MU-NLPC/Calc-aqua_rat huggingface dataset:
Mike took 5 mock tests before appearing for the GMAT. In each mock test he scored 9 points more than the previous mock test. If he scored 760 on the GMAT and his average score for the mocks and the GMAT was 726.67, what was the difference in the score of his last mock and his GMAT score? Choose the correct choice from the following answers
A) 22	B) 30	C) 40	D) 50	E) 60

Solution: One way to do this would be weighted average method..   1) let the average of 5 mocks be x...   so take it as a mix of5 quantitites of xand1 quantity of 760resulting in an average of 726.67...   By alligation/weighted average..   the difference in 760 and 726.67 is 5/6 of difference of 760 and x..   760-726.67 = 5/6 * (760-x)   760-x= 33.33*6/5=40...   so x = 720..   the last of mock test will be 720+9+9=738...   so ans = 760-738= 
760-738 = 22
22   22
Answer: A
IF x is an integer greater than 6, then all the following must be divisible by 3 EXCEPT	Choose the correct choice from the following answers:
A) 3x^3  B) x(x+1)(x+2)  C) 9x  D) 9x^2  E) x+3

Solution: *any number multiplied by 3, will be divided by 3   for option x+3 if we put value x=7, 7+3=10 is not divisible by 3   Answer : x+3
Answer: E
A man can row upstream at 25 kmph and downstream at 35 kmph, and then find the speed of the man in still water?
Choose the correct choice from the following options
A) 32 kmph B) 34 kmph C) 30 kmph D) 45 kmph E) 65 kmph

Solution: US = 25   DS = 35   M = (35 + 25)/2= 
(35 + 25)/2 = 30
30   Answer:30 kmph
Answer: C
If 15!/3^x is an integer, what is the greatest possible value of x?	Choose the most appropriate option.
A) 3  B) 4  C) 5  D) 6  E) 7

Solution: 15 - 5*3   12 - 4*3   9 - 3*3   6 - 2*3   3 - 1*3   Hence max of 3^6 is allowed. IMO 6.
Answer: D
A fence consists of m lengths of fence that are each n feet long. A fence post separates each length of fence by its width of x feet. What is the total length R of the fence including the fence posts on each end?
Choose the correct option:  A) mn  B) m(n + x)  C) R=m(n + x) + x  D) m(n + x) + 2x  E) 2mn

Solution: Notice that since a fence post separates each length of fence, then there will be m+1 posts, for example if there are m=2 fences, then there will be 3 posts: PFPFP. Thus the total length of the posts is (m+1)x.   The total length of the fence is mn, therefore the total length of the fence including the fence posts on each end is (m+1)x+mn=mx+x+mn=m(n+x)+x.   Answer: R=m(n + x) + x.
Answer: C
A 20% stock yielding 8% is quoted at? Choose the most appropriate option:
A) 165 B) 170 C) 250 D) 180 E) 185

Solution: Assume that face value = Rs.100 as it is not given   To earn Rs.8, money invested = Rs.100   To earn Rs.20, money invested = 100×20/8 = Rs.250   ie, market value of the stock = Rs.250   Answer is 250.
Answer: C
Jim bought edging to go around a circular garden with a radius of 6 feet. Later he decided to
double the diameter of the garden. How many more feet of edging must he buy? Pick:
A) 28.84' additional edging
B) 48.84' additional edging
C) 38.84' additional edging
D) 18.84' additional edging
E) 37.68' additional edging

Solution: circumference of small garden = 2 x 3.14 x 6 = 37.68'   double of the circumference of small garden = 2 x 37.68' = 75.36'   More feet to be buy =75.36 - 37.68= 
75.36 - 37.68 = 37.68
37.68   Answer : 37.68' additional edging
Answer: E
Find the amount of rs.7500 at compound interest at 4%per annum for 2 years?  Choose the correct choice.
A) 8112
B) 9110
C) 7160
D) 6210
E) 8021

