MU-NLPC/Calc-aqua_rat huggingface dataset:
A woman sold 100 oranges at $12.10, some at the rate of 3 for 35 cents and the rest at 4 for 85 cents. How many were sold at the first rate? Choose the correct choice from the following choices:
A) 45  B) 21  C) 9  D) 15  E) 12

Solution: This can be solved like a classical mixture problem but numbers are awkward to deal with.   It's easier to just look at the answer choices. You know that a multiple of 3 oranges has to be sold at the first rate, and a multiple of 4 at the second rate. You simple subtract the answer choices for the first rate from 100 and check whether the remainder (i.e. the number of oranges sold at the second rate) is a multiple of 4.   100 - 45= 
100 - 45 = 55
55=> not a multiple of 4 so exclude     100 - 21= 
  100 - 21 = 79
79=> not a multiple of 4 so   100 -9= 
100 -9 = 91
91=> nota multiple of 4 so exclude     100 - 15= 
  100 - 15 = 85
85=> not a multiple of 4 so exclude     100 - 12= 
  100 - 12 = 88
88=> a multiple of 4 so keep   Hence, answer choice 12 is correct.   12
Answer: E
A mother is planning a party for her child and buys some snacks. She buys 3 bags of chips, 1 bag of pretzels, and 2 packages of cookies. She pays $3.00 per bag of chips, $2.50 per bag of pretzels, and $4.00 per package of cookies. What is the average price per snack the mother paid?
Choose the correct choice from the following.
A) $2.25 B) $3.25 C) $2.00 D) $3.50 E) $3.00

Solution: Explanation:   3 1 2   $3.00 $2.50 $4.00   $9.00 + $2.50 + $8.00 = $19.50/6  9.00 +  2.50 +  8.00= 
 9.00 +  2.50 +  8.00 = 19.5
$19.50/6= 
19.50/6 = 3.25
$3.25   $3.25
Answer: B
Find the number of ways a batsman can score a double century only in terms of 4's & 6's?
Assume the batsman scored x 4's and y 6's. Choose the correct choice from the following answers:
A) 22
B) 16
C) 77
D) 91
E) 13

Solution: 4x + 6y = 200 ⇒2x+3y=100⇒2x+3y=100 ⇒x=100−3y2=50−32y⇒x=100−3y2=50−32y   As x is an integer, y should be a multiple of 2.   If   y = 0, x = 50   y = 2, x = 47   y = 4, x = 44   ...   y = 32, x = 2   So total ways are (32-0)/2 + 1= 
(32-0)/2 + 1 = 17
17 ( if 0 6's are possible) otherwise 16   Answer:16
Answer: B
A envelop weight 8.5 gm,if 820 of these envelop are sent with an advertisement mail. How much wieght?  Choose the correct choice from the following answers.
A) 6.6kg	B) 6.8kg	C) 6.7kg	D) 6.97kg	E) 7.8kg

Solution: 820*8.5   6970.0gm   6.97kg   ANSWER:6.97kg
Answer: D
Spheres A and B have their radil 40 cm and 10 cm respectively. The ratio of the surface area of A to the surface area of B is Choose the correct choice from the following:
A) 1 : 4  B) 1 : 16  C) 4 : 1  D) 16 : 1  E) None

Solution: Solution   Let the radil of A and B be r and R respectively.   Required ratio	= 4Πr2/ 4ΠR2   ‹=› r2 / R2   ‹=› (r/R)2   ‹=›(40/10)2   ‹=› 16 : 1.   Answer 16 : 1
Answer: D
Fence X is twice as long as fence Y, and fence Y is 4 feet shorter than fence Z. If 3 feet were added to each fence, which of the following must be true?
I) X is twice as long as Y.
II) Y is 2 feet shorter than Z.
III) X is longer than Z. Choose the correct choice.
A) I only  B) II only  C) III only  D) I and II  E) II and III

