MU-NLPC/Calc-aqua_rat huggingface dataset:
If a*b denotes the greatest common divisor of a and b, then ((12*16)*(18*12)) = ? Choose the correct choice from the following options.
A) 24 B) 12 C) 6 D) 4 E) 2

Solution: The greatest common divisor of 12 and 16 is 4. Hence 12*16 = 4 (note that * here denotes the function not multiplication).   The greatest common divisor of 18 and 12 is 6. Hence 18*12 = 6.   Hence ((12*16)*(18*12)) = 4*6.   The greatest common divisor of 4 and 6 is 2.   Answer; 2.
Answer: E
The speed of a railway engine is 42 kmph when no compartment is attached, and the reduction in speed is directly proportional to the square root of the number of compartments attached.
If the speed of the train carried by this engine is 24 kmph when 9 compartments are attached, the maximum number of compartments that can be carried by the engine is	Choose the correct answer.
A) 47
B) 48
C) 49
D) 50
E) 51

Solution: Explanation :   Let S = speed, and N = number of compartments, then   => S = 42 - k * √N.   Where k is a constant of the proportionality. In general, if A is directly proportional to B, we can write A = k * B and solve for k.   If N = 9, then S = 24   => 24 = 42 - k*√9 = 42 - 3k.   => 3k = 18.   => k = 6.   Now, we need to know: what value of N makes S go to zero?   => 0 = 42 - 6*√N   => 6*√N = 42   => √N= 7   => n = 7(2) = 49.   With 49 compartments, the train does not budge. Therefore, it would budge if there were one fewer cars.   Thus, 48 is the maximum number of cars the engine can pull and still move.   Answer : 48
Answer: B
A:B = 6:4, B:C = 1:4. Now if C is 38, what is A? Select the correct option: A) 14.25 B) 15.25 C) 16.25 D) 17.25 E) 18.25

Solution: b/c=1/4 && c=38   so b=c/4 => b=19/2   a=6b/4 => so a=57/4= 
57/4 = 57/4 = around 14.25
> 14.25   14.25NSWER:14.25
Answer: A
If x is an integer such that 0 < x < 7, 0 < x < 15, 5 > x > –1, 3 > x > 0, and x + 2 < 4, then x is
Choose the correct option.
A) 1  B) 2  C) 3  D) 4  E) 5

Solution: 0 < x < 7,   0 < x < 15,   5 > x > –1   3 > x > 0   x<2   From above: 0 < x < 2 --> x = 1.   1nswer: 1.
Answer: A
The angles of a triangle are in the ratio 1:3:8. Find the measurement of the three angles of triangle.  Pick one.
A) 90°	B) 110°	C) 120°	D) 150°	E) 180°

Solution: If the ratio of the three angles is 1:3:8, then the measures of these angles can be written as x, 3x and 8x. Also the sum of the three interior angles of a triangle is equal to 180°. Hence   x + 3x + 8x = 180   Solve for x   12x = 180   x = 15   The measures of the three angles are   x = 15°   3x = 3 × 15 = 45°   8x = 8 × 15 = 120°   120°
Answer: C
A man in train notice that he can count 51 telephone posts in 1 minute. If they are known to be 40 meters apart,then at what speed is the train traveling? Answers: A) 100km/hr B) 120km/hr C) 50km/hr D) 150km/hr E) 200km/hr

Solution: Number of gaps between 51 telephone posts = 50   Distance traveled in 1 minute = 50*40= 
50*40 = 2_000
2000m= 2.0km   Speed = 60*2.0= 
60*2.0 = 120
120km/hr   Answer is 120km/hr
Answer: B
In an elaction between two candidates, 20% of votes are were declares invalid. First candidate got 480 votes which were 60% of the total valid votes . The total number of votes enrolled in that election was: Options
A) 1000 votes B) 2000 votes C) 3000 votes D) 4000 votes E) 5000 votes