Solution: Compound interest=[7500*(1+(4/100))^2]   =7500*((104/100)^2)   =(7500*104*104)/(100*100)   =Rs.8112   Option 8112
Answer: A
10^196 - 10^9 = Which of the following best approximates the value of the expression above?  Choose the correct choice from the following answers:	A) 10^186	B) 10^196	C) 10^100	D) 10^150	E) 10^170

Solution: 10^196 - 10^9 =   Which of the following best approximates the value of the expression above?   Yes, answer 10^196 is correct. Note that we need approximate value of the given expression and as 10^(196) is much larger number than 10^(9) then 10^(9) is pretty much negligible in this case: 10^(196)-10^(9)=~10^(196).   Answer : 10^196
Answer: B
After decreasing 20% in the price of an article costs Rs.600. Find the actual cost of an article?	Choose the correct choice from the following answers
A) 775
B) 620
C) 53
D) 530
E) 220

Solution: CP* (80/100) = 600   CP= 7.75 * 100 => CP = 775   775nswer: 775
Answer: A
The cost price of 25 books is the same as the selling price of ’X’ books. If the profit is 25%, then the value of X is ?	Choose the correct choice from the following answers
A) 12.8  B) 18  C) 16  D) 15  E) 14

Solution: let S.P. of X books = Rs 100 = C.P. of 25 books   Therefore, C.P. of one book = Rs 6.25   Profit = 25 %   Therefore, S.P of one book = 7.8   S.P of X articles = 7.8 X   7.8 X = 100 => X = 12.8   12.8NSWER:12.8
Answer: A
total dinning bill of 3 people was $139.00 and 10% tip divided the bill evenly ?what is the bill amount each person shared .  Choose the correct choice from the following answers:
A) 21.84 B) 50.96 C) 53.84 D) 24.84 E) 50.26

Solution: dinner bill of 3 person = 139 + 10% tip   so,   10% of 139 = (139*10)/100= 
(139*10)/100 = 139/10 = around 13.9
13.9   So, the actual total amount= 139+13.9= 
139+13.9 = 152.9
$ 152.9   so per head bill= 152.9/3 = $ 50.96   ANSWER:50.96
Answer: B
The cash difference between the selling prices of an article at a profit of 2% and 6% is Rs. 3. The ratio of the two selling prices is?	Choices.
A) 52:56
B) 52:53
C) 52:50
D) 22:56
E) 51:53

Solution: Let C.P. of the article be Rs. x.   Then, required ratio = 102% of x / 106% of x   = 102/106 = 51/53 = 51:53   Answer: 51:53
Answer: E
Which of the following Equation is NOT equivalent to 25x^2 = y^2 - 16?Which of the following Equation is NOT equivalent to 25x^2 = y^2 - 16?
Choices:
A) 25x^2 + 4 = y^2
B) 75x^2 = 3y^2 - 12
C) 25x^2 = (y + 2)(y - 2)
D) 5x = y - 4
E) x^2 = (y^2 - 4)/25

Solution: 1) Take the original equation and try to manipulate it so that it becomes 4 of the 5 answers   2) Take each answer choice and see if you can manipulate it to make it into the original equation.   With Answer D, we have...   5X = Y - 2   If we square both sides, we end up with....   (5X)^2 = (Y-4)^2   (5X)(5X) = (Y-4)(Y-4)   25X^2 = Y^2 - 8Y + 16   This is NOT a match for the original equation, so it's the answer that is NOT equivalent. 5x = y - 4
Answer: D
A vessel of capacity 45 litres is fully filled with pure milk. Nine litres of milk is removed from the vessel and replaced with water. Nine litres of the solution thus formed is removed and replaced with water. Find the quantity of pure milk in the final milk solution? Choose the correct choice from the following options:
A) 28.8
B) 72.9
C) 38.3
D) 78.3
E) 79.3

Solution: Explanation:   Let the initial quantity of milk in vessel be T litres.   Let us say y litres of the mixture is taken out and replaced by water for n times, alternatively.   Quantity of milk finally in the vessel is then given by [(T - y)/T]^n * T   For the given problem, T = 45, y = 9 and n = 2.   Hence, quantity of milk finally in the vessel   = [(45 - 9)/45]^2 (45) = 28.8 litres.   28.8nswer: Option 28.8
Answer: A
Three distinct single digit no A,B,C are in G.P. If abs(x) for real x is the absolute value of x(x if x is positive or zero, and x if x is negative),then the no. of different possible values of abs(A+B-C) is	Choose the most appropriate option.
A) 6
B) 4
C) 3
D) 5
E) 2

