling price of x articles = 1.25y*x   1.25y*x = 30y   x = 30 / 1.25= 
30 / 1.25 = 24
24   The answer is 24.
Answer: D
By selling 66 bags, a shopkeeper gains the price of 33 bags. His gain per cent is  Choose the correct choice from the following choices
A) 91%  B) 100%  C) 95%  D) 98%  E) 93%

Solution: Suppose S.P of 66 bags = Rs 66   Therefore, Gain = Rs 33 => C.P = Rs 33   Gain % = 33/33 x 100 = 100%   Gain = 100%   ANSWER:100%
Answer: B
A trader cheats both his supplier and customer by using faulty weights. When he buys from the supplier, he takes 30% more than the indicated weight. When he sells to his customer, he gives the customer a weight such that 40% of that is added to the weight, the weight claimed by the trader is obtained. If he charges the cost price of the weight that he claims, find his profit percentage.  Pick one:
A) 28%
B) 82%
C) 24.33%
D) 29.109%
E) 78%

Solution: Anyways, one can infer that he 'steals' 30% from suppliers and then charges 40% extra to customers   So basically 1.3 * 1.4= 
1.3 * 1.4 = 1.82
1.82   Given that 1 is start point, we get 21% more   Hence answer is 82%
Answer: B
Two pipes A and B can fill a cistern in 20 and 30 minutes respectively, and a third pipe C can empty it in 40 minutes. How long will it take to fill the cistern if all the three are opened at the same time?  Choose the correct choice.
A) 17 1/5 B) 17 1/8 C) 17 1/7 D) 17 1/1 E) 17 1/2

Solution: 1/20 + 1/30 - 1/40 = 7/120   120/7 = 17 1/7   Answer:17 1/7
Answer: C
If two dice are thrown together, the probability of getting an even number on one die and an odd number on the other is? Options.
A) 1/5 B) 1/2 C) 1/9 D) 1/3 E) 1/4

Solution: The number of exhaustive outcomes is 36.   Let E be the event of getting an even number on one die and an odd number on the other. Let the event of getting either both even or both odd then = 18/36 = 1/2   P(E) = 1 - 1/2 = 1/2.   Answer:1/2
Answer: B
In a class, the average age of 35 boys is 15 years and the average of 25 girls is 10 years. what is the average age of the whole class? Choose the correct choice from the following.
A) 12 Years	B) 12.3 Years	C) 12.9 Years	D) 13 Years	E) 15 Years

Solution: Total age of 60 students   (35X 15+25 X 10) = 775   Average = 775/60 = 12.9 Years   12.9 Years
Answer: C
If w, z and r are positive integers greater than 1, and p and q are factors of r, which of the following must be the factor of r^(wz)?
I. w+z
II. z^w
III. w^2 * z^2  Select.
A) I only  B) II only  C) III only  D) I and II  E) II and III

Solution: given that p and q are factors of r.   so we can picture it this way r=w*z*n (n-some another factor of r)   so, r^wz= (w*z*n)^wz   I. w+z .since the question is MUST BE TRUE, we eleminate this option   II. (w*z*n)^wz / z^w= integer YII and IIIS!   III.(w*z*n)^wz/ w^2 * z^2 YII and IIIs, since we are said that integer w>1 and integer z>1
Answer: E
Simran started a software business by investing Rs.50,000. After six months, Nanda joined her with a capital of Rs.80,000. After 3 years , they earned a profit of Rs.24,500. What was Simran's share in the profit? Choose the correct choice from the following choices
A) Rs.9423  B) Rs.10,250  C) Rs.10,500  D) Rs.14,000  E) None

Solution: Solution   Simran : Nanda	=(5000x36):(80000x30)   = 3 : 4.   Simran's share	= Rs.(24500x3/7)   = Rs.10,500.   Answer Rs.10,500
Answer: C
Danny drove his old car 100 kilometers, from his home to a friend. To prevent the engine from overheating, he stopped his car for 9 minutes every time he completed 40 kilometers of continuous driving. When the car was moving, Danny drove it at an average speed of 60 kilometers per hour. What was Danny's average speed on that trip?	Choose the most appropriate option
A) 37.5 kilometers per hour B) 48 kilometers per hour C) 50.8 kilometers per hour D) 75 kilometers per hour E) 100 kilometers per hour

Solution: Time taken to reach first 40 km is 40/60 = 2/3 hr   Time taken to reach next 40 km is 40/60 = 2/3 hr   Time taken to reach next 20 km is 20/60 = 1/3 hr   Danny stopped twice on his way at 40 km from starting point and at 80km from the starting point...   Each stop was of 9 min , so two 9 min break = 2*3/20 => 3/10 hr   Total time taken to reach 100 km is (2/3 + 2/3 + 1/3+3/10 ) = 59/30 hrs   So, Average speed is 100/(59/30) = 50.8km/hour   Answer will be (50.8 kilometers per hour)
Answer: C
If 12 men and 16 boys can do a piece of work in 5 days and 13 men together will 24 boys can do it in 4 days. Compare the daily work done by a man with that of a boy.  Choose the correct choice from the following options:
A) 2:7 B) 2:1 C) 2:4 D) 2:2 E) 2:8

