MU-NLPC/Calc-aqua_rat huggingface dataset:
In how many ways can 7 distinct objects be divided among three people so that either one or two of them do not get any object?	Choices.
A) 281
B) 304
C) 316
D) 381
E) 391

Solution: Case 1: Two guys don't get anything. All items go to 1 person. Hence, 3 ways.   Case 2: 1 guy doesn't get anything. Division of 7 items among 2 guys. Lets say they are called A & B.   a) A gets 6. B gets 1. 7 ways.   b) A gets 5. B gets 2. 21 ways.   c) A gets 4. B gets 3. 35 ways.   d) A gets 3. B gets 4. 35 ways.   e) A gets 2. B gets 5. 21 ways.   f) A gets 1. B gets 6. 7 ways.   Total = 126 ways to divide 7 items between A & B.   Total number of ways for case 2 = 126*3= 
126*3 = 378
378 (Either A, or B, or C don't get anything).   Answer= Case 1 + Case 2 = 3 + 378= 
3 + 378 = 381
381   ANSWER:381
Answer: D
A basket has 5 apples and 4 oranges. Three fruits are picked at random. The probability that at least 2 apples are picked is ?
Select:
A) 27/42	B) 25/499	C) 25/45	D) 25/41	E) 25/42

Solution: Total fruits = 9   Since there must be at least two apples,   = 25/42.   27/42nswer: 27/42
Answer: A
A dishonest dealer professes to sell goods at the cost price but uses a weight of 800 grams per kg, what is his percent? Choose the most appropriate option:
A) 15%
B) 25%
C) 65%
D) 45%
E) 35%

Solution: Explanation:   800 --- 200   100 --- ? => 25%   Answer: 25%
Answer: B
X and Y are two points respectively on sides AB and AC of triangle ABC such that XY is parallel to BC. If the ratio of area of triangle AXY to that of the trapezium XYCB is 25:144 and XY=13 cm, then find the length of BC.  Choose the correct choice from the following choices: A) 12 B) 13 C) 14 D) 11 E) 15

Solution: ABC and AXY are similar triangles.   So (side of ABC/side of AXY)^2=169/25   side of ABC/side of AXY = 13/5   So the length of BC = 5   Answer - 11
Answer: D
8 couples (husband and wife) attend a dance show "Nach Baliye' in a popular TV channel ; A lucky draw in which 4 persons picked up for a prize is held, then the probability that there is atleast one couple will be selected is :
Pick:	A) 15/38	B) 15/39	C) 15/31	D) 15/32	E) 15/34

Solution: Explanation:   P( selecting atleast one couple) = 1 - P(selecting none of the couples for the prize)   =   Answer: 15/39) 15/39
Answer: B
Look at this series: 0.25, 1.75, ____, 85.75, 600.25, ... What number should fill the blank?  Pick: A) 11.25 B) 12.25 C) 13.25 D) 9.25 E) 10.75

Solution: This is a simple multiplication series. Each number is 7 times greater than the previous number.   Answer: 12.25
Answer: B
In how many years does a sum of Rs. 5000 yield a simple interest of Rs. 16500 at 15% p.a.?	Choose the correct choice from the following answers:	A) 22 years	B) 67 years	C) 88 years	D) 55 years	E) 33 years

Solution: T = (100 * 16500)/(15 * 5000)= 
(100 * 16500)/(15 * 5000) = 22
22 years.22 yearsnswer: 22 years
Answer: A
How many even number in the range between 10 to 170 inclusive are not divisible by 3  Choose the correct choice:
A) 15	B) 30	C) 31	D) 33	E) 54

Solution: We have to find the number of terms that are divisible by 2 but not by 6( as the question asks for the even numbers only which are not divisible by 3)   For 2,   10,12,14...170   using AP formula, we can say 170 = 10 + (n-1) *2   or n=81.   For 6,   12,18,...168   using AP formula, we can say 168 = 12 + (n-1) *6   or n=27.   Hence, only divisible by 2 but not 3 = 81-27= 
81-27 = 54
54. hence, Answer 54
Answer: E
Find the mean proportional between 49 & 64?	Choose the most appropriate option:
A) A)59	B) B)61	C) C)56	D) D)65	E) E)67