Solution: if a=1,r=2 then a=1,b=2,c=4 then abs(a+b-c)=1   if a=1,r=3 then a=1,a=3,a=9 then abs(1+3-9)=5   if a=2,r=2, then a=2,b=4,c=8 then abs(2+4-8)=2   if a=1,r=-2 then a=1,b=-2,c=4 the abs(1-2-4)=5   if a=1,r=-3 then a=1,b=-3,c=9 then abs(1-3-9)=11   if a=2,r=-2 then a=2,b=-4,c=-8 then abs(2-4-8)=10   so total 5 abs() values   ANSWER:5
Answer: D
15 men can complete a piece of work in 25 days. In how many days can 20 men complete that piece of work?
Choose the correct choice from the following options: A) 55 days B) 18.75 days C) 20 days D) 88 days E) 44 days

Solution: 15 * 25 = 20 * x => x   = 18.75 days   Answer: 18.75 days
Answer: B
What is the sum of the digits of integer k, if k = (10^45- 46) Select.
A) 356	B) 366	C) 363	D) 396	E) 408

Solution: There are 46 digits in 10^45   When we subtract 46 from it, there will be 45 digits left.   10^45 can be written as 9999999....(45 times) + 1   So,   10^45 - 46 = 9999999....(45 times) + 1 - 46 = 9999999....(45 times) -45   Consider the last 2 digits,   99-45= 
99-45 = 54
54   The last 2 digits will be 54.   And our number would be 99999......99954 with 2 less 9s after subtraction.   Number of 9s left are 43 and the last two digits are 54   The sum of the digits will be     (43*9) + 5 + 4= 
  (43*9) + 5 + 4 = 396
396   Answer:- 396
Answer: D
A grocery store bought some mangoes at a rate of 5 for a dollar. They were separated into two stacks, one of which was sold at a rate of 5 for a dollar and the other at a rate of 5 for a dollar. What was the ratio of the number of mangoes in the two stacks if the store broke even after having sold all of its mangoes?	Choose the correct answer:  A) 1:1  B) 1:5  C) 2:3  D) 1:2  E) 2:5

Solution: The cost price of a mango = 1/5 dollars.   The selling price of a mango from the first stack = 1/3 dollars --> the profit from one mango = 1/5 - 1/5= 
1/5 - 1/5 = 0
0 dollars.   The selling price of a mango from the second stack= 1/5 dollars --> the loss from one mango = 1/5 - 1/5= 
1/5 - 1/5 = 0
0 dollars.   no profit as whole 1:1   1:1nswer: 1:1.
Answer: A
Given
A+B+C=100
60A+40B+C=2000
Find A+B=?  Choose the most appropriate option
A) 76	B) 74	C) 40	D) 44	E) can't determine

Solution: (60A+40B+40=2000)-(A+B+40=100)   59A+39B=1900   So if we take A+B=40 so if A=17 and B=23 then 17+23= 
17+23 = 40
40 and   59*17+39*23= 
  59*17+39*23 = 1_900
1900   it satisfy the condition so correct answer is=40   ANSWER:40
Answer: C
A batsman scored 120 runs which included 3 boundaries and 8 sixes. What percent of his total score did he make by running between the wickets.	Pick one:  A) 40%  B) 50%  C) 60%  D) 70%  E) 80%

Solution: Explanation:   Number of runs made by running = 110 - (3 x 4 + 8 x 6)   = 120 - (60)= 
120 - (60) = 60
60   Now, we need to calculate 60 is what percent of 120.=> 60/120 * 100= 
60/120 * 100 = 50
50 %   Answer: Option 50%
Answer: B
The average of a couple was 18Yrs when they were married 20Yrs ago.The avg age of
the couple and a child, who was born during the interval, is 26Yrs now. How old is the
child now ?
Choose the correct choice from the following:
A) 2 Yrs  B) 4 Yrs  C) 3 Yrs  D) 1 Yrs  E) None of these