Solution: 12M + 162:1 ----- 5 days   13M + 242:1 ------- 4 days   60M + 802:1 = 52M + 962:1   8M = 162:1 => 1M = 22:1   M: 2:1 = 2:1   Answer:2:1
Answer: B
The number 95 can be written as the sum of the squares of 4 different positive integers in two ways. Of the following, which can be the sum of these 4 integers
Choose the most appropriate option:
A) 9
B) 10
C) 15
D) 18
E) 17

Solution: The only possible sum for 4 different squares of an integer with total sum number is 95 are :   49 + 36 + 9 + 1= 
49 + 36 + 9 + 1 = 95
95 which are the square from numbers : 7, 6, 3, 1 (total sum number is 17)   or     81 + 9 + 4 + 1= 
  81 + 9 + 4 + 1 = 95
95 which are the square from numbers : 9, 3, 2, 1 (total sum number is 15)   hence the answer is (17)
Answer: E
Three business people who wish to invest in a new company. Each person is willing to pay one third of the total investment. . After careful calculation, they realize that each of them would pay $ 7500 less if they could find two more equal investors. How much is the total investment in the new business.
Pick.
A) a)	$ 64,000
B) b)	$ 56,250
C) c)	$ 21,000
D) d)	$ 5,400
E) e)	$3,600

Solution: Initially each invest in x. Hence total investment is 3x.   Total investment is also 5(x-7500).   3x = 5(x-7500)   x= 5*7500/2= 
5*7500/2 = 18_750
18750   3x= 56250 and the answer is b)	$ 56,250.
Answer: B
A certain sum becomes Rs. 20720 in four years and 24080 in six years at simple interest. Find sum and rate of interest?
Choices:
A) Rs. 12000; 12% p.a. B) Rs. 22000; 12% p.a. C) Rs. 12000; 22% p.a. D) Rs. 12000; 14% p.a. E) Rs. 12000; 16% p.a.

Solution: Let the interest for one year be x.   As amount = Principal + Interest, we have   P + 4x = 20720 --- (1) ; P + 6x = 24080 --- (2)   Solving the equations (1) and (2), we can get   P = Rs. 14000 and x = Rs. 1680   Interest for one year on Rs. 14000 is Rs. 1680   So, R = (100 * 1680)/(14000 * 1)= 
(100 * 1680)/(14000 * 1) = 12
12% p.a.   Rs. 12000; 12% p.a.NSWER:Rs. 12000; 12% p.a.
Answer: A
Oil cans x and y are right circular cylinders and the height and radius of y are each 5 times those of x. If the oil in can x filled to capacity sells for $1, how much does the oil in y sell for if y is only 1/5th filled?	Select:
A) $25
B) $26
C) $27
D) $28
E) $30

Solution: formula for vol of a cyl is PI*r^2*h   so Vy = 125*Vy   y when half filled will cost 25 times x so ans is $25
Answer: A
If a and b are integers and (2^a)(3^b) is a factor of 300^40, what is the largest possible value of ab?  Select.
A) a	B) 5a	C) 20a	D) 40a	E) 80a

Solution: (2^a)(3^b) is a factor of 300^40   We need to find the largest possible value of ab.   We know that 300 = 2^2*5^2*3   Therefore 300^40 will have only one power of 3 in it.   Hence in (2^a)(3^b), b has to be 1   Therefore value of ab = a   Correct Option: a
Answer: A
A rectangular grass field is 75 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.3 per sq m?
Pick:
A) 675, Rs.2025  B) 575, Rs.1350  C) 1350, Rs.675  D) 1450, Rs.775  E) 1550, Rs.875

Solution: 675, Rs.2025rea = (l + b +2d) 2d   = (75 + 55 +2.5 * 2) 2*2.5 => 675   675 * 3 = Rs.2025   675, Rs.2025NSWER:675, Rs.2025
Answer: A
The triplicate ratio of 1:2 is?  Pick one:
A) 1:0	B) 1:8	C) 1:7	D) 1:2	E) 1:1

Solution: 13: 23 = 1:8   Answer: 1:8
Answer: B
What two-digit number is less than the sum of the square of its digits by 11 and exceeds their doubled product by 4?  Pick one:
A) 95	B) 99	C) 26	D) 73	E) None of the Above

Solution: Let the digits be x and y. The number would be 10x + y.   We are given that 2xy + 4 = 10x +y = x^2 y^2 -11   Thus 2xy +4 = x^2 + y^2 - 11   x^2 + y^2 -2xy = 16   (x-y)^2 = 16   (x-y) = 4 or -4   Substituting the values of (x-y) in the equation 2xy +5 = 10x + y   x comes out to be 1 or 9... thus the two numbers can be 26 or 98   Thus the answer is 26
Answer: C