Solution: If X= 6   Y= 3   Z= 7   Then, after adding 3 feet to each:   X= 9   Y=6   Z=10   And the answer would be II only, which is wrong.
Answer: B
There are ten 50 paise coins placed on a table. Six of these show tails and four show heads. A coin is chosen at random and flipped over (not tossed). This operation is performed seven times. One of the coins is then covered. Of the remaining nine coins, five show tails and four show heads. The covered coin shows	Choose the correct choice from the following answers
A) a head  B) a tail  C) more likely a head  D) more likely a tail  E) None

Solution: Explanation :   H-head T-tail   10 coins – 6T and 4 H -initial   9 coins - 5T and 4H -final   7 coins can be flipped for 6T + 1 H resulting in 1T and 9H. Not possible   7 coins can be flipped for 3T + 4 H resulting in 7T and 3 H. Not possible   7 coins can be flipped for 4T + 3 H resulting in 5T and 5 H. Possible   7 coins can be flipped for 5T + 2 H resulting in 3T and 7 H. Not possilbe   a headnswer : a head
Answer: A
A solution of 80 litres contains oil and water in the ratio 10:x. If five litres of water is added to the solution, the ratio becomes 20:10, find the value of x?	Choose the correct choice from the following:
A) 4.1
B) 4.9
C) 4.7
D) 5.7
E) 8.5

Solution: Exp. Total new quantity = original sol + water =80+5= 
80+5 = 85
85   New ratio= 20:10, New quantity of oil =20/30*85 = 56.6 Lit,   New quantity of water = 10/30*85 =28.3 Lit   Water present initially = (28.3-5)= 
(28.3-5) = 23.3
23.3 Lit   Ratio= 56.6/23.3 =10/x There for x = 4.11   4.1nswer: 4.1
Answer: A
A wheel that has 6 cogs is meshed with a larger wheel of 21 cogs. When the smaller wheel has made 21 revolutions, then the number of revolutions mad by the larger wheel is:	Pick one.
A) 49  B) 4  C) 12  D) 6  E) 27

Solution: Let the required number of revolutions made by larger wheel be x.   Then, More cogs, Less revolutions (Indirect Proportion)   21 : 6 :: 21 : x 21 * x = 6 x 21   x =	(6 x 21)/21   x = 6   Answer is 6.
Answer: D
howmany 3 digit numbers are there tens digit place is more than hundreds digit place and units place less than hundreds digit place?	Answers
A) 80
B) 100
C) 110
D) 120
E) 140

Solution: we have numbers {0,1,2,3,4,5,6,7,8,9}   now we would decide the cases on behalf of value of hundred place digit. and accordingly choose unit's digit and ten's digit.   value of hundred place digit must be choosen in such a manner that there should exist a greater digit for ten's place and a smaller digit for unit place.   thus we can have values of hundred's digit from 1,2,3,4,5,6,7,8 only   now starting from hundred's digit=8 :   hundred's digit possible values for ten's digit possible values for unit digit total ways   8 9 0,1,2,3,4,5,6,7 1*1*8=8   7 8,9 0,1,2,3,4,5,6 1*2*7=14   6 7,8,9 0,1,2,3,4,5 1*3*6=18   5 6,7,8,9 0,1,2,3,4 1*4*5=20   4 5,6,7,8,9 0,1,2,3 1*5*4=20   3 4,5,6,7,8,9 0.1.2 1*6*3=18   2 3,4,5,6,7,8,9 0,1 1*7*2=14   1 2,3,4,5,6,7,8,9 0 1*8*1=8   so, total no of cases=8+14+18+20+20+18+14+8= 
8+14+18+20+20+18+14+8 = 120
120   hence total no of possible 3 digit numbers= 120   ANSWER:120
Answer: D
If n is a positive integer, which of the following expressions must be even?	Choose the correct choice from the following choices
A) (n − 1)( n + 7)	B) (n − 2)( n + 7)	C) (n − 2)( n + 10)	D) (n − 3)( n + 7)	E) (n − 3)( n + 11)

Solution: Whether n is even or odd, (n-2)(n+7) will have one odd factor and one even factor.   The product will be even.   The answer is (n − 2)( n + 7).
Answer: B
What is the units digit of (3^13)(4^13)? Options
A) 2  B) 4  C) 6  D) 7  E) 8

