MU-NLPC/Calc-aqua_rat huggingface dataset:
Machine A takes 50 hours to complete a certain job and starts that job at 6AM. After four hour of working alone, machine A is joined by machine B and together they complete the job at 1PM. How long would it have taken machine B to complete the job if it had worked alone for the entire job? Choose the correct choice from the following answers: A) 9 B) 88.88 C) 4.88 D) 2.88 E) 3.88

Solution: Let us assume total job = 100 units   A finishes 100 units in 50 hrs(given)   Hence A (working rate)= 2 units /hr   Now Given that A works for 4 hr( so 8 units done) then A and B finish total work in 7 hours. Hence A and B finish 92 units in 3 hours. Of these 3x2=6 units were done by A. Hence B did 86 units in 3 hours.   Hence B(working rate)= 86/3 units /hr   Hence B takes 100x3/86 = 3.88 hours to complete the job.   Answer 3.88.
Answer: E
Mother is aged three times more than her daughter Rose. After 8 years, she would be two and a half times of Rose's age. After further 8 years, how many times would he be of Rose's age?  Choose the correct option.
A) A)15	B) B)2	C) C)20	D) D)21	E) E)26

Solution: Let Ronit's present age be x years. Then, father's present age =(x + 3x) years = 4x years.   (4x + 8) =	5	(x + 8)   2   8x + 16 = 5x + 40   3x = 24   x = 8.   Hence, required ratio =	(4x + 16)/(x + 16)	=	48/24= 
48/24 = 2
2.   2
Answer: B
If the average (arithmetic mean) of a list of numbers is 12 and the standard deviation of that list of numbers is 1.3, then which of the following numbers is more than two standard deviations from the mean?
I. 13.7
II. 12.3
III. 9.3  Choose the correct choice from the following choices:
A) I only B) I and II only C) II only D) III only E) I and III only

Solution: Mean = 12   SIII only = 1.3   2 SIII only above mean = 12+2*1.3= 
12+2*1.3 = 14.6
14.6   2 SIII only below mean= 12-2*1.3= 
12-2*1.3 = 9.4
9.4   12.3 and 13.7 lies in the range of 2SIII only from mean   Answer: Option III only
Answer: D
How many ways can 8 friends be arranged around a circular dinner table? Pick one
A) 1280	B) 2460	C) 5040	D) 40320	E) 85670

Solution: The number of ways to order 8 people is 8!   However, around a circular table, each pattern would be repeated 8 times.   So the number of ways to seat 8 friends around a circular table is 7! = 5040   The answer is 5040.
Answer: C
An uneducated retailer marks all his goods at 55% above the cost price and thinking that he will still make 25% profit, offers a discount of 25% on the marked price. What is his actual profit on the sales?
Select the correct option.
A) 12.50 %  B) 13.50 %  C) 14 %  D) 14.50 %  E) None

Solution: Sol.   Let C.P. = Rs. 100. Then, marked price = Rs. 155.   S.P. = 75% of Rs. 155 = Rs. 116.25.   ∴ Gain% = 16.25%.   Answer None
Answer: E
A and B start a business with Rs.6000 and Rs.18000 respectively. Hoe should they share their profits at the end of one year? Pick one:
A) 3:5  B) 3:4  C) 3:1  D) 1:3  E) 3:9

Solution: They should share the profits in the ratio of their investments.   The ratio of the investments made by A and B =   6000 : 18000 => 1:3   Answer:1:3
Answer: D
If f(x) = 12 - x^2/2 and f(2k) = 4k, what is one possible value for k?	Choices.
A) 2
B) 3
C) 4
D) 6
E) 8

