MU-NLPC/Calc-aqua_rat huggingface dataset:
If –2 < x < 2 and x ≠ 0, which of the following inequalities must be true?
I. x^3 < x
II. x^2 < |x|
III. x^4 – x^5 > x^3 – x^2	Select.
A) I only  B) II only  C) III only  D) II and III only  E) I, II, and III

Solution: Answer is D. Let's look at the statements one by one   Stmt I. x^3 < x   if 0<x<1 -1<x<0="" but="" if="" then="" x="" x^3="" x^3<="">x   So this statement is not always true   Stmt II. x^2 < |x|   Because we know that x is a number less than one but not equal to zero then x^2 will always be less than |x|.   Why? think of positive fractions (and you can think in terms of positive fractions because the inequality is in regards to |x|). Lets set x </x<1>= 1/2, then x^2 = 1/4 and 1/4<1/2   So Stmt II is always true   Stmt III. x^4 – x^5 > x^3 – x^2   This one may seem tricky but lets break it down. x^4 – x^5 > x^3 – x^2 = x^4(1-x)>x^2(x-1).   Because lets concentrate on (1-x) and (x-1). We are given that -1<x<1 (1-x)="" means="" that="" which="">0 and (x-1)<0. x^4 will always be positive and x^2 will always be positive so without doing any math we are looking at positive > negative... which is always true.   So Stmt III is always true   III only</x<1>
Answer: C
The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 12000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is:  Choose the correct choice from the following answers
A) 21 B) 20 C) 25 D) 30 E) 27

Solution: Let the total number of workers be x. Then,   8000x = (12000 * 7) + 6000(x - 7)   = 2000x = 42000   = x = 21.   21NSWER 21
Answer: A
Enrollment in City College in 1980 was 210 percent of enrollment in 1990. What was the percent increase in the college’s enrollment from 1980 to 1990?
Choose the correct choice from the following
A) - 10%	B) - 16 2/3 %	C) - 52.38%	D) - 25%	E) - 183 1/3%

Solution: Assume 100 enrollments present in 1990   210 % of 1990 = enrollments on 1980   enrollments on 1980 = 210   % change = (enrollment in 1990 - enrollment in 1980)*100/(enrollment in 1980)   =(100 - 210) *100 / 210   = -11000 / 210   = - 52.38 %   Ans - - 52.38%
Answer: C
Set S is the prime integers between 0 and 30. If three numbers are chosen randomly from set S, what is the probability that the sum of these three numbers is odd?  Choose the correct choice from the following choices
A) 15/56	B) 3/8	C) 15/28	D) 7/10	E) 3/4

Solution: Total number of combinations=10C3=120...............(1)   Total number of combinations including2and two other numbers=9C2=36......................(2)   Therefore the difference ie. (1)-(2) is the set of 3 primes without 2=(120-36)= 
(120-36) = 84
84   So, probability=84/120=7/10   7/10
Answer: D
Divide Rs. 1301 between A and B, so that the amount of A after 7 years is equal to the amount of B after 9 years, the interest being compounded at 4% per annum.  Select the correct option:
A) 625 B) 367 C) 288 D) 209 E) 198

Solution: Explanation:   Let the two parts be Rs. x and Rs. (1301 - x).   625x=676(1301-x) 1301x=676 x 1301x=676.   So,the parts are rs.676 and rs.(1301-676)i.e rs.676 and rs.625   625nswer: 625) Rs.625
Answer: A
If T < y < -1, which of the following is true?	Choose the correct choice from the following answers.
A) T/y > Ty
B) y/t > t+y
C) y/t > Ty
D) y/T < T+y
E) y/T > T/y

Solution: Consider :   T= -3   y= -2   then put for every option. U'll get ans y/t > t+y.
Answer: B
A, B and C started a business by investing Rs. 1,20,000, Rs. 1,35,000 and ,Rs.1,50,000 respectively. Find the share of each, out of an annual profit of Rs. 56,700.	Select:
A) 16800;18900;21000
B) 17800;19800;22500
C) 15500;17600;20500
D) 16400;17200;18900
E) None of them

Solution: Ratio of shares of A, Band C = Ratio of their investments   = 120000 : 135000 : 150000 = 8 : 9 : 10.   A’s share = Rs. (56700 x (8/27))= Rs. 16800.   B's share = Rs. ( 56700 x (9/27)) = Rs. 18900.   C's share = Rs. ( 56700 x (10/27))=Rs. 21000.   16800;18900;21000nswer is 16800;18900;21000.
Answer: A
If a and b are both prime numbers greater than 10, which of the following CANNOT be true?
I. ab is an even number.
II. The difference between a and b equals 117.
III. The sum of a and b is even.	Choose the correct choice from the following choices
A) I only  B) I and II only  C) I and III only  D) II and III only  E) I, II and III