Solution: -> The ones place of (~3)^n repeats after 4 times like 39713.   The ones place of (~4)^n repeats after 2 times like 464.   Then, 3^13=3^4*3+13^1.,   4^13=4^2*6+1=4^1=~4   which is (3^13)(4^13) (3^1)(~4)=(~3)(~4)=~2. Therefore, the answer is 2.
Answer: A
Two goods train 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. Select:
A) 12 sec
B) 24 sec
C) 48 sec
D) 60 sec
E) None

Solution: Solution   Relative speed	= (45 + 30 )km/hr   = (75 x 5/18)m/sec   =(125 / 6) m/sec   Total Distance covered	= (500 + 500)= 
(500 + 500) = 1_000
1000 m   Required time= (1000 x 6 /125)sec   = 48 sec   Answer 48 sec
Answer: C
All the milk in container A which was filled to its brim was poured into two containers B and C. The quantity of milk in container B was 62.5% less than the capacity of container A. If 148 liters was now transferred from C to B, then both the containers would have equal quantities of milk. What was the initial quantity of milk in container A?	Select
A) 1184	B) 1723	C) 1129	D) 2613	E) 1372

Solution: A   1184   B has 62.5% or (5/8) of the milk in A. Therefore, let the quantity of milk in container A(initially) be 8k.   Quantity of milk in B = 8k - 5k = 3k.   Quantity of milk in container C 8  - 5= 
8  - 5 = 3
3k.   Quantity of milk in container C= 8k - 3k = 5k   Container: A B C   Quantity of milk: 8k 3k 5k   It is given that if 148 liters was transferred from container C to container B, then both the containers would have equal quantities of milk.   5k - 148 8  - 3= 
8  - 3 = 5
5k   Container: A B C   Quantity of milk: 8k 3k 5k   It is given that if 148 liters was transferred from container C to container B, then both the containers would have equal quantities of milk.   5k - 148= 3k + 148 => 2k = 296 => k = 148   The initial quantity of milk in 1184 = 8k = 8 * 148= 
8 * 148 = 1_184
1184 liters.
Answer: A
How many seconds will a 770 m long train take to cross a man walking with a speed of 2.5 km/hr in the direction of the moving train if the speed of the train is 46.5 km/hr?	Choose the correct choice from the following answers:
A) 63 B) 88 C) 66 D) 44 E) 35

Solution: Speed of train relative to man = 46.5 - 2.5= 
46.5 - 2.5 = 44
44 km/hr.= 44 * 5/18 = 110/9 m/sec.   Time taken to pass the man = 770 * 9/110= 
770 * 9/110 = 63
63 sec.   63nswer: 63
Answer: A
At a blind taste competition a contestant is offered 3 cups of each of the 3 samples of tea in a random arrangement of 9 marked cups. If each contestant tastes 4 different cups of tea, what is the probability that a contestant does not taste all of the samples?	Answers: A) 1/12 B) 5/14 C) 4/9 D) 1/2 E) 2/3

Solution: "The probability that a contestant does not taste all of the samples" means that contestant tastes only 2 samples of tea (one sample is not possible as contestant tastes 4 cups>3 of each kind).   C23∗C46C49=514C32∗C64C94=514.   C23C32 - # of ways to choose which 2 samples will be tasted;   C46C64 - # of ways to choose 4 cups out of 6 cups of two samples (2 samples*3 cups each = 6 cups);   C49C94 - total # of ways to choose 4 cups out of 9.   Answer: 5/14
Answer: B
In a garment industry, 12 men working 8 hours per day complete a piece of work in 10 days. To complete the same work in 8 days, working 13.33 hours a day, the number of men required is:  Choose the correct answer:	A) 4	B) 5	C) 6	D) 8	E) 9