Solution: (100%-20%=80%   48%-32%=16%   16%  48 -32= 
 48 -32 = 16
16%   16%= 16×30 = 480   100% =100×30 =3000 votes)   3000 votes
Answer: C
If n is a positive integer and n^2 is divisible by 62, then the largest positive integer that must divide n is  Answers: A) 6 B) 12 C) 24 D) 36 E) 48

Solution: The question asks aboutthe largest positive integer that MUST divide n, not COULD divide n. Since the least value of n for which n^2 is a multiple of 72 is 12 then the largest positive integer that MUST divide n is 12.   Complete solution of this question is given above. Please ask if anything remains unclear.   I spent a few hours on this one alone and I'm still not clear. I chose 12 at first, but then changed to 48.   I'm not a native speaker, so here is how I interpreted this question:the largest positive integer that must divide n=the largest positive factor of n. Since n is a variable (i.e. n is moving), so is its largest factor. Please correct if I'm wrong here.   I know that if n = 12, n^2 = 144 = 2 * 72 (satisfy the condition). When n = 12, the largest factor of n is n itself, which is 12. Check: 12 is the largest positive number that must divide 12 --> true   However if n = 48, n^2 = 48 * 48 = 32 * 72 (satisfy the condition too). When n = 48, the largest factor of n is n itself, which is 48. Check: 48 is the largest positive number that must divide 48 --> true   So, I also notice that the keyword isMUST, notCOULD. The question is, why is 48 notMUST divide 48, but instead onlyCOULD divide 48? I'm not clear right here. Why is 12MUST divide 12? What's the difference between them?   Only restriction we have on positive integer n is that n^2 is divisible by 72. The least value of n for which n^2 is divisible by 72 is 12, thus nmustbe divisible by 12 (n is in any case divisible by 12). For all other values of n, for which n^2 is divisible by 72, n will still be divisible by 12. This means that n is always divisible by 12 if n^2 is divisible by 72.   Now, ask yourself: if n=12, is n divisible by 48? No. So, n is not always divisible by 48.   12
Answer: B
There is a sequence ni such, in which i is a positive integer, ni+1=2ni.
If n1=1, n2=2, n3=4, n4=8, what is the scope including n31? Choose the correct choice from the following answers.
A) 100~1,000 B) 1,000~10,000 C) 10,000~100,000 D) 100,000~1,000,000 E) 1,000,000,000~

Solution: -> ni=2^(i-1) -> 2^10=1,024>1,000=10^3 -> n31=2^30=(2^10)^3>(10^3)^3=10^9   Thus, the answer is 1,000,000,000~.
Answer: E
Uncle Bruce is baking chocolate chip cookies. He has 72 ounces of dough (with no chocolate) and 50 ounces of chocolate. How much chocolate is left over if he uses all the dough but only wants the cookies to consist of 40% chocolate?  Choose the correct choice from the following: A) 4 B) 6 C) 8 D) 2 E) 10

Solution: First, you must find the total weight of the mixture given that 80% of it will be dough.   60%*Total = 72 => (6/10)Total=72=> Total=720/6 => Total=120 oz,   From there, you must find 10% of the total 40 oz of the mixture.   40%*Total => (4/10)(120)=48 oz choclate used,   Not forgetting that the question asks how much chocolate is left over we must subtract the chocolate used from the initial chocolate. 50-48 oz = 2 oz chocolate left over.   Answer : 2
Answer: D
A cistern which could be filled in 10 hours takes 2 hour more to be filled owing to a leak in its bottom.If the cistern is full, in what time will the leak empty it?	Choose the correct choice from the following options
A) 50hours	B) 80hours	C) 100hours	D) 150hours	E) 110hours

Solution: Let the leak empty the full cistern in x hours   10x/x-10 = 10+1   x = 110 hours   Answer is 110hours
Answer: E
A company has 10 supervisors for every 1000 employees. For 5000 employees the company should have how many supervisors?	Pick:
A) 20 B) 16 C) 15 D) 18 E) 50

