MU-NLPC/Calc-aqua_rat huggingface dataset:
Nicole cycles at a constant rate of 10 kilometers per hour, and is passed by Jessica, who cycles at a constant rate of 30 kilometers per hour. If Jessica cycles at her constant rate for x minutes after passing Nicole, then stops to wait for her, how many minutes will Jessica have to wait for Nicole to catch up to her?
Options
A) x
B) x/2
C) 2x/3
D) 3x/2
E) 2x

Solution: In x minutes, Jessica travels (x/60)*30 = x/2 miles   The time it takes Nicole to travel x/2 miles is (x/2) / 10 = x/20 hours = 3x minutes   Jessica needs to wait 3x - x = 2x minutes.   The answer is 2x.
Answer: E
A fruit seller had some oranges. He sells 40% oranges and still has 540 oranges. How many oranges he had originally?	Answers
A) 700  B) 900  C) 720  D) 730  E) 740

Solution: 60% of oranges = 540   100% of oranges =(540×100)/6=900   total oranges = 900   ANSWER : 900
Answer: B
Count the two-digit whole numbers which yield a remainder of 5 when divided by 10 and also yield a remainder of 0 when divided by 3?
Choose the correct choice from the following
A) Two B) Five C) Three D) One E) Six

Solution: Answer = Three) Three   Two digit Numbers giving remainder 5 when divided by 10 = 15, 25, 35, 45, 55, 65, 75, 85, 95   The numbers giving remainder 0 when divided by 3 = 15, 45, 75 = 3
Answer: C
Find the amount on Rs.7000 in 2 years, the rate of interest being 4% per first year and 5% for the second year?  Choose the correct answer:
A) 5568  B) 6369  C) 5460  D) 7644  E) 6734

Solution: 7000 * 104/100 * 105/100= 
7000 * 104/100 * 105/100 = 7_644
> 7644   Answer:7644
Answer: D
A car is traveling 75 kilometers per hour. How many meters does the car travel in one minute? Choose the correct choice from the following options: A) 2,250 meters / minute B) 1,250 meters / minute C) 5,250 meters / minute D) 6,250 meters / minute E) 4,250 meters / minute

Solution: Convert hour into minutes ( 1 hour = 60 minutes) and kilometers into meters (1 km = 1000 m) and simplify   75 kilometers per hour = 75 km/hr   = (75 * 1000 meters) / (60 minutes) = 1,250 meters / minute   correct answer 1,250 meters / minute
Answer: B
Find the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.1120? Choices:
A) 1000
B) 1067
C) 1977
D) 1056
E) 1097

Solution: 1120 = P [1 + (5*12/5)/100]   P= 1000   1000nswer: 1000
Answer: A
If two typists can type two pages in two minutes, how many typists will it take to type 49 pages in seven minutes?
Choose the most appropriate option:  A) 3  B) 4  C) 6  D) 12  E) 14

Solution: In 2 minutes 2 typists type 2 pages which means that in 7 minutes they will type 7 pages but to type 49 pages (7 times) we need 7 times more typists i.e. 2 x 7 = 14 typists.   14
Answer: E
If a < 0, c > 0, and b > 5, which of the following is true?
I. a * b * c > 0
II. a * b * (-c) < 0
III. a^2 * b * c > 0 Choose the most appropriate option:
A) I only  B) II only  C) III only  D) I and III only  E) I, II, and III

Solution: I. Not true, example: a = -1, b = 6, and c = 1, so a * b * c= -6   II. Not true, a and (-c) are both negative and b is positive so the product will be positive   III. True, a^2 is positive and so are b and c so the product is positive   III only
Answer: C
In a school with 632 students, the average age of the boys is 12 years and that of the girls is 11 years. If the average age of the school is 11 years 9 months, then the number of girls in the school is
Choose the correct answer.
A) 150
B) 200
C) 250
D) 158
E) None