Solution: Explanation :   Let the required number of men be x.   Less days, More men (Indirect Proportion)   More working hrs per day, Less men (Indirect Proportion)   Days 8 : 10   Working Hrs 13.33 : 8 :: 12 : x   => 8 x 13.33 x x = 10 x 8 x 12   => x = 10 x 8 x 12 / (8 x 13.33)   => x = 9   Answer : 9
Answer: E
If 9x-3y=12 and 3x-5y=7 then 6x-2y = ?  Pick one:  A) -5  B) 4  C) 2  D) 8  E) 6

Solution: 9x-3y=12-----eq(1)   3x-5y=7------eq(2)   solving we get x=13/12 and y=-3/4   so, 6x-2y=6*(13/11)-2(-3/4)=8   ANSWER:8
Answer: D
In Solution P, the proportion of water to alcohol is 4:1. In Solution Q, the proportion of water to alcohol is 2:3. If the two solutions are combined, what is the concentration of alcohol in the new solution if the original solutions were mixed in equal amounts?  Select the correct option.
A) 40% B) 48% C) 50% D) 56% E) 60%

Solution: Let V be the total volume of the new solution.   The amount of alcohol added from Solution P is (1/5)*V/2=(1/10)*V   The amount of alcohol added from Solution Q is (3/5)*V/2=(3/10)*V   The total amount of alcohol in the new solution is (1/10+3/10)*V=(2/5)*V   The alcohol concentration is 2/5=40%   The answer is 40%.
Answer: A
A trader has 80 kg of rice, a part of which he sells at 14% profit and rest at 6% loss. On the whole his loss is 4% . What is the quantity sold at 14% profit and that at 6% loss?  Choose the correct option
A) 8 and 72 kg  B) 10 and 40 kg  C) 15 and 35 kg  D) 20 and 30 kg  E) 40 and 30 kg

Solution: 8 and 72 kglligation Method   I P8 and 72 kgRT II P8 and 72 kgRT   14 (x1) -6 (x2)   \ /   x   / \   (x2-x) (x-x1)   2 18   1 9   Ratio of quantities sold at 14% profit and 6% loss = 1: 9   Quantity sold at 14% profit = 80/1+9 *1 = 8 kg   Quantity sold at 6% loss = 80/1+9 *9 = 72 kg   8 and 72 kgNSWER:8 and 72 kg
Answer: A
A merchant sells an item at a 20% discount, but still makes a gross profit of 50 percent of the cost. What percent of the cost would the gross profit on the item have been if it had been sold without the discount?  Choose the most appropriate option:
A) 20% B) 40% C) 87.5% D) 60% E) 75%

Solution: original SP = X   87.5%ost =87.5%   current selling price = .8x ( 20% discount)   .8x = 1.587.5% (50% profit)   x= 1.5/.8 *87.5%   x= 15/8 87.5%   Original selling price is 1.87587.5% which is 87.5% profit   Answer 87.5%
Answer: C
If the average of a sequence of consecutive multiple of 18 is 153, and the greatest term is 270, how many terms Q in the sequence are smaller than the average? Choose the correct choice from the following:
A) 5
B) 6
C) 7
D) 8
E) 9

Solution: Let the sequence have N terms starting 18*K   --> 18K, 18(K+1), 18(K+2), .... , 18(K+N-1) is the sequence.   The sum of the sequence is   ---> 18K + 18(K+1) + 18(K+2) + .... + 18(K+N-1) =18*(K+(K+1)+...+(K+N-1)) = 18*(N*(2K+N-1)/2).   So the average is   153=[18*(N*(2K+N-1)/2)]/N = 18*(2K+N-1)/2 = 9 *(2K+N-1) ---> by cancelling 9 we get 2K+N-118*(2 + -1)/2= 
18*(2 + -1)/2 = 9
9 *(2K+N-1) ---> by cancelling 9 we get 2K+N-1=17 --> 2K+N=18 ---*).   On the other hand, since the greatest term is 270, 18(K+N-1)=270 --> by cancelling 18 we get K+N-1=15 --> K+N=16 ---**).   By *), **) we have K=2, N=14.   Since 153/18= 
153/18 = 17/2 = around 8.5
8.5, 18*8<153<18*9. So the number of terms Q which are smaller than the average is 18*2, 18*3, ..... ,18*8 ---> 7. The answer is 7.
Answer: C
If a and b are both prime numbers greater than 10, which of the following CANNOT be true?
I. ab is an even number.
II. a-b = 117.
III. ( a + B) is even.  Choose the correct answer:
A) I, II and III  B) I only  C) I and III only  D) II and III only  E) I and II only