Solution: 10/1000=x/5000   x=50   Answer is 50
Answer: E
Walking with 4/5 of my usual speed, I arrive at the bus stop 8 minutes later than normal. How many minutes does it take to walk to the bus stop at my usual speed?
Choose the correct choice from the following options:
A) 20
B) 24
C) 28
D) 32
E) 36

Solution: Let t = usual time = distance / usual speed   t + 8 = distance / (4* usual speed/5) = (5 * distance) / (4 * usual speed) = 5t/4   t = 32   The answer is 32.
Answer: D
A boat running downstream covers a distance of 22 km in 4 hours while for covering the same distance upstream, it takes 5 hours. What is the speed of the boat in still water?  Choose the correct choice from the following options:
A) 1.85
B) 3.75
C) 4.95
D) 2.45
E) 5.21

Solution: Explanation:   Speed downstream =22/4= 
22/4 = 11/2 = around 5.5
5.5 kmph   Speed upstream=22/5= 
22/5 = 22/5 = around 4.4
4.4 kmph   Speed of the boat in still water=5.5+4.4/2=4.95 kmph   Answer:4.95
Answer: C
What is the lowest possible common multiple K of 2 distinct integers, each greater than 329?	Choose the correct choice
A) 330·331
B) 330^2
C) 33·331
D) 660
E) 330

Solution: Lowest possible common multiple K of 2 distinct integers will have to be multiple of the number greater than 329...which 330..   so one number will be 330...another one will be 660..   Ans is 660.
Answer: D
6 persons a, b, c, d, e, and f are to be lined up in a row. If a, b, and c adhere always together, how many possible cases are there?
Select:	A) 24	B) 36	C) 48	D) 72	E) 144

Solution: There are 6 peoples. 3 have to be together, so take them as 1..   Now total= these 3 + 1+1+1= 4 total..   4 can be arranged in 4! ways..   now these 3 together can be arranged in 3! ways, so TOTAL ways= 4!*3!= 24*6= 
24*6 = 144
144   ANSW144R:144
Answer: E
If a and b are positive integers such that a-b and a/b are both even integers, which of the following must be an odd integer?
Choose the most appropriate option
A) a/2  B) b/2  C) (a+b)/2  D) (a+2)/2  E) (b+2)/2

Solution: Initially substitute a and b with 8 and 2 respectively.   a = 8   b = 2   8 - 2 = even number   8/2 = even number   so these numbers satisfy requirements   a) a/2: 8/2 = 4 EVEN   b) b/2: 4/2 = 2 EVEN   c) (a+b)/2: (8+4)/2 = 6 EVEN   d) (a+2)/2: (8+2)/2 = 5 O(a+2)/2(a+2)/2   substitute another set (a=4 & b=2) for check    (4+2)/2= 
 (4+2)/2 = 3
3 Again, O(a+2)/2(a+2)/2   e) (b+2)/2: (4+2)/2= 3 O(a+2)/2(a+2)/2   substitute another set (a=4 & b=2) for check    (2+2)/2= 
 (2+2)/2 = 2
2 EVEN   ANSWER: (a+2)/2
Answer: D
In how many different number of ways 5 boys and 2 girls can sit on a bench?  Choose the most appropriate option:
A) 5040	B) 730	C) 740	D) 750	E) 800

Solution: npn = n!   7p7 = 7 x 6 × 5 × 4 × 3 × 2 × 1 = 5040   5040
Answer: A
If a and b are positive integers, and a=2b+6, the greatest common divisor of a and b CANNOT be Choose the correct choice:
A) 1	B) 2	C) 3	D) 6	E) 12

