MU-NLPC/Calc-aqua_rat huggingface dataset:
A certain restaurant offers 6 different salads, 4 different main courses, and 6 different desserts. If customers choose one salad, one main course, and two different desserts for their meal, how many different meals are possible?
Answers:  A) 240  B) 280  C) 320  D) 360  E) 400

Solution: The number of possible choices for desserts is 6C2 = 15   The number of possible meals is   6*4*15= 
  6*4*15 = 360
360   The answer is 360.
Answer: D
When positive integer X is divided by positive integer Y, the remainder is 3. If X/Y = 96.12, what is the value of Y?  Choose the correct choice
A) 96
B) 75
C) 48
D) 25
E) 12

Solution: When positive integer x is divided by positive integer y, the remainder is 3 --> x=qy+3;   x/y=96.12 --> x=96y+0.12y (so q above equals to 96);   0.12y=3 --> y=25.   Answer: 25.
Answer: D
24 men working at 8 hours a day can finish a work in 10 days. Working at the rate of 10 hours a day, the number of men required to finish the same work in 6 days is?
Options:	A) 30	B) 32	C) 34	D) 36	E) 38

Solution: Using Using the chain rule,   M1 x T1 = M2 x T2   Therefore, 24 x 8 x 10 = 10 x X x 6   X= 32   Hence, the number of men required to finish the work = 32.   ANSWER:32
Answer: B
A driver would have reduced the time it took to drive from home to the store by 1/3 if the average speed had been increased by 21 miles per hour. What was the actual average speed, in miles per hour, when the driver drove from home to the store?	Choose one:  A) 36  B) 42  C) 45  D) 48  E) 51

Solution: Let R be the original speed and let T be the original time.   Since the distance remains the same (we're just changing the rate and time), any increase in rate or time is met with a decrease in the other term. Decreasing the time by 1/3 would give us:   D = (R)(T) = (2T/3)(x*R)   x = 3/2 since (2T/3)(3R/2) = (R)(T) = D   3R/2 = R + 21   R/2 = 21   R= 42   The answer is 42.
Answer: B
Train P crosses a pole in 30 seconds and train Q crosses the same pole in one minute and 15 seconds. The length of train P is three-fourths the length of train Q. What is the ratio of the speed of train P to that of train Q?	Pick
A) 15:8	B) 15:7	C) 15:1	D) 15:3	E) 15:2

Solution: Given that train P crosses a pole in 30 seconds and train Q crosses the same pole in one minute and 15 seconds.   Let the length of train P be LP and that of train Q be LQ   given that LP = 3/4 LQ   15:8s the train P and Q crosses the pole in 30 seconds and 75 seconds respectively,   => Speed of train P = VP = LP/30   Speed of train Q = VQ = LQ/75   LP = 3/4 LQ   => VP = 3/4 LQ/(30) = LQ/40   Ratio of their speeds = VP : VQ   = LQ/40 : LQ/75 => 1/40 : 1/75 = 15:8   15:8nswer:15:8
Answer: A
Three interviewers, A, B, and C are interviewing 30 applicants. Only with three interviewers' admission can an applicant be admitted. If interviewer A admitted 10 applicants, B admitted 12 applicants, and C admitted 15 applicants, at least how many applicants get the admission?
Choose the correct choice from the following choices:
A) 6	B) 2	C) 0	D) 8	E) 12

Solution: If A admitted 10 are overlapping with B admission of 12 But C does not overlap with anybody.   Then no student will get nod from all the 3.   Hence 0 student will get admission.   Answer : 0
Answer: C
How long does a train 110 m long running at the speed of 72 km/hr takes to cross a bridge 112 m length? Pick one:
A) 82.1 sec	B) 12.1 sec	C) 16.1 sec	D) 11.1 sec	E) 12.15sec

Solution: Speed = 72 * 5/18= 
72 * 5/18 = 20
20 m/sec   Total distance covered= 110 + 112= 
110 + 112 = 222
222 m.   Required time= 222/20= 
222/20 = 111/10 = around 11.1
11.1 sec.   Answer:11.1 sec
Answer: D
If p^2 – 13p + 40 = x, and p is a positive integer between 1 and 10, inclusive, what is the probability that x < 0?	Choose the correct choice from the following answers:
A) 1/10
B) 2/5
C) 1/5
D) 3/5
E) 3/10