Solution: Formula = √a×b   A = 49 and B = 64   √49×64 = 7 × 8 = 56   56
Answer: C
The sum of all the integers a such that -26 < a < 24 is Choose the correct option:  A) 0  B) -2  C) -25  D) -49  E) -51

Solution: Easy one -   -25, -24, -23,-22,...... -1,0, 1, 2...., 22, 23   Cancel everyhitng and we're left with - -25 and -24 a = -49.   -49 is the answer.
Answer: D
A is thrice as good a workman as B and therefore is able to finish a job in 60 days less than B. working together, they can do it in
Options:
A) 20 days
B) 22 ½ days
C) 25 days
D) 30 days
E) 35 days

Solution: Explanation:   B = 3A   3A – A =60 days   A = 30days   Then, B = 90 days   (A + B) = 30 × 90/ 120 = 45/2 = 22 ½ days .   Answer: Option 22 ½ days
Answer: B
After taking N tests, each containing 100 questions, John had an average of 70% of correct answers. How much does John need to score on the next test to make his average equal 70%?
M13-03.  Choose one.
A) N−35  B) N+69  C) 2N+70  D) 2N+72  E) 2N−35

Solution: Say N=1.   So, after 1 test John has 70 correct answers.   In 2 tests, so in 200 questions he needs to have  0.70*200= 
 0.70*200 = 140
140 correct answers, so in the second test he must get   140-70= 
  140-70 = 70
70 questions correctly.   Now, plug N=1 into the answer choices to see which one yields 70. Only option D fits.   Answer: N+69.
Answer: B
If a committee of 3 people is to be selected from among 5 married couples so that the committee does not include two people who are married to each other, how many C such committees are possible?  Choose the correct option:
A) 20
B) 40
C) C=50
D) C=80
E) C=120

Solution: Each couple can send only onerepresentativeto the committee. Let's see in how many ways we can choose 3 couples (as there should be 3 members) each to send onerepresentativeto the committee: 5C3=10.   But these 3 chosen couples can send two persons (either husband or wife): 2*2*2=2^3=8.   Total # of ways: 5C3*2^3=80.   Answer: C=80.
Answer: D
If a sample of data has mean of 20 and SD of 3, which of the following values is more than 2.6 SDs from the mean?	Choose the most appropriate option.
A) 13 B) 14 C) 12 D) 15 E) 16

Solution: 2.6 SD's mean is equal to: +/- 2.6*3 = +/- 7.8   ie. 12.2 to 27.8   Answer is: 12
Answer: C
Calculate the cost of j bottles of wine given that the cost of k bottles of said wine is c rupees? Choose the correct choice from the following options.
A) Rs.(c*k)
B) Rs.(j*k)
C) Rs.(j-k)
D) Rs.(c/k)
E) Rs.(jc/k)

Solution: Cost of k bottles = Rs. c.   Cost of 1 bottle = Rs.	c/k   Cost of j bottles = Rs.(c/k)* j= Rs.(jc/k)   Answer is Rs.(jc/k).
Answer: E
The average of 21 numbers is 44. Average of the first 11 of them is 48 and that of the last 11 is 41. Find the 11th number?  Choices:	A) 48	B) 51	C) 47	D) 49	E) 55

Solution: Sum of all the 21 numbers = 21 * 44= 
21 * 44 = 924
924Sum of the first 11 of them= 11 * 48= 
11 * 48 = 528
528Sum of the last 11 of them= 11 * 41= 
11 * 41 = 451
451So, the 11th number= 528 + 451 - 924= 
528 + 451 - 924 = 55
55.Answer: 55
Answer: E
A boat goes 100 km downstream in 10 hours, and 75 m upstream in 15 hours. The speed of the stream is?
Answers
A) 2 9 ½ kmph B) 8 2 ½ kmph C) 2 7 ½ kmph D) 2 2 ½ kmph E) 3 2 ½ kmph