Solution: MANHATTAN GMATOFFICIAL SOLUTION:   Since a and b are both prime numbers greater than 10, they must both be odd. Therefore ab must be an odd number, so Statement I cannot be true. Similarly, if a and b are both odd, then a - b cannot equal 117 (an odd number). This difference must be even. Therefore, Statement II cannot be true. Finally, since a and b are both odd, a + b must be even, so Statement III will always be true. Since Statements I and II CANNOT be true, but Statement III IS true,the correct answer is (E).   Answer : I and II only
Answer: E
A and B together have Rs. 1210. If 4/15 of A's amount is equal to 2/5 of B's amount, how much amount does B have?	Choose the correct option
A) 290
B) 570
C) 500
D) 484
E) 421

Solution: (4/15) * A = (2/5) * B   A / B = 3 / 2   Therefore B's share is = (1210 * (2/5))= 
(1210 * (2/5)) = 484
484   Ans - 484
Answer: D
In how many ways the letters of the word RAIXBON be arranged?	Choose the correct choice from the following answers.
A) 2535	B) 2754	C) 2966	D) 5040	E) 6454

Solution: Total ways of arranging the letters = 7! = 5040 ways.   5040)
Answer: D
The average weight of 8 person's increases by 2 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?  Choose the correct choice from the following answers:
A) 70 kg  B) 80 kg  C) 81 kg  D) 90 kg  E) 91 kg

Solution: Total weight increased = (8 x 2) kg = 16 kg.   Weight of new person = (65 + 16)= 
(65 + 16) = 81
81 kg.   81 kg)
Answer: C
If a store adds 30 chairs to its current inventory, the total number of chairs will be the same as three-halves the current inventory of chairs. If the manager wants to increase the current inventory by 50%, what will the new inventory of chairs be?	Answers: A) 40 B) 90 C) 100 D) 140 E) 160

Solution: Explanation:   Letâ€™s say t = total current inventory of chairs. The first sentence states that 30 + t = (3/2)t. First solve for the current inventory:   30 + t = (3/2)t   30 = (3/2)t âˆ’ t   60 = (1/2)t   60 = t   The manager wants to increase this by 50%.   50% of 60 is 30, so the new inventory will be 90   Answer: 90
Answer: B
An isosceles triangle with sides 13cm,13cm and base of 10cm is inscribed in a circle with radius r.what is the value of 'r'?  Pick:  A) 3  B) 4  C) 5  D) 6  E) 7

Solution: height of triangle = (13^2 - (10/2)^2)^1/2 = 12 cm   area of triangle = abc/4r = (1/2)*base*height   => 13*13*10/ 4r = 1/2 *10*12   => r = 169/24 = 7.04   ANSW7R:7
Answer: E
A, B and C shared the profit in a business in the ratio 5 : 7 : 8. They had partnered for 28 months, 8 months and 7 months respectively. What was the ratio of their investments?  Select the correct option:
A) 10:12:14
B) 12:24:28
C) 20:22:12
D) 10:49:64
E) None of these

Solution: Explanation :   Ratio in which A,B and C shared the profit = 5 : 7 : 8   Assume that the ratio of their investment = a:b:c   Then 28a : 8b : 7c = 5 : 7 : 8   Good to go, we got the equation. Now it's a matter of time to find a, b and c   28a/8b = 5/7   => 196a = 40b   => b = 196a/40 = 49a/20 ---(1)   28a/7c =5/8   => 4a/c =5/8   =>32a = 5c   => c =32a/5 ---(2)   a : b : c = a : 196a/40 : 32a/5 = 1 : 196/40 : 32/5 = 10 : 49 : 64. Answer : Option 10:49:64
Answer: D
The cost per pound of green tea and coffee were the same in June. In July, the price of coffee shot up by 100% and that of green tea dropped by 90%. If in July, a mixture containing equal quantities of green tea and coffee costs $3.15 for 3lbs, how much did a pound of green tea cost in July?
Choose the correct choice from the following choices
A) $4	B) $0.1	C) $1	D) $3	E) $1.65