Solution: since a =2b + 6,   so we can say b = (a/2 -3).   So we need to find not possible gcd values for a , (a/2 -3).   A. 1, We can easily get this value by making a = 8.   B. 2. we can again get this value as GCD by keeping a =10   C. 3 We will get this as GCD by keeping a =12   D. 6 We can get GCD 6 by keeping (a/2-3) = 6 and a as 18.   E. 12 This is not possible as for 12(2^2*3 ) to be GCD = 2^2*3 both a and a/2-3 should be divisible by 4 and 3 . So a has to be a multiple of 4 . this means a/2 has to be even and Even - odd will be odd and odd number wont be divisible by 4.   This 12 cant be the GCD.   Answer 12.
Answer: E
Three distinct single digit no A,B and c are in G.M ,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 number of different possible values of abs (A+B -C) is;	Select:
A) 3 B) 4 C) 5 D) 6 E) 7

Solution: 1,2,4   2,4,8   4,2,1   8,4,2   1,3,9   9,3,1   total=6   ANSWER:6
Answer: D
In how many different ways can pennies (1 cent), nickels (5 cents), dimes (10 cents), and quarters (25 cents) be combined for a total of $1.05 (105 cents), if at least one of each type of coin must be included?
Choose the correct choice from the following options
A) 49 B) 69 C) 73 D) 91 E) 99

Solution: I. Case I = Four Quarters = this is impossible, because if we already have a dollar in quarters, then we cannot have any dimes. We can't have all four coins represented if we have four quarters.   II. Case II = Three Quarters (75 cents)   This allows for two or one dime. Three dimes would bring us up to $1.05, and we wouldn't have room for any pennies or nickels.   Subcase 1 = 3 Q, 2 D (95 cents)   1) one nickel (N) and 5 pennies (P) (2 nickels would not allow for any pennies)   Subcase 2 = 3 Q, 1 D (85 cents)   2) 3 N and 5 P   3) 2 N and 10 P   4) 1 N and 15 P   Case II allows for a total of four ways.   III. Case III = Two Quarters (50 cents)   This allows for 1-4 dimes.   Subcase 1 = 2 Q, 4 D (90 cents)   (2 ways) we could have 1-2 nickels   Subcase 2 = 2 Q, 3 D (80 cents)   (4 ways) we could have 1-4 nickels   Subcase 3 = 2 Q, 2 D (70 cents)   (6 ways) we could have 1-6 nickels   Subcase 4 = 2 Q, 1 D (60 cents)   (8 ways) we could have 1-8 nickels   Case III allows for a total of 20 ways   IV. Case IV = One Quarter (25 cents)   This allows for 1-7 dimes   Subcase 1 = 1 Q, 7 D (95 cents)   (1 way) we could have 1 nickel   Subcase 2 = 1 Q, 6 D (85 cents)   (3 ways) we could have 1-3 nickels   Subcase 3 = 1 Q, 5 D (75 cents)   (5 ways) we could have 1-5 nickels   Subcase 4 = 1 Q, 4 D (65 cents)   (7 ways) we could have 1-7 nickels   Subcase 5 = 1 Q, 3 (55 cents)   (9 ways) we could have 1-9 nickels   Subcase 6 = 1 Q, 2 D (45 cents)   (11 ways) we could have 1-11 nickels   Subcase 7 = 1 Q, 1 D (35 cents)   (13 ways) we could have 1-13 nickels   Case IV allows for a total of 49 ways.   There's no other case, because we have to have at least one quarter and one dime. The total over the cases equals   Total = 4 + 20 + 49= 
4 + 20 + 49 = 73
73 ways.   OA=(73)
Answer: C
A cistern is filled by a tap in 5 1/2 hours. Due to leak in the bottom of the cistern, it takes half an hour longer to fill the cistern. If the cistern is full how many hours will it take the leak to empty it?
Choose the correct choice from the following choices: A) 60 B) 62 C) 64 D) 66 E) 68