Solution: First of all, see thisGMAT blog postand check the related lesson linked below for some background on function notation.   We can plug anything in for x and get a result. You can find f(1), for example, by plugging in 1 where x is, and you would get 12 - 1/2 = 11.5. Or we could find f(2), which would be  12 - 4/2= 
 12 - 4/2 = 10
10.   So the notation f(2k) means that we are going to plug a 2k in for x everywhere in the formula for f(x). That would be:   f(2k)= 12 - (2k)^2/2 = 12 - 2k^2.   Remember that we have to square both the 2 and the k, to get 4k2. Now, this expression, the output, we will set equal to 2k.   12 - 2k^2 = 2k --> k = -5 or k = 4.   All the answers are positive, so we choose k = 4.   Answer = 4
Answer: C
Two pipes A and B can fill a cistern in 12 and 15 minutes respectively. Both are opened together but after 2 minutes A is turned off. After how much more time will the cistern be filled?  Pick.
A) 8 1/7  B) 8 1/1  C) 8 1/4  D) 10 1/2  E) 8 3/7

Solution: 2/12 + (2 + x)/15 = 1   x = 10 1/2   Answer: 10 1/2
Answer: D
If MADRAS can be written as NBESBT, how can BOMBAY be written in that code ?  Choose the correct choice:
A) DHHIIIY B) CPNCBZ C) SYUOKJ D) SUOOHH E) WUHSW

Solution: Explanation:   Each letter in the word is moved one step forward to obtain the corresponding letter of the code.   Answer: CPNCBZ
Answer: B
There are two sets A and B. The range of set A is 7, and the range of set B is 13. If the two sets are combined and get a new set Y, which cannot be the range of the set Y?	Pick one:	A) 8	B) B.11	C) C.14	D) D.17	E) E.21

Solution: Let Set A has 1,8 as elements   B has 1,14 as elements.. So Range for Combined set Y becomes  14-1= 
 14-1 = 13
13   For range to be 14,   A= 1,8   B= 2,15 (Range=14)   For range to be 17   A=1,8   B= 5,18   For range to be 21:   A=1,8   B= 9 ,22   So we are left with A and B.   Now consider A has elements A= -1,-8 and Thus Range =-1-(-8)= 
-1-(-8) = 7
7   So for Range of combined set to be 11, B needs to have largest elementxso that x- (-8)=11 or x=3...But if x=3, the largest element in Combined Set then smallest element in the combined set will be 3-y=13 or y=-10....And the range of combined set 3-(-10)=13...   Consider Option A   A=-1,-8   B= y,x where y and x are smallest and largest element in Set B   Elements of Combined Set: -8,-1,y and x   Now x-(-8)= 
-(-8) = 8
8 or x=0, then x-y=13 or y=-13...   Range of Combined Set: 0-(-13)= 13...   I don't see how range can be 8 or 11...Can you please post the source and explanation for the OA in spoiler...=B.11
Answer: B
Find the face value of 6 in 654321  Choose the most appropriate option:  A) 6  B) 60000  C) 600  D) 6000000  E) 6000

Solution: Face value is the value of digit itself   face value of 6 = 6   6nswer : 6
Answer: A
If an object travels at eight feet per second, how many feet does it travel in one hour?	Choose one:
A) 34880	B) 3778	C) 12788	D) 18000	E) 28800

Solution: Explanation:   If an object travels at 5 feet per second it covers 5x60 feet in one minute, and 5x60x60 feet in one hour.   Answer = 28800   Answer: 28800) 28800
Answer: E
Two pipes A and B can separately fill a cistern in 10 and 15 minutes respectively. A person opens both the pipes together when the cistern should have been was full he finds the waste pipe open. He then closes the waste pipe and in another 4 minutes the cistern was full. In what time can the waste pipe empty the cistern when fill?  Choose one
A) 7  B) 9  C) 5  D) 4  E) 8

Solution: 1/10 + 1/15 = 1/6 * 4 = 2/3   1 - 2/3 = 1/3   1/10 + 1/15 - 1/x = 1/3   x = 8   ANSW8R 8
Answer: E
Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 64 hours respectively. The ratio of their speeds is? Pick one:
A) 4:5	B) 8:3	C) 8:4	D) 4:8	E) 4:1