Solution: (p-5)(p-8) = x   p = 6 or 7 for this to be true, so   2/10 = 1/5   Ans :1/5
Answer: C
A credit card company has a cash back option for their customers which is based on the annual amount that they charge on their credit cards. The customer receives 1.5% cash on their first $5000 of purchase, 2.5% on the next $5000 of purchase and a 3% on cash back on portion that exceeds $10,000. If a customer receives a cash back of 2.2% on their total annual charges made on the credit card, then what was the customer's annual charge? Choose the correct choice from the following answers: A) $12,500 B) $15,000 C) $17,500 D) $20,000 E) $22,500

Solution: The customer receives $75 for the first $5000.   The customer receives $125 for the next $5000.   Let x be the total amount of the customer's annual charge.   $200 + 0.03(x-10,000)=0.022x   0.008x=100   x=12,500   The answer is $12,500.
Answer: A
The length of a rectangular plot is 20 metres more than its breadth. If the cost of fencing the plot @ Rs. 26.50 per metre is Rs. 4240, what is the length of the plot in metres?	Select:
A) 20	B) 200	C) 50	D) 400	E) 140

Solution: Let length of plot = L meters, then breadth = L - 20 meters   and perimeter = 2[L + L - 20] = [4L - 40] meters   [4L - 40] * 26.50 = 4240   [4L - 40] = 4240 / 26.50= 
4240 / 26.50 = 160
160   4L= 200   L = 200/4= 
200/4 = 50
50 meters. Answer: 50
Answer: C
Positive integer x has z factors; 3x has 3 factors; Which of the following values can z take?
I. 1
II. 2
III. 3	Choose the correct answer
A) I or II
B) I only holds
C) II only holds
D) II or III
E) I or III

Solution: Squares have odd number of factors.The square which is a multiple of 3 is 9.   3 has factors 1,3 .   Therefore 2 factors   Answer II only holds
Answer: C
A certain number of men can do a work in 65 days working 6 hours a day. If the number of men are decreased by one-fourth, then for how many hours per day should they work in order to complete the work in 40 days?	Choose the correct choice.
A) 17 B) 14 C) 16 D) 13 E) 11

Solution: D   13   Let the number of men initially be x. we have M1 131 H1= M2 132 H2   So, x * 65 * 6 = (3x)/4 * 40 * h2   => h2 = (65 * 6 * 4)/(3 * 40)= 
(65 * 6 * 4)/(3 * 40) = 13
13.
Answer: D
How many positive three-digit integers have an odd digit in both the tens and units place? Choose the correct choice from the following answers:	A) 25	B) 225	C) 250	D) 450	E) 500

Solution: 1. Make empty spaces and try to fill up the empty spaces one by one   2. If a condition is given, you always find the condition space and fill the condition space first.   Here we need to form a 3 digit number given 2 conditions that the tens and units digit are odd. the digits we can use here are all the digits from 0 to 9 and since nothing is mentioned about the digits being repeated or not, we always consider the with repetition case.   So making 3 empty spaces _ Odd Odd.   The total number of ways of filling the units digit is 5, since we can use any one out of 1,3,5,7 and 9. Similarly the total number of ways of filling the tens digit is 5. Now since the digits can be repeated and we need to have a 3 digit number, we can fill the hundreds digit in 9 ways, since we can use any one out of 1,2,3,4,5,6,7,8,9. We cannot use 0 since we need a 3 digit number.   So the answer here will be 9 * 5 * 5= 
9 * 5 * 5 = 225
225 ANS:225
Answer: B
In a garden, there are 10 rows and 12 columns of mango trees. The distance between the two trees is 2 metres and a distance of two metres is left from all sides of the boundary of the garden. What is the length of the garden?  Choose the correct choice from the following answers.
A) 22 B) 24 C) 26 D) 28 E) 30

Solution: Between the 12 mango trees, there are 11 gaps and each gap has 2 meter length   Also, 2 meter is left from all sides of the boundary of the garden.   Hence, length of the garden = (11 Ã— 2) + 2 + 2 = 26 meter   Answer is 26.
Answer: C
On a map, 4.5 inches represent 45 miles. How many miles approximately is the distance if you measured 254 centimeters assuming that 1-inch is 2.54 centimeters? Choose the correct choice from the following choices:
A) 1000	B) 1100	C) 1200	D) 1250	E) 1300

Solution: 1 inch = 2.54 cm   4.5 inch = 2.54 * 4.5 cm   11.43 cm = 45 miles   254 cms = 45/11.43*254= 
45/11.43*254 = 1_000
1000 miles   1000nswer : 1000
Answer: A
The average age of a class of 32 students is 12 yrs. if the teacher's age is also included, the average increases by one year. Find the age of the teacher  Choose the correct choice from the following answers:  A) 45 Years  B) 46 Years  C) 49 Years  D) 52 Years  E) 54 Years