Solution: filling rate - leak rate = net rate   1/5.5 - leak rate = 1/6   leak rate = 2/11 - 1/6 = 1/66   The answer is 66.
Answer: D
In baseball, the batting average is defined as the ratio of a player’s hits to at bats. If a player had anywhere from 5 to 7 at bats in a recent game and had anywhere from 2 to 3 hits in the same game, the player’s actual batting average for that game could fall anywhere between
Choices:
A) 0.25 and 1.00
B) 0.25 and 0.75
C) 0.25 and 0.75
D) 0.33 and 0.50
E) 0.50 and 0.66

Solution: Average Range = Hits to Bats i.e 2/7 to 3/5 = 0.28 to 0.60   Answer: 0.25 and 0.75
Answer: C
An insect leaps 72 centimeters in 1.2 seconds. What is its speed? Choices:
A) 6 centimeters per second
B) 0.6 centimeters per second
C) 0.6 meters per second
D) 8.64 centimeters per second
E) 0.864 meters per second

Solution: 72 / 1.2= 
72 / 1.2 = 60
60 cm/s= 0.6 m/s   The answer is 0.6 meters per second.
Answer: C
In what ratio should a 20% methyl alcohol solution be mixed with a 50% methyl alcohol solution so that the resultant solution has 40% methyl alcohol in it?	Pick.
A) 1 : 3  B) 1 : 2  C) 2 : 3  D) 2 : 1  E) 3 : 1

Solution: TWO things to remember:-   1) the ratio of quantity mixed to get an average is related to the ratio of each qty's distance from average.   2) More the Qty of x from that of y, More CLOSER will be average to x..   Qty of 20%/Qty of 50%= (50−40)/(40−20)=1/2=1:2   ANSWER:1 : 2
Answer: B
A is faster than B. A and B each walk 24 km. The sum of their speeds is 7 km/hr and the sum of times taken by them is 14 hours. Then, A's speed is equal to?  Pick one:
A) 6 km/hr
B) 3 km/hr
C) 1 km/hr
D) 9 km/hr
E) 4 km/hr

Solution: Let A's speed = x km/hr. Then, B's speed = (7 - x) km/ hr.   So, 24/x + 24/(7 - x) = 14   x2 - 98x + 168 = 0   (x - 3)(x - 4) = 0 => x = 3 or 4.   Since, A is faster than B, so A's speed = 4 km/hr and B's speed = 3 km/hr.   Answer: 3 km/hr
Answer: B
In what time will a train 120 m long cross an electric pole, it its speed be 144 km/hr?
Pick one
A) 2.5 sec  B) 4.25 sec  C) 5 sec  D) 12.5 sec  E) 3 sec

Solution: Speed = 144 * 5/18= 
144 * 5/18 = 40
40 m/sec   Time taken= 120/40= 
120/40 = 3
3.0 sec.   ANSW3 secR:3 sec
Answer: E
What is the minimum number of square marbles required to tile a floor of length 5 metres 78 cm and width 3 metres 40 cm? Options.
A) 170
B) 187
C) 540
D) 748
E) 546

Solution: The marbles used to tile the floor are square marbles.   Therefore, the length of the marble=width of the marble.the length of the marble=width of the marble.   As we have to use whole number of marbles, the side of the square should a factor of both 5 m 78 cm and 3m 40. And it should be the highest factor of 5 m 78 cm and 3m 40.   5 m 78 cm = 578 cm and 3 m 40 cm = 340 cm.   The HCF of 578 and 340 = 34.   Hence, the side of the square is 34.   The number of such square marbles required,   =578×340/34×34   =170 marbles   Option(170)
Answer: A
A wholesaler wishes to sell 100 pounds of mixed nuts at $2.50 a pound. She mixes peanuts worth $1.50 a pound with cashews worth $7.00 a pound. How many pounds of cashews must she use?  Options:  A) 40  B) 45  C) 50  D) 55  E) 60