Solution: Sol.   Let the number of grils be x.   Then, number of boys = (632 - x).   Then, (11 3/4 × 632)   ⇔ 11x + 12(632 - x) ⇔ x = 7584 - 7426 ⇔ 158.   Answer 158
Answer: D
Two spherical balls lie on the ground touching. If one of the balls has a radius of 10 cm, and the point of contact is 12 cm above the ground, what is the radius of the other ball (in centimeters)?	Choose the correct answer.
A) 14	B) 15	C) 16	D) 18	E) 20

Solution: A straight line will join the two centers and the point of contact, thus making similar triangles.   2/10 = (r-12)/r   2r = 10r - 120   r = 15   The answer is 15.
Answer: B
In an examination, 5% of the applicants were found ineligible and 85% of the eligible candidates belonged to the general category. If 4275 eligible candidates belonged to other categories, then how many candidates applied for the examination?
Choose the correct choice from the following choices:
A) 28000  B) 30000 candidates  C) 32000  D) 33000  E) None of these

Solution: Explanation :   Let the number of candidates applied for the examination = x   Given that 5% of the applicants were found ineligible.   It means that 95% of the applicants were eligible (∴ 100% - 5% = 95%)   Hence total eligible candidates = 95x/100   Given that 85% of the eligible candidates belonged to the general category   It means 15% of the eligible candidates belonged to other categories(∴ 100% - 85% = 15%)   Hence Total eligible candidates belonged to other categories   = total eligible candidates × (15/100) = (95x/100) × (15/100)   = (95x × 15)/(100 × 100)   Given that Total eligible candidates belonged to other categories = 4275   ⇒ (95x × 15)/(100 × 100) = 4275   ⇒ (19x × 15)/(100 × 100) = 855   ⇒ (19x × 3)/(100 × 100) = 171   ⇒ (x × 3)/(100 × 100) = 9   ⇒ x/(100 × 100) = 3   ⇒ x = 3 × 100 × 100 = 30000   Answer : Option 30000 candidates
Answer: B
The number b yields a remainder p when divided by 15 and a remainder q when divided by 7. If p = q + 7, then which one of the following could be the value of b ? Choose the most appropriate option:
A) 45	B) 52	C) 66	D) 80	E) 96

Solution: I solved this question in the following way:   Q<7 so Q can be from 0 to 6 and P<15 so P can be from 0 to 14, BUT the constraint is P=Q +7 so this will mean that P can be in the range from 7 to 14.   b=15k + P or b= 15k + 7 to 14 and look at the answer as, place different values for k, 52 will give 52 which is 15*3 + 7, the other answers are out of the range
Answer: B
A trader bought a car at 20% discount on its original price. He sold it at a 55% increase on the price he bought it. What percent of profit did he make on the original price?  Choose the most appropriate option.
A) 17% B) 24% C) 12% D) 82% E) 16%

Solution: Original price = 100   CP = 80   S = 80*(155/100)= 
80*(155/100) = 124
124   100 - 124= 24%   Answer:24%
Answer: B
The average of 10 numbers is calculated as 16. It is discovered later on that while calculating the average, the number 45 was incorrectly read as 25, and this incorrect number was used in the calculation. What is the correct average? Options
A) 17  B) 18  C) 22  D) 26  E) 36

Solution: The total sum of the numbers should be increased by 20.   Then the average will increase by  20/10= 
 20/10 = 2
2.   The correct average is 18.   The answer is 18.
Answer: B
A fill pipe can fill 1/2 of cistern in 10 minutes. In how many minutes, it can fill 1/2 of the cistern? Choose the correct choice from the following choices.
A) 1 min
B) 4 min
C) 6 min
D) 10 min
E) 25min

Solution: Required time = 10*2*1/2= 
10*2*1/2 = 10
10 minutes   Answer is 10 min
Answer: D
20 carrots on a scale weigh 3.64 kg. When 4 carrots are removed from the scale, the average weight of the 16 carrots is 180 grams. What is the average weight (in grams) of the 4 carrots which were removed?  Select the correct option
A) 160
B) 170
C) 180
D) 190
E) 200