Solution: CONCEPT: Prime Numbers greater than 10 will all be ODD   I. ab is an even number - Can't be True because both a and b are ODD   II. The difference between a and b equals 117 - Can't be True because both a and b are ODD and Difference of two Odd No. must be EVEN   III. The sum of a and b is even - This will be True because both a and b are ODD and Sum of two Odd No. must be EVEN   ANSWER:I and II only
Answer: B
Two trains, one from P to Q and the other from Q to P, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is Choose the correct option:
A) 4:1
B) 4:2
C) 4:5
D) 4:3
E) 4:6

Solution: Ratio of their speeds = Speed of first train : Speed of second train   = 16−−√9√   = 4:3   Answer is 4:3.
Answer: D
It is given that 2^32 + 1 is exactly divisible by a certain number. Which one of the following is also divisible by the same number B?
Pick one
A) a. 2^96 + 1 B) b. 2^16 - 1 C) c. 2^16 + 1 D) d. 7 * 2^33 E) e. 2^64 + 1

Solution: a³ + b³ =(a+b)(a² -ab +b²)   Now, let (2^32 + 1) be (a+b)   a³ + b³ = (2^96 + 1)   Now, as mentioned in formula above,   a³ + b³ is always divisible by (a+b)   So any factor of B= (a+b) is a factor of (a³ + b³)   Henca a. 2^96 + 1
Answer: A
If two numbers, a and b, are to be chosen from a set of 4 consecutive integers starting with 1 and a set of three consecutive even integers starting with 6, respectively, what is the probability that b/a will not be an integer?	Choose the correct choice from the following answers:	A) 1/6	B) 1/4	C) 1/3	D) 1/2	E) 2/3

Solution: a is from the following set {1,2,3,4}   b is from the following set {6,8,10}   The total number of ways of choosing 2 integers, one from each set is  4*3= 
 4*3 = 12
12 ways.   The possibilities where b/a is not an integer is for the following outcomes:   {b,a}= {6,4},{8,3},{10,3},{10,4} = 4 ways   Thus the probability is 4/12 = 1/3   The answer is 1/3.
Answer: C
The maximum number of students among them 1048 pens and 828 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is:	Choose the correct choice
A) 4
B) 8
C) 16
D) 1911
E) None of these

Solution: Explanation:   Required number of students = H.C.F of 1048 and 828 = 4. 4nswer: 4
Answer: A
An art gallery owner is hanging paintings for a new show. Of the eight paintings she has to choose from, she can only hang two on the main wall of the gallery. Assuming that she hangs as many as possible on that wall, in how many ways can she arrange the paintings?
Choose the correct answer.
A) 18
B) 30
C) 56
D) 120
E) 216

Solution: Arrangment means permutations questions..   8P2 = 8!/2! = 56.   IMO option 56 is correct answer..
Answer: C
A watch passes through three hands and each person gains 25%. If the third person sells it for $125, what did the first person pay for it?
Choose the correct choice from the following options: A) $54 B) $60 C) $64 D) $72 E) $80

Solution: 1.25*1.25*1.25 * original price = 125   (5/4)^3 * original price = 125   original price = 64*125 / 125= 
64*125 / 125 = 64
$64   The answer is $64.
Answer: C
The distance between Delhi and Mathura is 140 kms. A starts from Delhi with a speed of 20 kmph at 7 a.m. for Mathura and B starts from Mathura with a speed of 25 kmph at 8 p.m. from Delhi. When will they meet?  Choose the most appropriate option.
A) 10.50 a.m.
B) 10.40 a.m.
C) 10.30 a.m.
D) 11.40 a.m.
E) 1.40 a.m.