Solution: Let us name the trains A and B.   Then, (A's speed) : (8:3's speed)   = √b : √a = √64 : √9   = 8:3   Answer: 8:3
Answer: B
Find the area of a parallelogram with base 15 cm and height 40 cm?
Choose the correct choice:
A) 200 cm2 B) 100 cm2 C) 42 cm2 D) 600 cm2 E) 230 cm2

Solution: Area of a parallelogram   = base * height   = 15 * 40= 
15 * 40 = 600
600 cm2   Answer: 600 cm2
Answer: D
The area of a triangle is with base 8m and height 4m? Choose the correct choice from the following answers:
A) 88 m2
B) 10 m2
C) 16 m2
D) 77 m2
E) 31 m2

Solution: 1/2 * 8 * 4= 
1/2 * 8 * 4 = 16
16 m2   Answer: 16 m2
Answer: C
What approximate value should come in place of the question mark (?) in the following equation ?
4⁄7 of 1596 + 3015 = ? – 2150	Choose the correct choice from the following answers:
A) 7200
B) 48000
C) 5300
D) 58000
E) 6070

Solution: ? ≈ 4 × 230 + 3000 + 2150   = 920 + 3000 + 2150= 
920 + 3000 + 2150 = 6_070
6070   Answer 6070
Answer: E
If a portion of a half water/half alcohol mix is replaced with 25% alcohol solution, resulting in a 30% alcohol solution, what percentage of the original alcohol was replaced?	Pick one:
A) 3%
B) 20%
C) 66%
D) 75%
E) 80%

Solution: let x be water, y - alcohol. so we have -   0.5x+0.5y -0.25y=0.3x+0.3y   x=1/4y   x/y=1/4   so in a new solution y 's portion is 4/5 or 80%   ANSW80%R:80%
Answer: E
A school’s annual budget for the purchase of student computers increased by 50% this year over last year. If the price of student computers increased by 20% this year, then the number of computers it can purchase this year is what percent greater than the number of computers it purchased last year? Answers
A) 33.33%
B) 40%
C) 25%
D) 28%
E) 60%

Solution: Lats year: budget = $100, price = $1 --> the number of computers purchased = 100/1= 
100/1 = 100
100;   This year: budget= $150, price = $1.2 --> the number of computers purchased = 150/1.2= 
150/1.2 = 125
125.   Increase in the number of computers purchased= 25%.   Answer: 25%.
Answer: C
A sells an article to B at a profit of 10% B sells the article back to A at a loss of 10%. In this transaction:  Options:	A) A neither losses nor gains	B) A makes a profit of 11%	C) A makes a profit of 20%	D) B loses 20%	E) None of these

Solution: Solution: First Method   Let CP was 100 for A originally.   A sells article to B at 10% profit,   CP for B = 100 + 10% of 100 = 110.   Now, B sells it A again with loss 10%.   Now, CP for A this time = 110 - 10% of 110 = 99.   A makes Profit = 110 - 99= 
110 - 99 = 11
11.   %profit for A= (11*100)/100 = 10%.   Second Method   It could be easily shown by net percentage change graphic.   100(A)==10%(Profit)==>110(B)==10%(Loss)==>99(A)   In this transaction A makes a profit of (110-99 = 11%) 11% .   [10% on selling to B and 1% profit on buying back from B].   Answer: Option A makes a profit of 11%
Answer: B
If the sides of a triangle are 65 cm, 60 cm and 25 cm, what is its area?  Answers.
A) 350 cm^2
B) 850 cm^2
C) 550 cm^2
D) 750 cm^2
E) 650 cm^2

Solution: The triangle with sides 65 cm, 60 cm and 25 cm is right angled, where the hypotenuse is 65 cm.   Area of the triangle   = 1/2 * 60 * 25= 
1/2 * 60 * 25 = 750
750 cm^2   Answer: 750 cm^2
Answer: D
If TIER is written as 8163 and BRAIN is written as 23415, how is RENT coded ?	Choose the correct choice:
A) 3653 B) 3658 C) 2977 D) 2790 E) 2711