Solution: 16*180= 
16*180 = 2_880
2880.   The other 4 carrots weigh a total of 760 grams.   The average weight is  760/4= 
 760/4 = 190
190 grams.   The answer is 190.
Answer: D
For a certain art exhibit, a museum sold admission tickets to a group of 30 people every 5 minutes from 9:00 in the morning to 5:55 in the afternoon, inclusive. The price of a regular admission ticket was $10 and the price of a student ticket was $5. If on one day 3 times as many regular admission tickets were sold as student tickets, what was the total revenue from ticket sales that day?  Pick:  A) $24960  B) $25920  C) $28080  D) $28350  E) $29160

Solution: From 9:00 in the morning to 5:55 in the afternoon, inclusive there are 9*12= 
9*12 = 108
108 five-minute intervals, thus total of 108*30 tickets were sold.   Say x student and 3x regular tickets were sold, then x+3x=108*30 --> x=27*30 and 3x=3*(27*30)=27*90.   Therefore, the total revenue from ticket sales that day was 27*30*5+27*90*10=$28,350.   Answer: $28350.
Answer: D
40 is subtracted from 60% of a number, the result is 50. Find the number? Answers
A) 150  B) 152  C) 278  D) 267  E) 261

Solution: (60/100) * X – 40 = 50   6X = 900   X = 150   150nswer:150
Answer: A
If a - b =4 and
a2+b2=52
, find the value of ab.	Choose the most appropriate option: A) 8 B) 26 C) 18 D) 42 E) 36

Solution: Explanation:   We know   2ab=(a2+b2)âˆ’(aâˆ’b)2   2ab=52âˆ’16=36   =>ab=18   Option 18
Answer: C
The Simplistic language has only 2 unique values and 3 unique consonants. Every noun in Simplastic has the structure CVCVC, where C stands for a consonant and V stands for a vowel. How many different nouns are possible in Simplastic?
Choose the most appropriate option.
A) 9	B) 12	C) 36	D) 72	E) 108

Solution: The nouns have fixed structure C-V-C-V-C. Now, each C can take 3 values (let's say X, Y or Z) and each V can take 2 values (let's say A or E), so there will be 3*2*3*2*3= 
3*2*3*2*3 = 108
108 nouns possible.   Answer: 108.
Answer: E
In a sample of associates at a law firm, 30 percent are second-year associates, and 60 percent are not first-year associates. What percentage of the associates at the law firm have been there for more than two years?	Pick one:
A) 10	B) 20	C) 30 %	D) 40	E) 50

Solution: Let the sample be 100.   Given 60% are not first year i.e. there could be second year (x) and more than 2 years(y) possibility.   60% = (x) + y   Given 30% = second year (x)   club both , we get y = 30%.   Answer: option 30 % is correct answer.
Answer: C
Braun invested a certain sum of money at 8% p.a. simple interest for 'n' years. At the end of 'n' years, Braun got back 7 times his original investment. What is the value of n?
Choose the correct choice from the following:  A) 50 years  B) 25 years  C) 12 years 6 months  D) 37 years 6 months  E) 75 years

Solution: Explanatory Answer   Let us say Braun invested $100.   Then, at the end of 'n' years he would have got back $700.   Therefore, the Simple Interest earned = 700 - 100= 
700 - 100 = 600
$600.   We know that Simple Interest= (Principal * number of years * rate of interest) / 100   Substituting the values in the above equation we get 600 = (100 * n * 8) / 100   Or 8n = 600   Or n = 75 years.   correct choice is (75 years)
Answer: E
Of the books standing in a row on a shelf, an atlas is the 30th book from the left and the 33rd book from the right. If 2 books to the left of the atlas and 5 books to the right of the atlas are removed from the shelf, how many books will be left on the shelf?  Choices: A) 55 B) 57 C) 58 D) 61 E) 63