Solution: D = 140 – 20 = 120   RS = 20 + 25= 
20 + 25 = 45
45   T= 120/45 = 2 2/3 hours   8 a.m. + 2 hrs 40 min = 10.40 a.m.   ANSWER:10.40 a.m.
Answer: B
A number when multiplied by 3 and then subtracted by 2 becomes the reverse of itself. Can you find out which smallest number is that?  Answers.
A) 33  B) 28  C) 55  D) 71  E) 23

Solution: B   28 is the required number.   28 * 3 - 2= 
28 * 3 - 2 = 82
82.
Answer: B
A batsman scored 100 runs which included 3 boundaries and 8 sixes. What percent of his total score did he make by running between the wickets?
Pick one: A) 50% B) 40% C) 60% D) 70% E) 80%

Solution: Number of runs made by running = 100 - (3 x 4 + 8 x 6)   = 100 - (60)= 
100 - (60) = 40
40   Now, we need to calculate 40 is what percent of 100.=> 40/100 x 100 = 40 %   ANSWER:40%
Answer: B
There are 10000 families, having 4 children for each family. In how many families 2 daughters are probable.	Choose the correct answer:
A) 625
B) 529
C) 425
D) 354
E) 725

Solution: Probability to have 2 daughter = 1/2^4 = 1/16   so answer = 10000*1/16= 
10000*1/16 = 625
625   625NSWER:625
Answer: A
If the average marks of three batches of 55, 60 and 45 students respectively is 40, 62, 58, then the average marks of all the students is  Pick.
A) 54.48	B) 53.31	C) 54.6	D) 54.58	E) None of these

Solution: Explanation:   (55Ã—40)+(60Ã—62)+(45Ã—58) / 55+60+45   8530 / 160=53.3   Option 53.31
Answer: B
How many odd three-digit integers greater than 600 are there such that all their digits are different? Choose the correct choice from the following answers.
A) 40	B) 56	C) 72	D) 81	E) 120

Solution: 3 (hundred's digit) * 9 (ten's digit) * 8 (unit's digit) = 216   Now take numbers in the range 600 - 900.   Total numbers where all digits are different = 216 (as before)   [highlight]Number of odd numbers = 3 * 8 * 5= 
3 * 8 * 5 = 120
120[/highlight] (now there are 5 possibilities for the unit's digit)   120
Answer: E
How many seconds will a 500 meter long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?  Choose the correct option:
A) 167 B) 266 C) 150 D) 776 E) 122

Solution: Let length of tunnel is x meter   Distance = 800+x meter   Time = 1 minute = 60 seconds   Speed = 78 km/hr = 78*5/18 m/s = 65/3 m/s   Distance = Speed*Time   800+x = (65/3) * 60   800+x = 20 * 65= 
20 * 65 = 1_300
1300   x= 1300 - 800= 
1300 - 800 = 500
500 meters   Answer: 150
Answer: C
Let Y be the smallest positive integer such that 12 and 8 are factors of 20*Y, So the value of Y is:	Choose the correct choice from the following choices
A) 7
B) 9
C) 11
D) 13
E) 15

Solution: You can calculate the LCM(12,8) (Least commom multiple of 12 and 8) = 36   and calculate the LCM(36,20) = 180   And making 180/20 we obtain 9.   So, the Answer is 9.
Answer: B
If the sales tax reduced from 3 1/2 % to 3 1/3%, then what difference does it make to a person who purchases an article with market price of $ 8400 ?	Choose the correct choice from the following options
A) 14 B) 24 C) 34 D) 12 E) 13

Solution: Required difference = [3 1/2 % of $8400] – [3 1/3 % of $8400]   = [(7/20)-(10/3)]% of $8400 =1/6 % of $8400   = $ [(1/6)*(1/100)*8400= 
(1/6)*(1/100)*8400 = 14
$ 14.   14nswer 14.
Answer: A
A number, x is chosen at random from the set of positive integers less than 20. What is the probability that (18/x) > x?
Choose the correct choice from the following answers:
A) 1/5
B) 2/9
C) 3/19
D) 4/19
E) 7/9

Solution: Number x has to be chosen from numbers 1-19   (18/x) > x   => 18 > x^2   =>x^2 - 18 < 0   x can have 2 values only 1 , 2 , 3 , 4   Therefore , probability = 4 / 19   Answer 4/19
Answer: D
If a committee of 3 people is to be selected from among 8 married couples so that the committee does not include two people who are married to each other, how many such committees are possible?	Choices:
A) 120	B) 240	C) 250	D) 380	E) 448