Solution: From the question stem we know that we need a mixture of 100 pounds of peanuts and cashews. If we represent peanuts as x and cashews as y, we get x + y = 100. Since the wholesaler wants to sell the mixture of 100 pounds @ $2.50, we can write this as: $2.5 * (x + y) = $1.5x + $4y   From the equation x + y = 100, we can rewrite y as y = 100 - x and substitute this into our equation to get:   $2.5 * (x + 100 - x) = $1.5x + $4(100 - x)   If you solve for x, you will get x = 60, and therefore y = 40. So the wholesaler must use 40 pounds of cashews.   You can substitute into the original equation to see that: $250 = $1.5(60) + $4(40)   Answer is 55.
Answer: D
How many prime numbers are between 13/3 and 83/6?	Choose the correct option
A) 1
B) 2
C) 3
D) 4
E) 5

Solution: 13/3 = 4.xxx   83/6 = 13.xxx   So we need to find Prime numbers between 4 (Exclusive) - 12 (Inclusive)   There are 2 Prime numbers 7 11   Hence answer will be (2) 2   2
Answer: B
Find the odd man out. 1, 3, 9, 12, 19, 29
Choices
A) 12 B) 9 C) 1 D) 3 E) 4

Solution: Explanation :   12 is an even number. All other given numbers are odd.. 12nswer : Option 12
Answer: A
In a certain school, the ratio of boys to girls is 5 to 13. If there are 64 more girls than boys, how many boys are there?	Pick one
A) 27  B) 40  C) 45  D) 72  E) 117

Solution: The ratio of b to G is 5:13 and the other data point is G are more than boys by 64...   Looking at the ratio we can say that the 8(13-5) extra parts caused this diff of 64. so 1 part corresponds to 64/8= 
64/8 = 8
8 and so   5 parts correspond to 5*8= 
5*8 = 40
40.   40
Answer: B
If Sharon's weekly salary increased by 20 percent, she would earn $600 per week. If instead, her weekly salary were to increase by 15 percent, how much would she earn per week? Choose the correct choice.
A) Rs.575 B) Rs.600 C) Rs.625 D) Rs.485 E) Rs.590

Solution: Soln:-   (600/120)115=575   In this case long division does not take much time.   (5/1)115=Rs.575   Rs.575NSWER:Rs.575
Answer: A
A reduction in the price of petrol by 10% enables a motorist to buy 5 gallons more for $280. Find the original price of petrol?  Choose the correct choice from the following options
A) $11  B) $5  C) $45  D) $400  E) $6.2

Solution: Price decreased by 10%, so 9/10 times, which means that original gallons bought increased 10/9 times. Since this increase equals to 5 gallons then 45 gallons were bought originally (45*10/9=50 --> increase 5 gallons). Hence original price was 280/45=$6.2   Answer: $6.2.
Answer: E
Convert the 13/36 m/s into kilometers per hour?
Choose the correct choice from the following answers: A) 1.9kmph B) 2.9kmph C) 1.3 kmph D) 1.8kmph E) 1.5kmph

Solution: 13/36 m/s = 13/36 * 18/5   = 13/10= 
13/10 = 13/10 = around 1.3
1.3 kmph.   Answer:1.3 kmph
Answer: C
On the independence day, bananas were be equally distributed among the children in a school so that each child would get two bananas. On the particular day 305 children were absent and as a result each child got two extra bananas. Find the actual number of children in the school?	Choose the correct choice from the following answers: A) 600 B) 610 C) 500 D) 520 E) 720

Solution: Let the number of children in the school be x. Since each child gets 2 bananas, total number of bananas = 2x.   2x/(x - 305) = 2 + 2(extra)   => 2x - 610 = x => x = 610.   ANSWER:610
Answer: B
Johnson has a corporate proposal. The probability that vice-president Adams will approve the proposal is 0.6. If VP Adams approves the proposal, then the probability that vice-president Baker will approve the proposal is 0.4. If VP Adams doesn’t approve the proposal, then the probability that vice-president Baker will approve the proposal is 0.3. What is the probability that at least one of the two VPs, approves Johnson’s proposal? Choices.
A) 0.12
B) 0.24
C) 0.28
D) 0.48
E) 0.72