Solution: 100%. There are total of   30+33-1= 
  30+33-1 = 62
62 books and   2+5= 
  2+5 = 7
7 books are removed, thus 62-7= 
62-7 = 55
55 books are left.   55nswer: 55.
Answer: A
If a is the sum of u consecutive positive integers. b is the sum of v consecutive positive integers. For which of the following values of u and v is it impossible that a = b?  Options
A) u = 2; v = 6	B) u = 3; v = 6	C) u = 7; v = 9	D) u = 10; v = 7	E) u = 10; v = 4

Solution: I approached this in a different way, although may be longer but it's certainly more intuitive   It is impossible that a = b if one of them is necessarily even while the other is necessarily odd   for two consecutive integers the sum is necessarily odd   for six consecutive integers the sum is necessarily odd (sum of 3two consecutive integerswhich are all odd)   Thus A is incorrect.   The sum of 3 consecutive integers can be even or odd (an odd integer from the first 2 + an additional integer which can be even or odd). Thus B is incorrect. You can do a similar approach for C and D (it follows that the sum of a specified odd number of consecutive integers can be odd or even).   Leaving us with E to be the only not-wrong answer. To confirm, you can easily deduce that the sum of 4 consecutive integers (sum of 2 odd integers) is necessarily even while the sum of 10 consecutive integers (sum of 5 odd integers) is necessarily odd. Thus u = 10; v = 4 is the right answer.
Answer: E
X and Y are positive integers. If X is a prime factor of Y^2 , which of the following MUST be true?  Pick one
A) X is even  B) X=Y^2  C) Y/X is even  D) X/Y is less than or equal to 1  E) X+1 is also a prime factor of Y^2

Solution: A. x is even --> not necessarily true: x=3=odd x=3=odd and y=3y=3;   B. x=y^2 --> never true, as x=primex=prime then it can not equal to square of another integer;   C. y/x is even --> not necessarily true: if x=3x=3 and y=3y=3 then yx=1=odd yx=1=odd;   D. x/y is less than or equal to 1 --> always true as shown above or by POE;   E. x+1 is also a prime factor of y^2 --> not necessarily true: if x=2x=2 and y=2y=2 then x+1=3x+1=3 and 3 is not a factor of y2=4y2=4.   Answer: X/Y is less than or equal to 1.
Answer: D
Which of the following is the product of two integers whose sum is 13?	Choose the correct choice from the following choices:	A) -42	B) -28	C) 12	D) 26	E) 32

Solution: I solved this Question like this,   Let the two integers are x,y   x+y=13 (Given)   xy=? (Needed)   instead of solving this algebraically, Test the Answer choices   C. 12   Do the factorization : (1,12)----> There sum is 13 Bingo!!!!   So, my answer is C...   As the answer is in C, it took me very less time to answer the question. but i think this method is be simple and efficient.
Answer: C
A, B and C invest in the ratio of 3 : 4: 5. The percentage of return on their investments are in the ratio of 6 : 5 : 4. Find the total earnings, If B earns Rs. 150 more than A :  Choose the correct choice
A) 2348 B) 7250 C) 4350 D) 1998 E) 2771

Solution: Explanation:   A B 4350   investment 3x 4x 5x   Rate of return 6y% 5y% 4y%   Return \inline \frac{18xy}{100} \inline \frac{20xy}{100} \inline \frac{20xy}{100}   Total = (18+20+20)= 
(18+20+20) = 58
\inline \frac{58xy}{100}   B's earnings - A's earnings= \inline \frac{2xy}{100} = 150   Total earning = \inline \frac{58xy}{100} = 4350   Answer: 4350) Rs.4350
Answer: C
If x and y are integers such that x^2= 2y and xy = 32, then x – y = ? Answers:
A) -30
B) -20
C) -5
D) -4
E) 20