Solution: You now have your Committee of 3 people. But you've selected them in an order, when order doesn't matter.   Selection #1 = Jack   Selection #2 = Susan   Selection #3 = Mary   Assume this is a good committee where Jack is not married to Susan or Mary and Susan and Mary are not married. The above committee will be the same as the following committee:   Selection #1 = Susan   Selection #2 = Mary   Selection #3 = Jack   To account for the fact that the order does not matter, we must divide out the number of ways a single committee can be the same members but in different order. 3 places = 3!, 3*2*1 = 6.   16*14*12 / 6= 
16*14*12 / 6 = 448
448. Answer 448.
Answer: E
A certain restaurant offers 8 kinds of cheese and 2 kinds of fruit for its dessert platter. If each dessert platter contains an equal number of kinds of cheese and kinds of fruit, how many different dessert platters could the restaurant offer?  Pick one:
A) 8
B) 12
C) 15
D) 21
E) 44

Solution: As dessert platter should contain equal number of kinds of cheese and fruits, desert can contain:   A. 2 kinds of cheese and 2 kinds of fruits --> 8C2*2C2=28*1= 
28*1 = 28
28   B. 1 kind of cheese and 1 kind of fruit --> 8C1*2C1=8*2= 
8*2 = 16
16   A+B=28+16= 
28+16 = 44
44   Answer: 44.
Answer: E
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 4 times his original investment. What is the value of n?
Choose the correct choice from the following answers:
A) 50 years B) 25 years C) 12 years 6 months D) 37 years 6 months E) 40 years

Solution: Explanatory Answer   Let us say Braun invested $100.   Then, at the end of 'n' years he would have got back $400.   Therefore, the Simple Interest earned = 400 - 100= 
400 - 100 = 300
$300.   We know that Simple Interest= (Principal * number of years * rate of interest) / 100   Substituting the values in the above equation we get 300 = (100 * n * 8) / 100   Or 8n = 300   Or n = 37.5 years.   choice is (37 years 6 months)
Answer: D
A train covers a distance of 12 km in 10 min. If it takes 3 sec to pass a telegraph post, then the length of the train is?
Choices:
A) 60 m B) 188 m C) 120 m D) 80 m E) 189 m

Solution: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec   = 20 m/sec.   Length of the train = 20 * 3= 
20 * 3 = 60
60 m.   60 mnswer:60 m
Answer: A
A lady bought five books namely A,B,C,D,E to distribute her 3 child. How many ways she can distribute books? Choose the correct choice.
A) 3^3	B) 3^4	C) 3^5	D) 3^6	E) 3^2

Solution: 3*3*3*3*3   3^5   ANSWER:3^5
Answer: C
A man invested Rs. 1552 in a stock at 97 to obtain an income of Rs. 128. The dividend from the stock is:  Choices.
A) 8%	B) 6%	C) 7%	D) 9%	E) 10%

Solution: By investing 1552 income = 128   by investing rs 97 income = (128/1552 * 97)= 
(128/1552 * 97) = 8
rs 8=>8%   8%NSWER 8%
Answer: A
In final exam of class IX there are 50 students 10 % students failed. How many students passed to class X?
Answers
A) 33 B) 378 C) 37 D) 39 E) 45

Solution: Percentage of students passed to class X = 100 % - 10 % = 90 %   90 % of 50   = 90/100 × 50   = 4500/100= 
4500/100 = 45
45   Therefore, 45 students passed to class X.   Answer:45
Answer: E
16 men can complete a piece of work in 25 days. In how many days can 20 men complete that piece of work?	Choose the correct answer:
A) 55 days	B) 77 days	C) 20 days	D) 88 days	E) 44 days

Solution: 16 * 25 = 20 * x => x   = 20 days   Answer: 20 days
Answer: C
Find the principal which yields a simple interest of Rs. 20 and compound interest of Rs. 22 in two years, at the same percent rate per annum?
Pick.
A) s. 520
B) s. 480
C) s. 420
D) s. 100
E) s. 200

Solution: Explanation:   SI in 2 years = Rs. 20, SI in 1 year = Rs. 10   CI in 2 years = Rs. 22   % rate per annum = [(CI – SI) / (SI in 1 year)] *100   = [(22 – 20) / 20] * 100   = 10 % p.a.   Let the principal be Rs. X   Time = T = 2 years   % rate = 10% p.a.   SI = (PRT/100)   20 = (X*10*2) / 100   X = Rs. 100   ANSWER: s. 100
Answer: D
When positive integer N is divided by positive integer J, the remainder is 25. If N/J = 204.05, what is value of J?  Choose the correct choice from the following:
A) 600 B) 500 C) 800 D) 200 E) 900