Solution: 100 --- 10 2 2 ½ kmphS = 10   ? ---- 1   75 ---- 15 US = 5   ? ----- 1 S = (10 - 5)/2   = 2 2 ½ kmph   Answer: 2 2 ½ kmph
Answer: D
Laxmi and Prasanna set on a journey. Laxmi moves northwards at a speed of 15 kmph and Prasanna moves southward at a speed of 45 kmph. How far will be Prasanna from Laxmi after 60 minutes ? Options:  A) 11  B) 50  C) 28  D) 27  E) 60

Solution: Explanation:   We know 60 min = 1 hr   Total northward Laxmi's distance = 15 kmph x 1hr = 15 km   Total southward Prasanna's distance = 45 kmph x 1hr = 45 km   Total distance between Prasanna and Laxmi is = 15 + 45= 
15 + 45 = 60
60 km.   Answer: 60
Answer: E
A car covers a distance of 624 km in 6 ½ hours. Find its speed?	Pick one
A) 106 kmph
B) 104 kmph
C) 114 kmph
D) 108 kmph
E) 110 kmph

Solution: 104 kmph   104 kmph     624/6= 
  624/6 = 104
104 kmph
Answer: B
The line C represented by which of the following equation does not intersect with the line represented by y = 3x^2+5x+1	Options: A) y = 2x^2+5x+1 B) y = x^2+5x+2 C) y = 3x^2+5x+2 D) y = 3x^2+7x+2 E) y = x^2+7x+1

Solution: concept of slope for linesparabolas are different. Bunuel, please correct if I am wrong. Also please help to solve this problem if its a GMAT type question.   The general form of parabolic equ. is y^2= 4ax which implies the axis is x or x^2 = 4ay where axis is y.   We have a similar form as x^2 = 4ay.   here the vertex is origin.   So if we have same values of x and y but constant term changes then we will have parallel parabolas.   This is same as for straight line C which are parallel for different values of constant term c   ax + by +c1 = 0 and ax +by+ c2 =0   We have quadratic equations. These equations when drawn give parabolas, not lines. The question is: which of the following parabolas does not intersect with the parabola represented by y=3x^2+5x+1.y = 3x^2+5x+2
Answer: C
On July 1 of last year, total employees at company E was decreased by 10 percent. Without any change in the salaries of the remaining employees, the average (arithmetic mean) employee salary was 10 percent more after the decrease in the number of employees than before the decrease. The total of the combined salaries of all the employees at Company E after July 1 last year was what percent W of thatbeforeJuly 1 last year? Choose the correct choice from the following answers
A) 90%	B) 99%	C) 100%	D) 101%	E) 110%

Solution: the total number of employees = n   the average salary = x   total salary to all emplyoees = xn   after   the total number of employees = n - 0.1n = 0.9n   the average salary = x + 10% of x = 1.1x   total salary to all emplyoees = 0.9n (1.1x)   total salary after as a % of total salary before W= [0.9n (1.1x)]/xn= 0.99 or 99%=99%
Answer: B
If X = 2 + 1/(1+1/(1-1/2))then the value of 6x+7/3? Choose the correct answer:
A) 9 2/3  B) 16 1/3  C) 11  D) 11 2/3  E) 12

Solution: X = 2 + 1/(1+1/(1-1/2))   = 2 + 1/(1+2)   = 2 + 1/3   X = 7/3 ==> 6X + 7/3 => 6(7/3) + 7/3   ==> 42/3 + 7/3   ==> 49/3   ==> 16 1/3.   16 1/3)
Answer: B
A security guard at a certain store is instructed to check the receipt of one out of every five customers as they are leaving the store. If, on the guard's shift, 15 customers leave the store, how many different samples of customers could have been selected to have their receipts checked?	Choose one:
A) 20
B) 105
C) 59
D) 90
E) 100