Solution: here x and y are integers .   x^2=2y,xy =32.   substitute (x^2)/2=y in xy => x^3=32*2=>x^3=64.   here X3 is positive ,   X is also positive.   x=4 then y=8.   X-y=-4   so option -4 is correct
Answer: D
A certain sum of money is divided among A, B and C such that A gets one-third of what B and C together get and B gets two-seventh of what A and C together get. If the amount received by A is $15 more than that received by B, find the total amount shared by A, B and C.  Select.
A) $250
B) $340
C) $640
D) $440
E) $540

Solution: A = 1/3 (B+C) => C = 3A - B ---(1)   B = 2/7 (A+C) => C = 3.5 B - A --(B)   A-B = $15   A = 15+B   (1)===> C = 45+3B - B = 2B+45 ==> 2B-C = -45 ---(3)   (2)===> C = 3.5 B - B-15 = 2.5B-15==>2.5B-C = 15---(4)   from (4) and (3) 0.5B = 60   B = $120   A= $135   C =405-120= 
405-120 = 285
$285 Total amount= 135+120+285= 
135+120+285 = 540
$540   Answer: $540
Answer: E
find the number of 6 digit numbers that can be formed using digits 1,2,3,4,5,6 once such that the 6digit number is divisible by its unit digit.
Options
A) 648 B) 649 C) 650 D) 651 E) 652

Solution: when unit digit 1,2,3,5,6 then no. formed will be divisible by the digit at the unit place.   => 5*5p5 numbers   when unit place is 4, tenth place should be 2 or 6   => 2*4p4 numbers   total = 5*5p5 + 2*4p4 = 5*5! + 2*4! = 648   648NSWER:648
Answer: A
In the rectangular coordinate system Point O has coordinates (0,0) and Point B has coordinates (2,2) and if point A is equidistant from points O and B and the area of the triangle OAB is 16, which of the following are the possible coordinates of point A.	Choose one
A) (-2,6)  B) (0,4)  C) (2,-6)  D) (2,6)  E) (4,0)

Solution: Area.pngSince A is equidistant from points O and B, then it must be somewhere on the green line (perpendicular bisector of OB).   (2,-6) and (2,6) are not on that line. If A is at (0,2) or (2,0), then the area is 1/2*2*2= 
1/2*2*2 = 2
2. Thus A must be at (4,0).   Answer: (4,0).
Answer: E
3 candidates in an election and received 1136, 7636 and 11628 votes respectively. What % of the total votes did the winningcandidate got in that election?	Choose the correct choice from the following answers
A) 45%
B) 47%
C) 57%
D) 60%
E) 62%

Solution: Total number of votes polled = (1136 + 7636 + 11628)= 
(1136 + 7636 + 11628) = 20_400
20400   So, Required percentage= 11628/20400 * 100= 
11628/20400 * 100 = 57
57%   57%
Answer: C
In Orange County one eighth of the people are gathering mushrooms and one seventh of the people are collecting apples. What can be the number of people in Orange County? Choose the correct choice from the following answers:
A) 60.
B) 42.
C) 85.
D) 142.
E) 112.

Solution: The number must be an integer and multiple of both 8 and 7.   Only option 112. fulfill this condition and hence is the answer.
Answer: E
In how many ways can 6 apples (identical) be distributed among 3 children? (Some children may get no apples.) Answers.
A) 32  B) 34  C) 36  D) 28  E) 30

Solution: Generalised form for n = number of identical objects, and r = number of children is n+r-1Cr-1.   n=6 r= 3   8C2 =28   Answer : 28
Answer: D
Two employees A and B are paid a total of Rs. 570 per week by their employer. If A is paid 150 percent of the sum paid to B, how much is B paid per week?  Select the correct option: A) s.130 B) s.140 C) s.150 D) s.228 E) s.282

Solution: Let the amount paid to A per week = x   and the amount paid to B per week = y   Then x + y = 570   But x = 150% of y = 150y/100 = 15y/10   ∴15y/10 + y = 570   ⇒ y[15/10 + 1] = 570   ⇒ 25y/10 = 570   ⇒ 25y = 5700   ⇒ y = 5700/25 = Rs.228   s.228)
Answer: D
If X, Y and Z are consecutive numbers (X>Y>Z). X +2Y +3Z = 5Y + 4. What is the value of Z?
Choose the correct option:  A) 6.  B) 5.  C) 4.  D) 3.  E) 2.