Solution: Total age of students is 32X12 = 384 Years Total age inclusive of teacher = 33X (12+1) = 429 So, Teacher's age is 429-384= 
429-384 = 45
45 Yrs There is a shortcut for these type of problems Teacher's age is 12+(33X1)= 45 Years 45 Yearsnswer : 45 Years
Answer: A
In how many ways a committee, consisting of 5 men and 6 women can be formed from 8 men and 10 women?
Answers:
A) 524	B) 1024	C) 15247	D) 11760	E) 11470

Solution: Required number of ways	= (8C5 x 10C6)   = (8C3 x 10C4)   = 11760.   ANSWER 11760 11760
Answer: D
Find a sum for first 5 prime no's?  Pick one:
A) 23  B) 28  C) 26  D) 27  E) 29

Solution: Required sum = (2 + 3 + 5 + 7 + 11)= 
(2 + 3 + 5 + 7 + 11) = 28
28.   Note: 1 is not a prime number.   28
Answer: B
A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 37, the how old is B?
A.	7
B.	8
C.	9
D.	10
Explanation:  Pick one.
A) 5 B) 7 C) 9 D) 10 E) 14

Solution: Let C's age be x years. Then, B's age = 2x years. A's age = (2x + 2) years.   (2x + 2) + 2x + x = 37   5x = 35   x = 7.   Hence, B's age = 2x = 14 years.   Answer: Option 14
Answer: E
800 students took the test on English and Maths. 35% students failed in english and 45% failed in maths. 40% of those who passed in maths also passed in english, then how many students failed in both ? Choose the most appropriate option:
A) a) 162  B) b) 138  C) c) 16  D) d) 38  E) e) 12

Solution: Passed in english = 65%   Passed in maths = 55%   Passed in both = 40% of 55% = 2/5 * (55%) = 22%   Passed in (English + Maths - Both + Neither) 2/5 * (55 )= 
2/5 * (55 ) = 22
22%   Passed in (English + Maths - Both + Neither)= 100%   65 + 55 - 22 + Neither = 100   Neither = 100 - 98= 
100 - 98 = 2
2%= 0.02 * 800= 
0.02 * 800 = 16
16   Answer: c) 16
Answer: C
A person was asked to state his age in years. His reply was , "Take my age 4 years hence, multiply it by 4 and subtract 4 times my age 4 years ago and you will know how old I am." What was the age of the person ?  Choose the correct choice from the following
A) 18	B) 32	C) 27	D) 26	E) 19

Solution: Explanation:   Let the present age of person be x years.   Then, 4(x + 4) - 4(x - 4 ) = x <=> (4x + 16) - (4x - 16) = x <=> x = 32..   Answer: 32
Answer: B
A, B, C subscribe Rs. 50,000 for a business. If A subscribes Rs. 4000 more than B and B Rs. 5000 more than C, out of a total profit of Rs. 39,000, what will be the amount A receives?
Select
A) 14700	B) 14500	C) 14900	D) 16380	E) 14000

Solution: Total amount invested = 50000   Assume that investment of C =x.   Then investment of B =5000+x,   Investment of A =4000+5000+x=9000+x   x+5000+x+9000+x=50000   ⇒3x+14000=50000   ⇒3x=50000–14000=36000   ⇒x=36000/3= 
36000/3 = 12_000
12000   Investment of C=x=12000   Investment of B =5000+x=17000   Investment of A =9000+x=21000   Ratio of the investment of A, B and C   =21000:17000:12000   =21:17:12   Share of A = Total profit ×21/50   =39000×21/50=16380   Answer is 16380
Answer: D
The average weight of 6 person's increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?
Select:  A) 76 kg  B) 80 kg  C) 85 kg  D) Data inadequate  E) None of these

Solution: Explanation:   Total weight increased = (6 x 2.5) kg = 15 kg.   Weight of new person = (65 + 15)= 
(65 + 15) = 80
80 kg.   Answer: 80 kg
Answer: B
Find the cost of fencing around a circular field of diameter 14 m at the rate of Rs.2.50 a meter?
Choose the correct choice from the following choices:
A) 288 B) 110 C) 772 D) 592 E) 261