Solution: to choose the sample of 2 customers from 15. it can be done 15C2 possible ways.   So the answer is 105 105
Answer: B
A photo-mat shop charges $0.55 for the first photo inside a film, and 30% cents less for each additional photo. How many photos can we develop with $52.58 if each film contains 32 photos?	Choose the correct answer
A) 4 films and 12 photos
B) 5 films and 6 photos
C) 5 films and 14 photos
D) 6 films and 4 photos
E) 6 films and 28 photos

Solution: 1st photo = 0.55   Subsequent = 0.55*0.6= 
0.55*0.6 = 0.33
0.33   Price of 1 full film=0.55+0.33*35= 
0.55+0.33*35 = 12.1
12.1   Price of 4 full film= 12.1*4= 
12.1*4 = 48.4
48.4   52.58-48.4= 
52.58-48.4 = 4.18
4.18   4.18=0.55+0.33x   x=11   52.58--->5 full films and 1+11=14 photos   Answer: 5 films and 14 photos
Answer: C
A and B together can do a piece of work in 30 days. A having worked for 16 days, B finishes the remaining work alone in 44 days. In how many days shall B finish the whole work alone?
Choose the correct option.
A) 30 days	B) 40 days	C) 50 days	D) 60 days	E) 70 days

Solution: Let A's 1 day's work = x and B's 1 day's work = y.   Then, x + y =1/30 and 16x + 44y = 1.   Solving these two equations, we get: x =1/60	and y =1/60   B's 1 day's work =	1/60	.   Hence, D alone shall finish the whole work in 60 days.   Answer : 60 days
Answer: D
A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?	Choices.
A) 286	B) 278	C) 255	D) 150	E) 287

Solution: Speed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train   = (Speed x Time) = (50/3 * 9)= 
(50/3 * 9) = 150
150 m.   Answer:150
Answer: D
Buses leave town B at 3 pm and every 10 hours after that. Buses leave town C at 4pm and every 15 hours after that. If the buses follow this schedule beginning on a Monday, what is the earliest day A on which the buses leave at the same time. Select:
A) A=Tuesday	B) Wednesday	C) Thursday	D) Sunday	E) A=The busses will never leave at the same time

Solution: The answer is E.   I think the best way to do it is to look at the times on a 24 hour clock. Town B busses start at 15:00, and Town C start at 16:00. If you think about it that way, then for Town B you'd add 10 hours each time, and the number will always end in a 5. Town C you'd add 15 hours each time, and the numbers would always end in a 1 or 6. So you can see they'd never coincide.   Alternatively, you could see that if they left at the same time, they'd coincide every 30 hours, but since C is one hour ahead of B, every 30 hours C will still be one hour ahead of B.A=The busses will never leave at the same time
Answer: E
In what ratio should the profit of Rs.8000 be divided if X starts a business with an investment of Rs. 20000, Y invests Rs.7500 for 4 months and Z invests Rs.15000 after 3 months from the start of the business.
Choose the correct choice from the following answers:
A) 16 : 2 : 3  B) 8 : 3 : 6  C) 16 : 2 : 9  D) 6 : 9 : 1  E) None of these

Solution: Explanation:   Let the profit of X be P1, that of Y be P2 and of Z be P3.   P1:P2:P3 = 20000*12 : 7500*4 : 15000*9 = 240 : 30 : 135 = 80 : 10 : 45   = 16 : 2 : 9   ANSWER: 16 : 2 : 9
Answer: C
If the circus were to sell all of its 220 tickets for this month's performance at its usual price, the revenue from sales would be 10% greater than that collected last month. If the circus raised the ticket price by 5% and sold only 205 tickets as a result, what percent less would last month's revenue be compared to this month's revenue?
Choices.
A) 2	B) 5	C) 6100/861	D) 110/20	E) 9/4