Solution: Let the 3 consecutive integers be k-1 (Z), k (Y) and k+1 (X). Given : X +2Y +3Z = 5Y + 4.   k+1 + 2k + 3k - 3   +2  +3= 
  +2  +3 = 5
5Y + 4.   k+1 + 2k + 3k - 3= 5k+ 4 => k =6.   Thus Z = k-1 = 5.   ANSWER:5.
Answer: B
Four students, Jackie, Mandy, Bertrand, and Tao, took a science quiz. If Mandy scored 30% higher than Bertrand did, Tao scored 20% lower than Jackie did, and Jackie scored 40% higher than Mandy did, how much lower did Bertrand score than Tao?
Choose the correct choice from the following choices:
A) 50% lower B) 20% lower C) 5% lower D) 40% lower E) 30% lower

Solution: In this word problem, the first key is to turn the story into equations:   Mandy scored 30% higher than Bertrand did: M = 0.30 + B   Tao scored 20% lower than Jackie did: T = J - 0.20   Jackie scored 40% higher than Mandy did: J = 0.40 + M   Then, in classic GMAT style, the problem doesn't ask you to solve for a single variable, but instead to solve for the difference between B and T (how much higher did Bertrand score than Tao did?). This means that your goal is to get the equations in terms of B and T so that you can solve for the expression B - T.   Taking the first equation and solving for B, you have B = M - 0.30.   Taking the second equation and solving for T you have T = J - 0.20, and then with the third equation you can replace J with 0.40 + M so that both B and T are in terms of M: T = (0.40 + M) - 0.20.   So if B = M - 0.30 and T = M + 0.20, then:   B - T = (M - 0.30) - (M + 0.20)   B - T = M - 0.30 - M - 0.20 (remove the parentheses by distributing the multiplication)   B - T = -0.50, so the answer is 50% lower.
Answer: A
How many times digit 20 is used while writing numbers from 100 to 500?  Choose the correct option:
A) 20	B) 30	C) 15	D) 25	E) 20

Solution: in 100 to 200 there are 5 20's   in 200 to 300 there are 5 20's   in 300 to 400 there are 5 20's   in 400 to 500 there are 5 20's   so, total 20 is 20's   CORRECT OPTION : 20
Answer: A
The sale price sarees listed for Rs.400 after successive discount is 10% and 5% is?	Select the correct option
A) 321	B) 276	C) 342	D) 265	E) 162

Solution: Explanation:   400*(90/100)*(95/100)= 
400*(90/100)*(95/100) = 342
342   Answer: 342
Answer: C
Find the middle one when The sum of three consecutive even numbers is 42?
Pick
A) 10 B) 12 C) 14 D) 15 E) 16

Solution: 3 consecutive numbers can be a - 1, a, a + 1   So sum of numbers = 3a = 42.   Hence a = 14.   14
Answer: C
A shopkeeper buys mangoes at the rate of 4 a rupee and sells them at 3 a rupee. Find his net profit or loss percent?	Choose the correct choice from the following.
A) 31%  B) 38 1/3%  C) 33 1/3%  D) 33%  E) 35%

Solution: C   33 1/3%   The total number of mangoes bought by the shopkeeper be 12.   If he buys 4 a rupee, his 33 1/3%P = 3   He selling at 3 a rupee, his SP = 4   Profit = SP - 33 1/3%P = 4 - 3= 
4 - 3 = 1
1   Profit Percent= 1/3 * 100 = 33 1/3 %
Answer: C
A train 100 meters long completely crosses a 300-meter long bridge in 40 seconds. What is the speed of the train in km/h?
Choices:	A) 28 km/h	B) 32 km/h	C) 36 km/h	D) 40 km/h	E) 44 km/h