Solution: (a+b-20-20)/2=18;   a+b=76;   a+b+c/3=26;   solving both c=2   2 YrsNSWER:2 Yrs
Answer: A
If x and y are positive integers such that x/y=33.375, which of the following could be the remainder when x is divided by y?  Choose the correct choice from the following:	A) 8	B) 21	C) 25	D) 44	E) 47

Solution: The answer is 21 - 21 because 21/0.375 yields an integer (= 56) and none of the other options does   x/y = Integer + Remainder   => x/y = 33 + 0.375   Multiplying both sides by 56,   56(x/y) = 56*33 + 21   ALTERNATIVELY,you may calculate as follows:   x/y = 33.375   => x/y = 33375/1000 = 267/8 = (33*8 + 3)/8   Multiply both sides by 7 to get   x/y = (33*56 + 21)/8 which can be written as 33*56/8 + 21/8   Once we know that we can get 3 as a remainder, we can select the answer choice that is a multiple of 3 (21 in this case)   The answer is therefore choice (21)
Answer: B
An artist wishes to paint a circular region on a square poster that is 3 feet on a side. If the area of the circular region is to be 1/2 the area of the poster, what must be the radius of the circular region in feet?	Choose the most appropriate option: A) 1/pi B) sqrt(2/pi) C) sqrt(4.5/pi) D) 2/sqrt(pi) E) pi/2

Solution: Area of the poster is 3x3 = 9   1/2 the area = 4.5   pi*r^2 = 4.5   r^2 = 4.5/pi   r = sqrt(4.5/pi) answer (sqrt(4.5/pi))
Answer: C
Train A is stopped at a railway station and train B is passing the train A with a speed of 62kph. Train A and B are having lengths of 200m and 185m respectively. How long it will take the train B to pass train A? Answers
A) 14.45
B) 19.82
C) 22.36
D) 28.38
E) 31.91

Solution: Relative speed of train B with respect to train A = 62-0= 
62-0 = 62
62kph=17.22m/s   Distance needs to be covered by train B=200+185= 
200+185 = 385
385m   Time taken by the train B to pass train A= 385/17.22 = 22.36s   Answer: 22.36
Answer: C
A man purchases 8 pens for Rs.9 and sells 9 pens for Rs.8, how much profit or loss does he make?	Answers.
A) 20.88%loss  B) 20.98%loss  C) 20.78%loss  D) 20.38%loss  E) 10.98%loss

Solution: 81 ---- 17   100 ----- ? è 20.98%loss   Answer:20.98%loss
Answer: B
Paul's income is 40% less than Rex's income, Quentin's income is 20% less than Paul's income, and Sam's income is 40% less than Paul's income. If Rex gave 60% of his income to Sam and 40% of his income to Quentin, sam's new income would be what fraction of Quentin's new income?	Choices
A) 11/12
B) 12/11
C) 13/19
D) 12/19
E) 11/19

Solution: MAKE R = 10   P = 0.6R = 6   Q = 0.8P = 4.8   S= 0.6P = 3.6   FOR THAT WE GET S = 9.6   AND Q 8.8   SO 9.6/8.8= 1.2/1.1   Ans:12/11
Answer: B
Out of first 20 natural numbers, one number is selected at random. The probability that it is either an even number or a prime number is -.	Select the correct option:
A) 1/2
B) 16/19
C) 4/5
D) 17/20
E) 3/5

Solution: n(S) = 20   n(Even no) = 10 = n(E)   n(Prime no) = 8 = n(P)   P(EᴜP) = 10/20 + 8/20 - 1/20 = 17/20   ANSWER:17/20
Answer: D
Find the odd man out 17, 39, 171, 347 Choose the correct choice from the following options.
A) 18 B) 18 C) 83 D) 82 E) 39