Solution: Lets assume price of Coffee in June =100x   Price of green Tea in June =100x   Price of Coffee in July = 200x (because of 100% increase in price)   Price of green Tea in July = 10x (because of 90% Decrease in price)   Price of 1.5 pound of Coffee 1.5 pound of green Tea in July will be = 300x + 15x = 315x   As per question   315x300  + 15= 
300  + 15 = 315
315x   As per question   315x= 3.15$   x = 0.01S   So the Price of green Tea in July = 10x = 10 x 0.01 = 0.1$/pound   Answer $0.1
Answer: B
Twenty identical machines, running continuously at the same constant rate, take 14 days to complete a shipment. How many additional machines, each running at the same constant rate, would be needed to reduce the time required to complete a shipment by four days?	Choose the most appropriate option:  A) 8  B) 9  C) 12  D) 14  E) 16

Solution: From the question you know that 20R = 1/14. The question asks you (partially) to make the rate from 1/14 to 1/10 (drop from 14 day to 10). So the only thing that you need to do is to find the magic number than can convert 1/14 to 1/10.   So 1/14 * x = 1/10 (1 equation with one unknown). So by solving this you get x = 14/10 or 7/5. Thats it then! Take the magic number 7/5 and multiply BOTH sides of the original equation and you have:   20*(7/5)*R = (7/5) * 1/14   4 * 7 * R = 1/10, Hence 28R = 1/10, therefore 8 more machines!   8
Answer: A
The integer 6 is the product of two consecutive integers (6 = 2 × 3) and the product of three consecutive integers (6 = 1 × 2 × 3). What is the next integer greater than 6 that is both the product of two consecutive integers and the product of three consecutive integers? Pick:	A) 153	B) 210	C) 272	D) 336	E) 600

Solution: Since the question asks the lowest possible so let us start with 153:   Any number divisible by 6 would satisfy that.   153 - 17 x 9   210 - divisible by 6 so it will have the pair 1 x 2 x 3   ANSWER:210
Answer: B
The distance between Delhi and Mathura is 155 kms. A starts from Delhi with a speed of 20 kmph at 7 a.m. for Mathura and B starts from Mathura with a speed of 25 kmph at 8 p.m. from Delhi. When will they meet?
Choose the correct choice from the following answers:  A) 10.50 a.m.  B) 11.00 a.m.  C) 10.30 a.m.  D) 11.40 a.m.  E) 1.40 a.m.

Solution: D = 155 â€“ 20 = 135   RS = 20 + 25= 
20 + 25 = 45
45   T= 135/45= 
135/45 = 3
3 hours   8 a.m. + 3 hrs= 11.00 a.m.   ANSWER:11.00 a.m.
Answer: B
How many ways can you arrange 16 people into 4 rows of 4 desks each?  Choose the correct choice from the following
A) 14! B) 15! C) 16! D) 17! E) 18!

Solution: for 1st person there are 16 places   for 2nd person there are 15 places   for 3rd ..... 14 places   no. of ways will be = 16*15*14......3*2*1   = 16!   ANSWER:16!
Answer: C
The total marks obtained by a student in Mathematics and Physics is 60 and his score in Chemistry is 20 marks more than that in Physics. Find the average marks scored in Mathamatics and Chemistry together?
Choose the correct choice:  A) 40  B) 99  C) 88  D) 77  E) 66