Solution: Explanation:   Given :   Letter : T I E R B A N   Code : 8 1 6 3 2 4 5   Thus, the code for RENT is 3658.   ANSWER:3658
Answer: B
From a pack of cards two cards are drawn one after the other, with replacement. The probability that the first card is a queen and the second card is a jack is?	Select the correct option.
A) 1/169  B) 1/52  C) 1/26  D) 1/120  E) 1/4

Solution: Probability of a queen = 4/52 = 1/13   Probability of a jack = 4/52 = 1/13   Probability of both = P1*P2 = 1/(13*13) = 1/169   1/169nswer is 1/169.
Answer: A
How many prime numbers F exist such that 90 < F < 106 and F is a factor of 99999919?  Choose the most appropriate option:
A) 1. Zero  B) 2. One  C) 3. Two  D) 4. Three  E) 5. More than three

Solution: I found that considering the constraint..F is a prime num in between 90 to 106 not inclusive , only 3 numbers (91,97 and 101) are present but those numbers are not the factors of the number mentioned....Therefore, i doubt the answer.3. Two
Answer: C
If x and y are positive integers, and x^3*y^4 = 648, which of the following is the value of xy?	Choose one.
A) 2  B) 4  C) 6  D) 8  E) 10

Solution: 648 = 2^3*3^4   xy = 2*3= 
2*3 = 6
6   The answer is 6.
Answer: C
Abhijit started a business investing 70000. Anuja joined him after 4 months with an amount of 105000 and Sunil joined them with 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Abhijit, Anuja and Sunil respectively, three years after Abhijit started the business?	Choose the correct choice from the following answers
A) 9: 13: 26  B) 9 :12 :13  C) 8 :14: 24  D) 12:14:16  E) 8 :15: 12

Solution: Ratio of their investments   = 70 × 36 : 105 × 32: 140 × 26 = 9 : 12 : 13   Answer 9 :12 :13
Answer: B
There are 10 points on a circle. A hexagon can be formed by linking 8 of the 10 points. How many such hexagons are possible?	Pick one
A) 45  B) 120  C) 200  D) 210  E) 600

Solution: 8 points can be selected out of 10 points in 10C8 ways   =10 !/8!*2!=45   45ns 45
Answer: A
A certain bus driver is paid a regular rate of $16 per hour for any number of hours that does not exceed 40 hours per week. For any overtime hours worked in excess of 40 hours per week, the bus driver is paid a rate that is 75% higher than his regular rate. If last week the bus driver earned $1004 in total compensation, how many total hours did he work that week?  Choose the correct choice from the following answers
A) 36
B) 40
C) 44
D) 48
E) 53

Solution: For 40 hrs = 40*16= 
40*16 = 640
640   53xcess= 1004-640= 
1004-640 = 364
364   For extra hours=.75(16)=12+16= 
12+16 = 28
28   Number of extra hrs=364/28= 
364/28 = 13
13   Total hrs=40+13= 
40+13 = 53
53   Answer 53 53
Answer: E
Three friends, returning from a movie, stopped to eat at a restaurant. After dinner, they paid their bill and noticed a bowl of mints at the front counter. Sita took one-third of the mints, but returned four because she had a momentary pang of guilt. Fatima then took one-fourth of what was left but returned three for similar reason. Eswari then took half of the remainder but threw two back into the bowl. The bowl had only 17 mints left when the raid was over. How many mints were originally in the bowl? Options: A) 38 B) 31 C) 41 D) None of these E) Cannot be determined

Solution: Explanation :   Let there be x mints originally in the bowl.   Sita took 1/3 but returned 4. So, noe the bowl haa (2x/3) + 4 mints   Fatima took 1/4 of the remainder but returned 3. So, the bawl now has (3/4)((2x/3) + 4) + 3 mints.   Eshwari took half of the remainder that is (1/2) [ (3/4) ( (2x/3) + 4 ) + 3 ]   She returns 2, so the bawl now has   => (1/2) [ (3/4) ( (2x/3) + 4) + 3 ] + 2 = 17.   => x = 48.   Answer : None of these
Answer: D
How many liters of water must be evaporated from 50 liters of a 4-percent sugar solution to get a 10-percent solution?  Select:
A) 30
B) 32
C) 34
D) 36
E) 38