Solution: 6 x 2+5=17   17 x 2+5=39   39 x 2+5=83   83 x 2+5=171   ANSWER:83
Answer: C
The radius of a semi circle is 6.3 cm then its perimeter is?  Choose the correct answer
A) 32.7
B) 32.4
C) 32.5
D) 32.9
E) 32.2

Solution: 36/7 r = 6.3   =32.4   Answer: 32.4
Answer: B
In a certain game, a large container is filled with red, yellow, green, and blue beads worth, respectively, 7, 5, 3, and 2 points each. A number of beads are then removed from the container. If the product of the point values of the removed beads is 72,030,000, how many red beads were removed?
Choose the correct choice from the following options.
A) 1
B) 2
C) 3
D) 4
E) 5

Solution: 72,030,000   = 2^4 * 5^4 * 7203   = 2^4 * 3 * 5^4 * 2401   = 2^4 * 3 * 5^4 * 7 * 343   = 2^4 * 3 * 5^4 * 7^4   The answer is 4.
Answer: D
A card game called “high-low” divides a deck of 52 playing cards into 2 types, “high” cards and “low” cards. There are an equal number of “high” cards and “low” cards in the deck and “high” cards are worth 2 points, while “low” cards are worth 1 point. If you draw cards one at a time, how many ways can you draw “high” and “low” cards to earn 5 points if you must draw exactly 3 “low” cards?
Choose the correct choice from the following choices.
A) 1  B) 2  C) 3  D) 4  E) 5

Solution: To get a 5, you need one high and three lows (you could have had 2 highs and one low, but the constraint is that you must have three low cards)   HLLL = 4!3! =4   4! is the number of ways you can arrange these four spaces. divide by 3! because you you repeat three low cards   ANS:4
Answer: D
A and B invest in a business in the ratio 3 : 2. If 5% of the total profit goes to charity and A's share is Rs. 855. the total profit is
Pick:
A) Rs. 1425 B) Rs. 1500 C) Rs.1537 D) Rs.1576 E) None

Solution: Solution   Let the total profit be Rs.100   After playing to charity, A's share	= Rs. (95 x 3/5)   If A's share is Rs.57, total profit	= Rs. 100.   If A's share is 855, total profit	= (100/57 x 855)   ‹=›1500   Answer Rs. 1500
Answer: B
In how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together?	Select.
A) 10080  B) 4989600  C) 120960  D) 180960  E) None of these

Solution: The given words contain 8 letter MTHMTCS(AEAT), so 8!.   Then the 4 vowels can be formed differently, 4!.   But there are three words have repeated in the given words. So it should be divided by 2!*2!*2!.   Hence the solution is (8! * 4!) / (2! * 2! * 2!) = 120960   ANSWER:120960
Answer: C
In a Lake, there is a patch of lily pads. Every day, the patch doubles in size. It takes 34 days for the patch to cover the entire lake, how many days would it take the patch to cover half of the lake?	Options
A) 33 B) 2^4*3 C) 24 D) 38 E) 47

Solution: Working backward from the day it's covered:   day 34: fully covered   day 33: half covered   So 33 days   33NSWER:33
Answer: A
Murali travelled from city A to city B at a speed of 4 kmph and from city B to city C at 6 kmph. What is the average speed of Murali from A to C given that the ratio of distances between A to B and B to C is 2 : 3?
A. 48 kmph Select the correct option: A) 33 B) 5 C) 28 D) 7 E) 16

Solution: Let the distances between city A to B and B to C be 2x km and 3x km respectively.   Total time taken to cover from A to C   = (2x)/4 + (3x)/6 = (6x + 6x)/12 = 12x/12 = x Average speed = (2x + 3x)/(x) = 5 kmph.   Answer: 5
Answer: B
There are 134 toys coloured red and white in a box. Two red toys are removed from the lot and now there are twice as many red ones as white ones. How many of red colour toys are there now?
Answers:
A) 76	B) 86	C) 90	D) 88	E) 78