Solution: 2 * 22/7 * 7= 
2 * 22/7 * 7 = 44
44   44 * 2.5= Rs.110   Answer: 110
Answer: B
Winson earns $10.00 per hour for the first 40 hours he works per week, and twice this rate for overtime. If Michael earned $363 last week, how many hours did he work? Choose the correct choice
A) 43
B) 44
C) 45
D) 46
E) 47

Solution: $10*40 + $12*x = $363 --> x = 3 hours.   Total working hours = 40 + 3= 
40 + 3 = 43
43.   43nswer: 43.
Answer: A
The ratio between the present ages of P and Q is 6 : 7. If Q is 4 years old than P, what will be the ratio of the ages of P and Q after 4 years? Choose the correct choice from the following: A) 3 : 4 B) 3 : 5 C) 4 : 3 D) 7 : 8 E) None

Solution: Sol.   Let P's age and Q's age be 6x years and 7x years respectively.   Then, 7x - 6x = 4 ⇔ x = 4.   ∴ Required ratio = (6x + 4) : (7x + 4) = 28 : 32 = 7 : 8.   Answer 7 : 8
Answer: D
The radius of a circle is 4/π cm then its perimeter is?	Choose the correct option
A) 10	B) 9	C) 8	D) 12	E) 15

Solution: perimeter=2πr   2π*4/π=8 cm   Answer: 8
Answer: C
There are n cities. What is the number of airlines that connected 3 different cities (airline from city A to city B is different with airline from city B to city A)?
Choose the correct choice from the following:
A) n(n-1) B) n(n+1) C) n(n-1)/2 D) n(n+1)/2 E) n(n-2)

Solution: First of all, the possible number of airlines is n. Then, the possible number of airlines departing from one city to another becomes (n-2). Hence, the answer is n(n-2), which makes A an answer choice.   n(n-2)
Answer: E
The average of non-zero number and its square is 5 times the number. The number is?  Pick one
A) 9	B) 37	C) 98	D) 8	E) 2

Solution: Let the number be x. Then,   (x + x2)/2 = 5x => x2 - 9x = 0   => x(x - 9) = 0   => x = 0 or x = 9   So, the number is 9.   9nswer:9
Answer: A
Find the annual income derived by investing $ 6800 in 60% stock at 136.	Choose the correct choice from the following:
A) 550 B) 3000 C) 250 D) 300 E) 400

Solution: By investing $ 136, income obtained = $ 60.   By investing $ 6800, income obtained = $ [(60/136)*6800= 
(60/136)*6800 = 3_000
$ 3000.   Answer 3000.
Answer: B
If ab^2c = b^4 , which of the following must be true?
I. ac = b^2
II. b = 0
III. ac = 1  Choose the correct option:  A) none  B) I  C) II  D) III  E) I &II

Solution: to fulfill conditions some assumptions are to be made b#0 etc.   none
Answer: A
A is thrice as good a workman as B and therefore is able to finish a job in 70 days less than B. working together, they can do it in  Choose the correct choice from the following options:
A) days	B) ½ days	C) days	D) days	E) 1/4 days

Solution: Explanation:   B = 3A   3A – A =70 days   A = 35days   Then, B = 90 days   (A + B) = 35 × 90/ 120 = 26 1/4 days .   Answer: Option 1/4 days
Answer: E
15 men take 20 days of 8 hours each to do a piece of work. How many days of 6 hours each would 21 women take to do the same. If 3 women do as much work as 2 men? Options:  A) 27.57  B) 28.57  C) 29.57  D) 30.57  E) 32

Solution: 3W = 2M   15M ------ 20 * 8 hours   21 W ------ x * 6 hours   14 M ------ x * 6   15 * 20 * 8 = 14 * x * 6   x = 28.57   ANSWER:28.57
Answer: B
The length of a train and that of a platform are equal. If with a speed of 108 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is? Choose the correct option.
A) 757 B) 758 C) 718 D) 900 E) 738

Solution: Speed = [108 * 5/18] m/sec = 30 m/sec; Time = 1 min. = 60 sec.   Let the length of the train and that of the platform be x meters.   Then, 2x/60 = 30 è x = 30 * 60 / 2= 
30 * 60 / 2 = 900
900   Answer:900
Answer: D
Mark has a rectangular driveway with a line painted diagonally across. The length of the driveway is 5 feet longer than its width. If the total area of the driveway is 36 square feet, what is the length of the painted line (in feet)? Choose the correct answer:  A) between 9 and 10  B) between 10 and 11  C) between 11 and 12  D) between 12 and 13  E) between 13 and 14