Solution: 4% of a 50 liter solution is 2L which is 10% of the solution at the end.   The solution at the end must be 20 L.   We need to evaporate 30 liters.   The answer is 30.
Answer: A
A batsman makes a score of 64 runs in the 16th innings and thus increased his average by 3. Find his average after the 16th inning?  Choose the correct choice from the following choices
A) 17	B) 21	C) 22	D) 23	E) 24

Solution: Let the average after the 16th inning be P.   So, the average after the 15th inning will be (P-3) Hence, 15(P-30) + 62 = 16P => P = 17.   17NSWER:17
Answer: A
In a certain furniture store, each week Nancy earns a salary of $240 plus 5% of the amount of her total sales that exceeds $800 for the week. If Nancy earned a total of $450 one week, what were her total sales that week ?
Select:	A) $2,200	B) $3,450	C) $4,200	D) $4,250	E) $5,000

Solution: 450 = 240 + (5/100)*(Total Sales - 800)   i.e. (Total Sales - 800) = 20*(450-240) = 20*210= 
20*210 = 4_200
4200   i.e. Total Sales= 4200 + 800= 
4200 + 800 = 5_000
5000   Answer: Option $5,000
Answer: E
If B + A < B - A < A - B, which of the following is correct? Choose the correct choice from the following answers:  A) A<B<0  B) B<A<0  C) B<0<A  D) 0<B<A.  E) B>A>0.

Solution: Check first inequality   B<a<0 +="" -="" -2a<-2b<a<0="" -ve="" <="" a="" a<-a="" another="" b<a<0="" check="" equality="" is="">B<a<0 0="" both="" combining="">A>B<A<0   Option B<A<0 fits only   Ans B<A<0</a<0></a<0>
Answer: B
80,873,72,72,64,81,56,?
Pick: A) 96 B) 98 C) 89 D) 90 E) 88

Solution: odd place numbers 80, 72, 64, 56 are divisible by 8.   even place numbers 873, 72, 81 are divisible by 9,so required number is in even place, from options 90 is only value visible by 9, so 90 is the answer.   ANSWER:90
Answer: D
What is the sum of all the numbers between 300 and 1000 which are divisible by 179? Select the correct option:
A) 2506
B) 2550
C) 2450
D) 3000
E) 3500

Solution: 358/179 â€¦.. 895/179   179(2 + 3 + 4 + 5) => 2506   2506NSWER 2506
Answer: A
A table is bought for Rs.600/- and sold at a loss of 12% find its selling price  Choose the correct choice:  A) s.500/-  B) s.530/-  C) s.528/-  D) s.600/-  E) s.700/-

Solution: 100 % ------> 600 (100 * 6 = 600)   88 % ------> 528 (88 * 6 = 528)   Selling price = Rs.528/-   s.528/-
Answer: C
Two Equal Amounts of Money are lent out at 6% and 5 % simple Interest respectively at the same time. The former is recovered two years earlier than the latter and the amount so recovered in each case is Rs.2800. Determine the amount that is lent out? Answers:
A) 3348 B) 368 C) 37077 D) 1750 E) 2701

Solution: Explanation:   Let the first amount lent for t + 2 years and second at t years. and amount = P   Now amount = P + P×t×6100P×t×6100 = P×(t+2)×5100P×(t+2)×5100 = 2800.   Equating first two parts, we get t×6100=(t+2)×5100t×6100=(t+2)×5100   ⇒ t = 10.   Now P+P×10×6100=2800P+P×10×6100=2800   ⇒ 1610P=28001610P=2800   ⇒ P = 1750.   Answer: 1750
Answer: D
Three sets of 40, 50 and 60 students appeared for an examination and the pass percentage was 50, 90 and 75 respectively. the pass percentage of the whole set is
Choices.
A) 73.33%
B) 73.44%
C) 74.33%
D) 85.33%
E) 71.33%