Solution: Let price be 10/ticket   then 220 tickets for this month's performance at its usual price=2200   which is 10%greater than last month(let X)---->x(1+10/100)=2200----->x=2000   now new revenue this month=205*10.5= 
205*10.5 = 2_152.5
2152.50   as per question asked 2000=2152.50(1-A/100)----->A=6100/861%   Ans 6100/861
Answer: C
How long does a train 180 meters long running at the rate of 54 kmph take to cross a bridge 660 meters in length?	Choose the correct option.
A) 33 B) 56 C) 55 D) 82 E) 62

Solution: Explanation:   T = (660 + 180)/54 * 18/5= 
(660 + 180)/54 * 18/5 = 56
56   Answer: Option 56
Answer: B
In the junior basketball league there are 21 teams, 1/3 of them are bad and ½ are rich. What can't be the number of teams that are rich and bad?	Select the correct option.
A) 4.
B) 6.
C) 7.
D) 8.
E) 11.

Solution: total teams =21   bad teams=(1/3)*21= 
(1/3)*21 = 7
7   rich teams=10   so maximum value that the both rich and bad can take will be 10. so E= 11 can not be that value.   ans 11..
Answer: E
A certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 2 of 10 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions?	Pick:
A) 42 B) 70 C) 140 D) 165 E) 315

Solution: 1C7*2C10 = 7*45= 
7*45 = 315
315   the answer is (315)
Answer: E
The average age of applicants for a new job is 10, with a standard deviation of 8. The hiring manager is only willing to accept applicants whose age is within one standard deviation of the average age. Assuming that all applicants' ages are integers and that the endpoints of the range are included, what is the maximum number of different ages of the applicants?	Pick one
A) 8
B) 16
C) 17
D) 18
E) 34

Solution: Minimum age = Average - 1 Standard deviation = 10 - 8= 
10 - 8 = 2
2   Maximum age= average + 1 Standard deviation = 10+ 8= 
10+ 8 = 18
18   Maximum number of different ages of the applicants= 18 - 2 + 1= 
18 - 2 + 1 = 17
17   Answer 17
Answer: C
Robert purchased $2000 worth of US saving bonds. If bonds are sold in $50 or $100 denominations only, which of the following CANNOT be the number of US saving bonds that Robert purchased?
Choose the correct option.
A) 20 B) 27 C) 30 D) 60 E) 70

Solution: I started off with looking at the answer choices... 20-27-30 are in a tight range, so my guess was to look and rule out the bigger numbers.   The total amount is $3000. So with 70 bonds, each $50 = $3500 , we already exceed the $3000 limit. Hence 70 is the answer.
Answer: E
The 8 spokes of a custom circular bicycle wheel radiate from the central axle of the wheel and are arranged such that the sectors formed by adjacent spokes all have different central angles, which constitute an arithmetic series of numbers (that is, the difference between any angle and the next largest angle is constant). If the largest sector so formed has a central angle of 80°, what fraction of the wheel’s area is represented by the third largest sector?	Answers.
A) 1/72	B) 1/6	C) 1/18	D) 1/12	E) 1/9

Solution: Its an AP question .... it is given clearly in the question .   Let the smallest angle be a   and the circle has 8 sectors and hence 8 angle with a common difference d   hence all the angles can be written in AP form with Cd as d ,   a, a+d, a+2d, a+3d ,a+4d, a+5d, a+6d ,a+7d,   given that a+7d = 80 --------1   also   a + a+d + a+2d + a+3d +   a+4d + a+5d + a+6d + a+7d = 360 ( as sum of all the angle is 360)   which is 8a + 28d = 360 --------2   solving 1 and 2   we get a=10   We are almost done ,   now the question ask what fraction of the wheel’s area is represented by the smallest sector ?   (60/360)( pie r*r)/ (pie r*r) = 60/360= 1/6   1/6 ans ....
Answer: B
Find the unit digit in the product 274*318*577*313	Choices:
A) 5 B) 2 C) 10 D) 26 E) 89