Solution: (1at approves * second rejects ) + (1st rejects * 2nd approves ) + (both approves )   =0.6*0.2+0.4*0.3+0.6*0.4   = 0.12+0.12+0.24= 
0.12+0.12+0.24 = 0.48
0.48   0.48
Answer: D
What is the normal price of an article sold at $36 after two successive discounts of 10% and 20%?	Options.
A) $45	B) $48	C) $50	D) $54	E) $56

Solution: 0.8*0.9*cost price = $36   cost price = $50   The answer is $50.
Answer: C
Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one? Options:
A) 12 sec	B) 24 sec	C) 48 sec	D) 60 sec	E) 65 sec

Solution: Explanation:   Relative speed = 45 + 30= 
45 + 30 = 75
75 km/hr.   75 * 5/18= 125/6 m/sec.   Distance covered = 500 + 500= 
500 + 500 = 1_000
1000 m.   Required time= 1000 * 6/125= 
1000 * 6/125 = 48
48 sec.   ANSWER IS 48 sec
Answer: C
A cube 125 mt is colored pink on two opposite surfaces and then cut in to 125 smaller cubes then find how many number of cubes have pink color?
Options.
A) 3	B) 4	C) 5	D) 6	E) 7

Solution: Answer:4
Answer: B
Difficulty:
There are five sales agents in a certain real estate office. One month Andy sold six as many properties as Ellen, Bob sold 3 more than Ellen, Cary sold six times as many as Bob, and Dora sold as many as Bob and Ellen together. Who sold the most properties that month?  Choose the most appropriate option:
A) Andy
B) Bob
C) Cary
D) Dora
E) Ellen

Solution: a= 6e   b =3 +e   c = 6b = 18+ 6e (highest of all)   d = b + e = 3+ e +e = 3 + 2e   Ans. Cary
Answer: C
Two trains started at the same time, one from A to B and the other from B to A . If they arrived at B and A respectively 4 hours and 16 hours after they passed each other the ratio of the speeds of the two trains was Choose the correct choice from the following choices.
A) 2:1  B) 3:2  C) 4:3  D) 5:4  E) 1:2

Solution: Explanation:   Note : If two trains (or bodies) start at the same time from points A and B towards each other and after crossing they take a and b sec in reaching B and A respectively, then: (A's speed) : (B's speed) = (b : a)   Therefore, Ratio of the speeds of two trains = = 2 : 1. 2:1nswer: 2:1
Answer: A
The price of sugar is increased by 5%. By how much percent should a home maker reduce her consumption of sugar to have no extra expenditure? Choose the correct choice from the following options:
A) (700/107) %
B) (107/100) %
C) (500/105)%
D) (5/100)%
E) (100/500)%

Solution: Old price = $100 (assume);   Old consumption = 1 kg (assume).   New price = $105.   We want the spendings to remain at $100.   (New consumption)*105 = 100 --> (New consumption) = 100/105 kg.   Percent decrease = Change/Original *100 = (1 - 100/105)/1*100 = 500/105%.   Answer: (500/105)%.
Answer: C
At a certain conference, 76% of the attendees registered at least
two weeks in advance and paid their conference fee in full. If
10% of the attendees who paid their conference fee in full did
not register at least two weeks in advance, what percent of
conference attendees registered at least two weeks in
advance?
Choose the correct choice from the following.
A) 18.0% B) 62.0% C) 79.2% D) 84.4% E) 82.0%

Solution: I do not think that Venn will be helpful here. A table will make more sense. But here is my approach.   76% regestered at least 2 weeks and paid full fee.   10% paid full fee and did not registered at least 2 weeks in advance. Then 90% paid full fee and registered at least 2 weeks before.   90% *X=76% where X is the number of people who registerd 2 weeks in advance and paid full fee.(answer 84.4%)
Answer: D