Solution: speed = distance / time = (100 + 300)/40 = 400/40 (m/s) * 3600/1000 = 36 km/h   The answer is 36 km/h.
Answer: C
Henrikh lives x blocks from his office. It takes him 1 minute per block to walk to
work and 20 seconds per block to ride his bicycle to work. If it takes him exactly
10 minutes more to walk to work than to ride his bicycle, then x equals	Options:
A) 4
B) 7
C) 10
D) 15
E) 20

Solution: The best way would be...   Per km, he takes 40 secs extra if he walks   So he will take 10 mins or 10*60 secs in 10*60/40= 
10*60/40 = 15
15 km   ANSWER:15
Answer: D
A cube is painted red on all faces. It is then cut into 27 equal smaller cubes. How many cubes are painted on only 2 faces?
Answers.
A) 12	B) 8	C) 6	D) 10	E) 16

Solution: The mini-cubes with 2 painted sides are ALL on the edge of the cube, in the "middle" of the edge.   There are 4 in front, 4 in back and 4 more on the "strip" that runs around the left/top/right/bottom of the cube.   4 + 4 + 4= 
4 + 4 + 4 = 12
12.   12nswer 12
Answer: A
Which of the following is equal to the value of 2^6 + 2^6 + 3^6 + 3^6 + 3^6 ?
Answers:
A) 2^7  B) 2^7 + 3^7  C) 3^7  D) 2^8 + 3^8  E) 2^7 + 3^8

Solution: 2^6 + 2^6 + 3^6 + 3^6 + 3^6   = 2 (2^6) + 3 (3^6)   = 2^1 (2^6) + 3^1 (3^6)   = 2^(1+6) + 3^(1+6)   = 2^7 + 3^7   Ans: 2^7 + 3^7
Answer: B
For how many integer values of n will the value of the expression 4n + 7 be an integer greater than 1 and less than 40? Choose the correct choice:	A) 10	B) 12	C) 14	D) 16	E) 18

Solution: 4n+7 > 1   4n> -6   n > -(3/2)   n> -1.5 (n = -1, 0, 1 ,2 3........ upto infinity)   From second constraint   4n+7 < 40   4n< 33   n < 8. 25   n = (-infinity, .......-3, -2, -1, 0, 1, 2, .........upto 8)   Combining the two   -1.5 < n<8.25   n = 1 to 8 (48 integers)   and n = -1 and 0   so 10 integers.   10
Answer: A
Points A, B, C, and D, in that order, lie on a line. If AB = 3 cm, AC = 4 cm, and BD = 9 cm, what is CD, in centimeters?  Choose the most appropriate option.
A) 1 B) 8 C) 3 D) 4 E) 5

Solution: Putting a value to each point, lets use the following:   A - 0   B - 3 (AB = 3)   C - 4 (AC = 4)   D - 12 (BD = 9)   CD is 12-4= 
12-4 = 8
8.   Ans 8
Answer: B
A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?  Choose the correct choice from the following
A) 40 sec B) 22 sec C) 27 sec D) 17 sec E) 37 sec

Solution: Speed = 45 * 5/18 = 25/2 m/sec   Total distance covered = 360 + 140= 
360 + 140 = 500
500 m   Required time= 500 * 2/25= 
500 * 2/25 = 40
40 sec   40 secnswer:40 sec
Answer: A
A and B enter into a partnership with capitals in the ratio 2 : 3. At the end of 9 months, A withdraws from the business. If their profits are in the ratio 1 : 2, how long did B invest his capital?
Pick one.
A) 12 months	B) 8 months	C) 10 months	D) 14 months	E) None of these

Solution: Explanation:   Let the initial investment of A and B be Rs. 2x and Rs. 3x respectively.   Let B invested for a period of y months.   Then, ratio of capitals of A and B   = (2x × 9) : (3x × y) = 1 : 2   => 18x/(3x × y) = 1/2   => 6/y = 1/2   => y = 12   Hence, B's investment is for 12 months.   12 monthsnswer: Option 12 months
Answer: A