Solution: r+w=134   Two red toys are removed from the lot and now there are twice red ones as white ones   r-2=2w sub 1st one we get   134-w-2=2w   132=3w   w=44   r=88   actually red will be 90   now 88   ANSWER:88
Answer: D
8 and 2 are the first two terms in a geometric sequence. What is the arithmetic difference between the 3rd term and the 4th term? Answers
A) (3) * (1/4)^3 B) (6) * (1/4)^3 C) (6) * (1/8)^3 D) (6) - (1/4)^3 E) (6) / (1/4)^3

Solution: Common ratio = 2/8 =1/4   3rd term = 8*(1/4)^3   4th term = 8*(1/4)^4   Difference = 8 * ((1/4)^3 - (1/4)^4)   = 8 * (1/4)^3 *(1 - (1/4))   = 8 * (1/4)^3 * (3/4)   = (1/4)^3 * (3/4) * 8   = (6) * (1/4)^3   (6) * (1/4)^3
Answer: B
A person crosses a 600 m long street in 5 minutes. What is his speed in km per hour?
Choose the correct choice from the following answers.
A) 3.6 B) 7.2 C) 8.4 D) 10 E) 9

Solution: Speed=(600/5 * 60) m/sec   = 2 m/sec.   Converting m/sec to km/hr   =(2*18/5) km/hr   = 7.2 km/hr.   Answer : 7.2.
Answer: B
Due to 10% decrease in the price of sugar and John can buy 5kg more sugar in Rs100 , then find the CP of sugar?	Answers:
A) Rs. 1(2/9)	B) Rs. 2(2/7)	C) Rs. 2(2/11)	D) Rs. 2(2/13)	E) Rs. 2(1/9)

Solution: Here r = 10 % ,x = 100 and A = 5 kg   Actual price of sugar = 10*100/((100-10 )*5) = Rs. 2(2/9)   Rs. 2(2/7)
Answer: B
A man invests Rs. 3,000 at the rate of 5% per annum. How much more should he invest at the rate of 8%, so that he can earn a total of 6% per annum?
Options
A) Rs. 1200
B) Rs. 1300
C) Rs. 1500
D) Rs. 2000
E) None of these

Solution: Explanation :   Interest on Rs.3000 at 5% per annum = ( 3000 × 5 × 1) / 100 = Rs. 150   Let his additional investment at 8% = x   Interest on Rs.x at 8% per annum = ( x × 8 × 1 ) / 100 = 2x/25.   To earn 6% per annum for the total, interest = (3000 + x) × 6 × 1/100.   => 150 + 2x/25 = (3000 + x) × 6 × 1/100.   => 15000 + 8x = (3000 + x) × 6.   => 15000 + 8x = 18000 + 6x.   => 2x=3000.   => x=1500.   Answer : Rs. 1500
Answer: C
If we have 12 people in a meeting, in how many ways they can sit around a table?	Choose the correct answer
A) 11*10!  B) 9*8!  C) 8*7!  D) 7*6!  E) 6*5!

Solution: If there arenpeople sitting around a table, there are(n-1)!possible arrangements:   Here, n=12   (n-1)!=11!=11*10!   11*10!ns:11*10!
Answer: A
A cistern is normally filled in 8 hours but takes two hours longer to fill because of a leak in its bottom. If the cistern is full, the leak will empty it in?	Choose the correct choice from the following choices.
A) 33 B) 88 C) 40 D) 99 E) 11

Solution: 1/8 - 1/x = 1/10   x = 40   Answer: 40
Answer: C
An arithemetic sequence of numbers begins p, 2p + 2, 4p + 3... What is the 12th member of this sequence? Choose the correct option
A) A)37
B) B)40
C) + 13
D) D)34
E) + 13

Solution: Common difference of an arithmetic series is constant.   2p+2-p=4p+3-2p-2   p=1   1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37   Ans:34
Answer: D
Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 5 sec. What is the length of the fast train?	Select the correct option:	A) 22	B) 23	C) 25	D) 27 7/9	E) 27

Solution: Relative speed = (40 - 20)= 
(40 - 20) = 20
20 km/hr.= 20 * 5/ 18 = 50/9 m/sec.   Length of faster train = 50/9 * 5 = 250/9 = 27 7/9 m.   Answer: Option 27 7/9
Answer: D
A man sells a horse for Rs.800 and loses something, if he had sold it for Rs.980, his gain would have been double the former loss. Find the cost price of the horse?  Choose the correct choice
A) 337  B) 278  C) 288  D) 860  E) 721