Solution: To solve this, we first need to set up an equation for the area of the room. If x is the width, then we have   x(x + 5) = 36. By putting the equation in standard form, we get x^2+5x-36=0. By using the quadratic formula, we get roots of 4 and -9. We know that x is the width, and x+5 is the length, so by using the roots, we get 4 as the width (x), and 9 as the length (x+5).   Once we have this, we can use the Pythagorean Theorem to solve for the diagonal. Plugging in the length and width, we will get d^2=4^2+9^2   =16+81= 
16+81 = 97
97   The square root of 97 is less than 10, since 10^2= 100. Going down a number, we can compute 9^2 = 81 < 97. Therefore, the length of the diagonal must be between 9 and 10.   The correct answer is between 9 and 10.
Answer: A
The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle? Choose the correct choice from the following choices:
A) 18 cm
B) 20 cm
C) 24 cm
D) 28 cm
E) 38 cm

Solution: 2(l + b) = 5   b 1   2l + 2b = 5b   3b = 2l   b = 2 l   3   Then, Area = 216 cm2   l x b = 216   l x 2 l = 216   3   l2 = 324   l = 18 cm.   18 cm)
Answer: A
Nitin ranks 12th in a class of 56 students. What is rank from the last ?
Answers:
A) 33
B) 38
C) 45
D) 28
E) 19

Solution: Explanation:   Number students behind the nitin in rank = (56 - 12)= 
(56 - 12) = 44
44   Nitin is 45th from the last   Answer: 45) 45
Answer: C
In a college students can play cricket or basketball. 500 play cricket.220 played both and 600 played basketball. What is the total strength of college?
Choose the correct choice from the following
A) 800 B) 880 C) 920 D) 950 E) 980

Solution: P(C)= 500   P(880)=600   P(C n 880) =220   P(C U 880)= P(C)+ P(880) - P(C n 880)   = 500+600-220= 
500+600-220 = 880
880   ANSWER:880
Answer: B
Three numbers which are co-prime to each other are such that the product of the first two is 551 and that of the last two is 1073. The sum of the three numbers is?  Options:
A) 65  B) 67  C) 70  D) 72  E) 85

Solution: Three numbers which are co-prime to each other are such that the product of the first two is 551 and that of the last two is 1073. The sum of the three numbers is:   A.	75   B.	81   C.	85   D.	89   Answer: Option C   Explanation:   Since the numbers are co-prime, they contain only 1 as the common factor.   Also, the given two products have the middle number in common.   So, middle number = H.C.F. of 551 and 1073 = 29;   First number = 551 = 19; Third number = 1073 = 37.   29	29   Required sum = (19 + 29 + 37)= 
(19 + 29 + 37) = 85
85   85)
Answer: E
A and B started a partnership business investing Rs. 20,000 and Rs. 15,000 respectively. C joined them with Rs. 20,000 after six months. Calculate B's share in total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business?	Options.
A) 7500
B) 8500
C) 9000
D) 8000
E) 7000

Solution: Explanation:   7500 : B : C   =20000×24:15000×24:20000×18   =20×4:15×4:20×3   =4×4:3×4:4×3   =4:3:3   B's share = 25000×3/10=7500   7500nswer: Option 7500
Answer: A
Find the invalid no.from the following series 15, 16, 34, 104, 424, 2124, 12756  Select:
A) 16
B) 34
C) 104
D) 424
E) 2124

Solution: 2nd term = (1st term) * 1 + 1 = 15 *1 + 1= 
15 *1 + 1 = 16
16.   3rd term= (2nd term) * 2 + 2 = 16 * 2 + 2= 
16 * 2 + 2 = 34
34   4th term= (3th term) *3 + 3 = 34 * 3 + 3= 
34 * 3 + 3 = 105
105   5th term= (4th term) * 4 + 4 = 105 * 4 + 4= 
105 * 4 + 4 = 424
424   6th term= (5th term) * 5 + 5 = 424 * 5 + 5= 
424 * 5 + 5 = 2_125
2125   4th term should 105 instead of 104.   104
Answer: C
With what number must 1020.5 be multiplied in order to obtain the number10205? Select the correct option.
A) 10	B) 1,000	C) 10,000	D) 100,000	E) None of these

Solution: Explanation: The decimal must be moved one places to the right. To do this, we must multiply by a number with one zeroes. The correct answer is 10.The decimal must be moved one places to the right. To do this, we must multiply by a number with one zero. The correct answer is 10.   10nswer : (10)
Answer: A
Find the average of the series : 120, 148, 420, 150 and 162?	Choose the correct choice from the following:	A) 174	B) 240	C) 200	D) 202	E) 230