Solution: Let the marks obtained by the student in Mathematics, Physics and Chemistry be M, P and C respectively.   Given , M + C = 60 and C - P = 20 M + C / 2 = [(M + P) + (C - P)] / 2   = (60 + 20) / 2= 
(60 + 20) / 2 = 40
40.   40nswer:40
Answer: A
Employees of a certain company are each to receive a unique 7-digit identification code consisting of the digits 0, 1, 2, 3, 4, 5, and 6 such that no digit is used more than once in any given code. In valid codes, the second digit in the code is exactly twice the first digit. How many valid codes are there?  Choose the correct choice from the following answers:  A) 42  B) 120  C) 210  D) 360  E) 840

Solution: One can use slot method to solve this.   7 digit identification code has 7 slots to fill.   For the first slot there are three possible options. (1,2 and 3 because first digit has to be half of second)   For the second slot there are three possible options. (2,4 and 6 because second digit has to be twice the second)   To fill the first two slots there are only three possible ways. Because if the ,   if the first is 1 the second has to be 2 (only 1 way)   if the first is 2 the second has to be 4 (only 1 way)   if the first is 3 the second has to be 6 (only 1 way) . So total ways to fill first two slots = 3ways   You are now left with 5 digits and 5 slots to fill, which can be filled in 5! ways i.e. 120 ways.   Total no: of valid codes will be therefore : 120 * 3= 
120 * 3 = 360
360 ways.   Answer : 360
Answer: D
In what time will a train 50 m long cross an electric pole, it its speed be 360 km/hr?	Choose the correct choice from the following options.
A) 0.25 B) 0.5 C) 1.5 D) 2.5 E) 3.5

Solution: Speed = 360 * 5/18= 
360 * 5/18 = 100
100 m/sec   Time taken= 50/100= 
50/100 = 1/2 = around 0.5
0.5 sec.   Answer: 0.5
Answer: B
Two trains travel in opposite directions at 36 kmph and 45 kmph and a man sitting in slower train passes the faster train in 8 seconds.The length of the faster train is
Pick one:
A) 80 m
B) 100 m
C) 120 m
D) 180 m
E) 160 m

Solution: Relative speed= 81 km/h   = 81 x 5/18 m/sec   =22.5 m/sec   length of slower train= speed x time   =36 x 8 km/hr   =288 x 5/18 m/sec   =80 m/sec   Let length of faster train= b   time cross to each other 8 = (80+b)x 18/(81 x 5)   =3240-1440=18b   1800/18= b   b=100 m   ANSWER:100 m
Answer: B
A man buys 12 lts of liquid which contains 20% of the liquid and the rest is water. He then mixes it with 10 lts of another mixture with 30% of liquid. What is the % of water in the new mixture?  Options
A) 75.45  B) 76.45  C) 77.45  D) 74.45  E) 73.45

Solution: 20% in 12 lts is 2.4. So water = 12-2.4= 
12-2.4 = 9.6
9.6 lts. 30% of 10 lts= 3. So water in 2nd mixture = 10-3= 
10-3 = 7
7 lts. Now total quantity= 12 + 10= 
12 + 10 = 22
22 lts. Total water in it will be 9.6 + 7= 
9.6 + 7 = 16.6
16.6 lts. % of water= (100*16.6)/22 = 75.45   75.45NSWER:75.45
Answer: A
In how many ways can 6 arts and 3 science students be arranged in a row so that the arts and the science students are placed alternately? Choose the correct choice from the following choices
A) 2880	B) 1850	C) 3260	D) 5200	E) 4320

Solution: The six art students can be arranged in those 6 A-slots in 6! = 720 ways.   The three science students can be arranged in those 3 S-slots in 3! = 6 ways.   Total arrangements = 720*6= 
720*6 = 4_320
4320   Answer=(4320)
Answer: E
For every even positive integer m, f(m) represents the product of all even integers from 2 to m, inclusive. For example, f(12)=2x4x6x8x10x12. What is the greatest prime factor of f(36)?
Answers:  A) 2  B) 5  C) 11  D) 17  E) 23

Solution: f(36) = 2*4*6*8*10*12*14*16*18*20*22*24*26*28*30*32*34*36   The greatest prime factor in this list is 17.   The answer is 17.
Answer: D