Solution: Explanation:   total passed student =20+45+45= 
20+45+45 = 110
110   110 is 73.33% of 150   73.33%NSWER:73.33%
Answer: A
For 600 km journey it will take 8hrs, if 120 km is done by bus and the rest by car. It takes 20 minutes more, if 200 km is done by busand the rest by car. The ratio of the speed of the train to that of the cars is?	Choices
A) 1:2  B) 3 : 4  C) 1:4  D) 2:5  E) 3:7

Solution: Let the speed of the train be x km/hr and that of the car be y km/hr.   Then, 120 + 480 = 8 1 + 4 = 1 ....(i)   x y x y 15   And, 200 + 400 = 25 1 + 2 = 1 ....(ii)   x y 3 x y 24   Solving (i) and (ii), we get: x = 60 and y = 80.   Ratio of speeds = 60 : 80 = 3 : 4   3 : 4
Answer: B
the sum of 4th and 20th term of A.P. is equal to the sum of 8th , 15th and 12 th term . find the term which is 0 Select.
A) 10 B) 7 C) 11 D) 5 E) 3

Solution: t4 + t20 = t8 + t15 + t12   => a+3d + a+19d = a+7d + a+14d + a+11d   => a + 10d = 0   => t11 = 0 i.e. 11th term is zero.   ANSWER: 11
Answer: C
Train A & B leave from same station and reaches same destination but train A leaves half an after Train B & travels 2 times faster than B. Total distance is 100 miles & train B travels 50 miles/hour. Which train reaches the destination first & what is the time difference between the train	Choose the correct choice from the following choices.
A) Train A reaches 30 minutes before Train B
B) Train B reaches 30 minutes before Train A
C) Train A reaches 60 minutes before Train B
D) Train B reaches 60 minutes before Train A
E) None of the above

Solution: Time taken for train Train A reaches 30 minutes before Train B = 30 minutes + d1/s1 = 30 minutes + 100 / 100= 
+ 100 / 100 = 1
1 hours 30 minutes   Since Train B travels 50 miles / hour ; train Train A reaches 30 minutes before Train B travels twice the speed of B which gives s1= 100 miles/ hour   Time taken for train B = d2/s2 = 100 / 50= 
100 / 50 = 2
2 Hours   So Train Train A reaches 30 minutes before Train B reaches 30 minutes before Train B   Train A reaches 30 minutes before Train Bnswer: Train A reaches 30 minutes before Train B
Answer: A
Seven children â€” A, B, C, D, E, F, and G â€” are going to sit in seven chairs in a row. The children C & F have to sit next to each other, and the others can sit in any order in any remaining chairs. How many possible configurations are there for the children? Choices.
A) 600  B) 720  C) 1440  D) 4320  E) 4800

Solution: There are six different pairs of â€œnext to each otherâ€ chairs. For each pair, children C & F could be in either order, so thatâ€™s  6*2= 
 6*2 = 12
12 possibilities for these two.   Now, consider the other five children. For any configuration of C & F, the remaining five children could be seated in any order among the five remaining seats. Five items in any order â€” thatâ€™s a permutation of the 5 items â€”- 5P5= 5! = 120. For any single configuration of C & F, there are 120 ways that the other children could be seated in the remaining seats.   Finally, weâ€™ll combine with the Fundamental Counting Principle. We have 12 ways for the first two, and 120 ways for the remaining five. Thatâ€™s a total number of configurations of  12*120= 
 12*120 = 1_440
1440. Answer= 1440
Answer: C
Find the odd man out. 18, 27, 36, 38, 45 Choose the correct choice from the following choices.
A) 18  B) 27  C) 36  D) 45  E) 38