Solution: Average = (120 + 148 + 420 + 150 + 162)/5   = 1000/5= 
1000/5 = 200
200   Answer: 200
Answer: C
What will come in place of the x in the following Number series? 279936, 46656, 7776, 1296, 216, x
Pick one.
A) 30
B) 31
C) 36
D) 38
E) 42

Solution: Go on dividing by 6 to the next number   36)
Answer: C
In a certain game there are 8 steps, referred to as step 1, step 2, and so on with the final step being step 8. The steps are played one after the other. In each step a score of 1, 2, 3, 4, or 5 is obtained. Andrea played the game, getting at least one score of each of 1, 2, 3, 4, and 5, and never getting the same score in consecutive steps. What is the greatest possible score that Andrea could have gotten?  Pick one
A) 28 B) 29 C) 30 D) 36 E) 40

Solution: There are two conditions:   1. Andrea got at least one score of each of 1, 2, 3, 4, and 5.   2. She never got the same score in consecutive steps.   Taking that into account, the greatest possible score that Andrea could have gotten is   5 + 1 + 5 + 2 + 5 + 3 + 5 + 4= 
  5 + 1 + 5 + 2 + 5 + 3 + 5 + 4 = 30
30.   Answer: 30.
Answer: C
By selling an umbrella for Rs. 300, a shop keeper gains 100%. During a clearance sale, the shopkeeper allows a discount of 10% on the marked price. His gain percent during the sale is?  Choose the correct choice from the following choices:
A) 23.23  B) 32.32  C) 33.33  D) 30  E) 31

Solution: Marked price = Rs. 200   C.P. = 100/100 * 300 = Rs. 300   Sale price = 90% of Rs. 300 = Rs. 270   Required gain % = 100/300 * 100 = 33.33%.   Answer:33.33
Answer: C
In a family with 3 children, the parents have agreed to bring the children to the pet store and allow each child to choose a pet. This pet store sells only dogs, cats, and monkeys. If each child chooses exactly one animal, and if more than one child can choose the same kind of animal, how many different arrangements of animals could the family leave with?
Choose the most appropriate option.
A) 6 B) 8 C) 9 D) 10 E) 12

Solution: The question has a catch.. It would seem on the face of it it would be 3 x 3 x3 = 27 arrangements, but what it is asking is how many arrangements the family leaves with.. so that is going to be   Pick all 3 = 1 way   Pick all of a kind = 3 x 1 = 3 ways   Pick 2 of a kind = 3 x 1 x 2 = 6 ways   Total of 10   ANS:10
Answer: D
how many feet is 24 inches Choose one:
A) 6
B) 3
C) 2
D) 8
E) 9

Solution: 2
Answer: C
If x, y, and z are consecutive positive odd integers, not necessarily in that order, which of the following must be true? I. xz > y^2 II. (x + z)^3 > y III. x+y>z^2  Choose the correct option:  A) I only  B) I,II only  C) II,III only  D) III only  E) II only

Solution: Lets suppose that a,b,c can take any one of following three value 1,5,7. Most important point is that the options MUST BE TRUE under any condition.   x+y>z^2   Not necessarily true as 1+5<49   xz>y^2   Not necessarily true as 1.7<25   We don't need to check option as all the options except E can be discarded.   Thus Answer II only
Answer: E
Two pipe fill a empty tank in 14 hours and 16 hours respectively.when both pipe open together then it came to know that because of a hole in a tank it takes 32 more minutes to fill the tank.then in how much time that hole take to empty the full tank?  Options.
A) 125
B) 106
C) 85
D) 112
E) 76

Solution: both pipe filling work in 1 hour=[1/14+1/16]=15/112   so,time both pipe take to full the tank =112/15hour=7hour28minute   because of hole time taken to fill the tank=7 hour 28 minutes+32 minute=8 hour   all three resultant work in 1 hour=1/8   hole 1 hour empty work=[15/112-1/8]=1/112   so time taken to empty the full tank=112 hours   answer 112
Answer: D
Without stoppages, a train travels certain distance with an average speed of 200 km/h, and with stoppages, it covers the same distance with an average speed of 160 km/h. How many minutes per hour the train stops ?	Choose the correct choice from the following answers.
A) 8	B) 9	C) 10	D) 11	E) 12

Solution: Due to stoppages, it covers 40 km less .   Time taken to cover 40 km = 40â„200h = 1â„5h   = 1â„5 Ã— 60 min = 12 min   Answer 12
Answer: E