Solution: CP = SP + 1CP = SP - g   800 + x = 980 - 2x   3x = 180 => x = 60   CP = 800 + 60= 
800 + 60 = 860
860   Answer: 860
Answer: D
What is the remainder when 570 is divided by 6?	Select
A) 1	B) 5	C) 4	D) 0	E) 2

Solution: Explanation:   52 = 25, on division by 6, the remainder is 1.   53 = 125, on division by 6, the remainder is 5.   54 = 625, on division by 6, the remainder is 1.   55 = 3125, on division by 6, the remainder is 5.   Hence, for 5 (2x) on division by 6, the remainder is 1, and for 5(2x-1) on division by 6, the remainder is 5.   Therefore, for 570, on division by 6, the remainder is 1.   1NSWER: 1
Answer: A
a,b,c are positive numbers such that they are in increasing Geometric progression then how many such numbers are there in (loga+logb+logc)/6 =log6
Choose the correct choice from the following answers.
A) 1  B) 2  C) 3  D) 4  E) 5

Solution: given that a,b,c are in gp   so b/a=c/b =>b^2=ac   (loga+logb+logc)/6=log6   =>log(abc)=6*log6   =>log(ac*b)=log(6^6)   =>log(b^3)=log(6^6)   =>b^3=6^6=>b^3=(6^2)^3   =>b=6^2=36   it means a=2,c=18 or a=3 c=12 or a=4 c=9 or a=6 c=6.   hence there are four such numbers   ANSWER:4
Answer: D
Two trains T1 and T2 start simultaneously from two stations X and Y respectively towards each other. If
they are 85 km apart both 3 and 6 hours after start, then find the distance between the two stations. Choose the correct choice from the following:	A) 255km	B) 210km	C) 220km	D) 180km	E) 200km

Solution: In first 3 hours T1 travels R km and T2 travels S km.   255kmfter 6 hours they traveled R+S+85+ 85   2(R+S ) = R+S +170   R+S = 170   Hence distance between XY is R+S+ 85 = 170 +85= 
170 +85 = 255
255   255kmnswer : 255km
Answer: A
In a series of football matches, the probability that Team P wins a match against Team Q is 1/4 and the probability that the match ends in a draw is 1/6. If the two teams play five matches, what is the probability that all five matches end in a draw?  Pick one.
A) 1/4436 B) 1/5546 C) 1/6656 D) 1/7776 E) 1/8886

Solution: P(5 draws)=(1/6)^5=1/7776   The answer is 1/7776.
Answer: D
For a light that has an intensity of 60 candles at its source, the intensity in candles, S, of the light at a point d d feet from the source is given by the formula S=60k/d^2 60, where k is a constant. If the intensity of the light is 40 candles at a distance of 6 feet from the source, what is the intensity of the light at a distance of 30 feet from the source?
Choose the correct choice from the following: A) 3/10 candles B) 1/2 candles C) 8/5 candles D) 2 candles E) 3 candles

Solution: ANS = 3/10   S= 60k/d^2   At 6 feet   40 = 60k/36 so k = 24   At 30 feet   S = 60 *24/30^2 = 8/5   8/5 candles
Answer: C
Jemma takes 2 hours to swim the 4 miles from buoy A to buoy B. Tired from her swim, she then continues to buoy C at half her previous speed. If buoy C is 6 miles away from buoy B, how many more hours will pass before Jemma reaches Buoy C? Choose the correct choice from the following choices.
A) 4
B) 5
C) 6
D) 7
E) 8

Solution: Time taken for Jemma to reach buoy B is 2 hours.   The distance between the buoys is 4 miles.   Distance travelled/time taken = Average speed   Hence the average speed to travel the distance is 2m/hr   Now, she would have to travel 6 miles .   However as she is tired the speed is half or 1m/hr   Hence, it will take her 6 hours   (Option 6)
Answer: C