Solution: All numbers except 38 are multiples of 9   Answer is 38
Answer: E
If 222 = 6
333 = 12
444 = 20
Then, 555 = ?? Select the correct option:	A) 30	B) 35	C) 40	D) 45	E) 50

Solution: 222=2*2+2= 
2*2+2 = 6
6   333=3*3+3= 
3*3+3 = 12
12   444=4*4+4= 
4*4+4 = 20
20   555=5*5+5= 
5*5+5 = 30
30   30NSWER:30
Answer: A
A room is 15m long, 4m broad and 3m height. Find the cost of white washing its four walls at 50p per m2 ?	Options.
A) 28  B) 57  C) 58  D) 83  E) 73

Solution: Explanation:   2 *3(15 + 4) = 114   114 * 1/2 = Rs.57   Answer: Option 57
Answer: B
If a2 + b2 + c2 = 281 and ab + bc + ca =4, then a + b + c is	Answers:
A) 16	B) 18	C) 22	D) 17	E) 20

Solution: by formula ,   (a + b + c)^2= a^2 + b^2 + c^2 + 2(ab + bc + ca),   since, a^2 + b^2 + c^2 = 281 and ab + bc + ca = 4,   (a + b + c)^2 = 281 + 2(4)   = 289   = 17^2   therefore: a + b + c = 17   ANSWER:17
Answer: D
Of all the students in a certain dormitory, 1/2 are first-year students and the rest are second-year students. If 4/5 of the first-year students have not declared a major and if the fraction of second-year students who have declared a major is 2 times the fraction of first-year students who have declared a major, what fraction of all the students in the dormitory are second-year students who have not declared a major?  Choose one
A) 1/15 B) 1/5 C) 4/15 D) 3/10 E) 2/5

Solution: tot students=x   1st year student=x/2----> non majaor=4/5(x/2)-----> maj=1/5(x/2)   2nd year student=x/2---->maj=2(1/5(x/2))=2/10(x)--->non major=x/2-2/10(x)=3/10(x)   hence 3/10   3/10
Answer: D
How many integers between 400 and 1000 are there such that their unit digit is odd?  Choose the correct choice from the following answers.
A) 250	B) 150	C) 300	D) 400	E) 450

Solution: There are 600 numbers from 401 to 1000 (inclusive).   Half of the numbers are odd, so there are 300 odd numbers.   The answer is 300.
Answer: C
Divide $450 among A,B in the ratio 1:4. How many $ that A get?
Answers:
A) $90	B) $500	C) $150	D) $250	E) $600

Solution: Sum of ratio terms = 1+4= 
1+4 = 5
5   $90= 450*1/5= 
450*1/5 = 90
$90   $90nswer is $90
Answer: A
If 16,666 – n is divisible by 11, and 0 < n < 11, what is n? Choose the correct choice from the following.
A) 1 B) 3 C) 5 D) 7 E) 9

Solution: 16,666 / 11 = 1515 with a remainder of 1.   We need to subtract the remainder to get a multiple of 11.   The answer is 1.
Answer: A
If 3f+ 1 < 2f < 9 - f, which of the following must be true?
I. -1 < f < 3
II. f < -1
III. f < 3  Select.
A) II only  B) III only  C) I and II only  D) II and III only  E) I, II and III

Solution: Just try plugging f in a number like 0 or 1, and you'll quickly find that the inequality doesn't hold.   So you can immediately cross out any answers with I or III, leaving just (II only) II only.
Answer: A
Two trains 150 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is? Choose the correct choice from the following.
A) 10.7	B) 10.9	C) 10.26	D) 11.16	E) 18.8

Solution: Relative speed = 60 + 40= 
60 + 40 = 100
100 km/hr.= 100 * 5/18 = 250/9 m/sec.   Distance covered in crossing each other = 150 + 160= 
150 + 160 = 310
310 m.   Required time= 310 * 9/250= 
310 * 9/250 = 279/25 = around 11.16
11.16 sec.   Answer:11.16
Answer: D