Solution: Explanation:   Required digit=Unit digit is in(4*8*7*3)=2   Answer 2
Answer: B
The sum of two numbers is 528 and their H.C.F is 33.The number of pairs of numbers satisfying the above conditions is: Pick one.
A) 4 B) 6 C) 8 D) 12 E) none of these

Solution: Let the required numbers be 33a and 33b.Then,33a+33b=528,   a+b=16.   now, co-primes with sum 16 are (1,15), (3,13), (5,11)and(7,9);   required numbers are (33*1,33*15), (33*3,33*13), (33*5,33*11), (33*7, 33*9).   The number of such pairs is 4.   Correct Options:4
Answer: A
In a function they are distributing noble prize. In how many ways can 3 prizes be distributed among 5 boys when No boy gets more than one prize?  Choose one:	A) 12	B) 14	C) 17	D) 24	E) 60

Solution: Sol. In this case, repetitions are not allowed. So, the first prize can be given in 5 ways. The second in 4 ways and the third in 3 ways. But fundamental principle, (5 x 4 x 3) ways = 60 ways   60
Answer: E
If a: b :: 3 : 4, then what is (5a+6b): (a-2b)?  Choices:
A) 57:11	B) -57:11	C) 11 : 10	D) -39 : 5	E) -1 : 10

Solution: a/b= 3/4   -39 : 5ividing numerator & denominator of ' (5a+6b)/(a-2b) 'by b,   [5(a/b)+6]/[(a/b)-2]= [5*(3/4)+6]/[(3/4)-2]= -39/5   ANSWER:-39 : 5
Answer: D
If 40% of the 880 students at a certain college are enrolled in biology classes, how many students at the college are NOT enrolled in a biology class? Select:  A) 540  B) 528  C) 530  D) 520  E) 510

Solution: We know 37.5 % people study biology,therefore the no of people not studying = 100 - 40= 
100 - 40 = 60
60%   > Therefore the people not studying biology out of a total 880 people are= 60 % of 880   >   (60/100)*880= 
  (60/100)*880 = 528
528 people   528
Answer: B
How many integers between 1 and 10^20 are such that the sum of their digits is 2?	Choose the correct choice: A) 190 B) 210 C) 211 D) 230 E) 231

Solution: The integers with a sum of 2 are:   2, 20, 200,...,2*10^19 and there are 20 integers in this list.   Also, these integers have a sum of 2:   11   101, 110   1001, 1010, 1100   etc...   The number of integers in this list is 1 + 2 + ... + 19   Thus, the total number of integers is 1 + 2 + ... + 19 + 20 = 20*21/2= 
20*21/2 = 210
210   The answer is 210.
Answer: B
If g(x) = ax^5 + bx^3 + 5, and g(5) = 10, then g(–5) =?  Choose the correct option:
A) – 10 B) – 8 C) – 6 D) 0 E) 4

Solution: g(5) = 10   or, 5^5 a + 5^3 b + 5 = 10   or, 5^5 a + 5^3 b = 5   g(-5) = -5^5 a - 5^3 b + 5 = - (5^5 a + 5^3 b) + 5 = - 5 + 5= 
- 5 + 5 = 0
0= (0)
Answer: D
The average mark obtained by 22 candidates in an examination is 49. The average of the first ten is 55 while the last eleven is 40 .The marks obtained by the 11th candidate is ?
Choices:
A) 22 B) 0 C) 99 D) 88 E) 66

Solution: It is clear that 22 x 49 = 10 x 55 + K + 11 x 40 ⇒⇒ K = 88   Answer:88
Answer: D
In how many ways can a cricket eleven be chosen out of a batch of 15 players ? Answers
A) 1365
B) 5263
C) 4512
D) 7845
E) 1549

Solution: Required number of ways = 15c11 = 15c(15-11) = 11c4   = 15x14x13x12/4x3x2x1 = 1365.   1365ns: 1365
Answer: A
A shopkeeper has 280 kg of apples. He sells 50% of these at 20% profit and remaining 60% at 30% profit. Find his % profit on total.	Choose the correct choice from the following choices.
A) 24%  B) 25%  C) 26%  D) 28%  E) 35%

Solution: If the total quantity was 100   Then 50X 20% + 60 X30%= 28   This profit will remain same for any total quantity unless the % of products remains the same. Hence '28%' is the answer
Answer: D
A number is doubled and 9 is added. If the resultant is trebled, it becomes 75. What is that number?
Choices.
A) 3.5 B) 6 C) 8 D) None of these E) Cannot be determined

Solution: Solution   Let the number be x.   Then, 3(2x + 9)	‹=› 75   ‹=› 2x+9 = 25   ‹=› 2x= 16   x= 8.   Answer 8
Answer: C
A brick measures 20 cm * 10 cm * 7.5 cm how many bricks will be required for a wall 24 m * 2 m * 0.75 m?  Select the correct option:  A) 29798  B) 27908  C) 24000  D) 25000  E) 27991

Solution: 24 * 2 * 0.75 = 20/100 * 10/100 * 7.5/100 * x   24 = 1/100 * x => x   = 24000   Answer: 24000
Answer: C
A bullet train is moving at a speed of 132 km/hr. If the length of the bullet train is 110 metres, how long will it take to cross a railway platform 165 metres long? Options:
A) 5 ½ sec	B) 9 ½ sec	C) 3 ½ sec	D) 7 ½ sec	E) 6 ½ sec

Solution: D   7 ½ sec   Speed of train = 132 *(5/18) m/sec = 110/3 m/sec.   Distance covered in passing the platform = (110 + 165)= 
(110 + 165) = 275
275 m.   Time taken=275 *(3/110) sec =15/2 sec = 7 ½ sec
Answer: D
If x is an odd integer and y = 2x + 8, which of the following CANNOT be a divisor of y? Choose the correct choice from the following:	A) 10	B) 14	C) 18	D) 21	E) 22

Solution: x takes odd values as 1,3,5,7.,   y=2x+8   x is an odd term so 2x must be an even term when it adds with 8 so it must be a even integer   21 didn't follows this condition ans is 21
Answer: D
Due to 10% decrease in the price of sugar and John can buy 3kg more sugar in Rs100 , then find the CP of sugar? Answers.
A) s. 1(2/9)
B) s. 2(2/9)
C) s. 2(1/9)
D) s. 3(19/27)
E) s. 4(2/9)

Solution: Here r = 10 % ,x = 100 and A = 3 kg   Actual price of sugar = 10*100/((100-10 )*3) = Rs. 3(19/27)   s. 3(19/27)
Answer: D
Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:	Choose the correct choice from the following.
A) 1 : 3	B) 3 : 2	C) 3 : 4	D) 4:2	E) None of these

Solution: Explanation:   Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 27 x meters, and length of the second train = 17 y meters. (27 x + 17 y) / (x + y) = 23 ==> 27 x + 17 y = 23 x + 23 y ==> 4 x = 6 y ==> x/y = 3/2.   ANSWER IS 3 : 2
Answer: B
A bag contains 7 red, 9 blue and 5 green balls. If 3 balls are picked at random, what is the probability that both are red?	Choose one:	A) 2/21	B) 3/41	C) 5/26	D) 1/38	E) 5/32

Solution: P(Both are red),   =7C3/21C3=(7*6*5)/21*20*19   =1/38   1/38
Answer: D
In what ratio should a variety of rice costing Rs. 6 per kg be mixed with another variety of rice costing Rs. 8.75 per kg to obtain a mixture costing Rs. 7.50 per kg?  Choose the correct choice from the following answers.
A) 5/6
B) 6/5
C) 7/3
D) 5/9
E) 5/3

Solution: Let us say the ratio of the quantities of cheaper and dearer varieties   = x : y   By the rule of allegation,   x/y = (87.5 - 7.50) / (7.50 - 6) = 5/6   5/6nswer:5/6
Answer: A