Solution: When a number is divided by another number, we can represent it as : Dividend = Quotient * Divisor + Remainder   So, Dividend/Divisor = Quotient + Remainder/Divisor   Given that N/J = 204.05   Here 204 is the quotient.   Given that Remainder = 25   So, 204.05= 204 + 25/J   So, J = 500   Answer: 500
Answer: B
Anu can do a work in 6 days and Binu alone in 9 days. Anu and Binu undertook to do it for Rs.5400. With help of Minu, they completed the work in 3 days. How much is to be paid to Minu and Anu?	Pick.
A) s.750, Rs.2250	B) s.2000, Rs.750	C) s.750, Rs.2000	D) s.800, Rs.1250	E) s.900, Rs.2700

Solution: Minuâ€™s one dayâ€™s work = 1/3 - 1/6 + 1/9= 1/3 - 5/18 = 1/18   Anuâ€™s wages: Binuâ€™s wages: Minuâ€™s wages = 1/6 : 1/9 : 1/18 = 6: 4: 2   Minuâ€™s share = Rs.5400* 2/12 = Rs.900   Anuâ€™s share = Rs.5400* 6 /12= 
.5400* 6 /12 = 0.27
Rs.2700   ANSWs.900, Rs.2700R:s.900, Rs.2700
Answer: E
If money is invested at r percent interest, compounded annually, the amount of the investment will double in approximately 50/r years. If Luke's parents invested $15,500 in a long term bond that pays 12 percent interest compounded annually, what will be the approximate total amount of the investment 12 years later, when Luke is ready for college?	Choose the correct choice from the following choices.
A) 62,000  B) 85,500  C) 95,500  D) 100,500  E) 120,000

Solution: Answer equals E in 48 years. I thought by 50th year it would reach 120,000. Options should have been separated more widely for clarity.
Answer: E
If log72 = m, then log4928 is equal to Pick.
A) 2(1 + 2m)
B) (1 + 2m)/2
C) 2/(1 + 2m)
D) 1 + m
E) 1 + 2m

Solution: log4928 = 1/2log7(7x4) = 1/2(1 + log74)   = 1/2 + (1/2). 2log72   = 1/2 + log72   = 1/2 + m = (1 + 2m)/2.   ANSWER:(1 + 2m)/2
Answer: B
The simple interest accrued on an amount of ₹ 84000 at the end of 3 yr is ₹ 30240. What would be the compound interest accrued on the same amount at the same rate in the same period? Choose one:	A) 22	B) 77	C) 66	D) 88	E) 61

Solution: Answer:88
Answer: D
Rs.2500 is divided into two parts such that if one part be put out at 5% simple interest and the other at 6%, the yearly annual income may be Rs.140. How much was lent at 5%?	Choices.
A) 2333	B) 2777	C) 2688	D) 1000	E) 2871

Solution: (x*5*1)/100 + [(2500 - x)*6*1]/100 = 140   X = 1000   Answer: 1000
Answer: D
ACME’s manufacturing costs for sets of horseshoes include a $11,450 initial outlay, and $19.75 per set. They can sell the sets for $52.50. If profit is revenue from sales minus manufacturing costs, and the company produces and sells 987 sets of horseshoes, what was their profit?  Choose the correct choice from the following choices.
A) $20,874.25	B) $30,943.25	C) $41,308.50	D) $51,817.50	E) $53,624.25

Solution: The numbers are ugly, and the answer choices are widely spread out. This problem is absolutely screaming for estimation!   So here’s some more fast and furious estimation. Initial manufacturing outlay: round that from $11450 to $10000. Cost per set: round to $20. Sales revenue per set: $50. Number produced & sold: 1000. OK, now we’re in business.   Cost equals 10000 + 20*1000 = 10000 + 20000= 
10000 + 20000 = 30_000
$30000. Sales revenue= 50*1000= 
50*1000 = 50_000
$50000. Profit= (Sales Revenue) – (Cost) =$50000 – $30000 = $20000. Answer choice (A) is the only answer even close to that. Single digit calculations all the way, and it was enough to get the answer!   $20,874.25nswer $20,874.25
Answer: A
A person purchased a TV set for Rs. 13000 and a DVD player for Rs. 5000. He sold both the items together for Rs. 21600. What percentage of profit did he make?	Choose the correct choice from the following answers:
A) 48%	B) 70%	C) 40%	D) 45%	E) 20%

Solution: The total CP = Rs. 13000 + Rs. 5000   = Rs. 18000 and SP   = Rs. 21600   Profit(%)   = (21600 - 18000)/18000 * 100= 
(21600 - 18000)/18000 * 100 = 20
20%   Answer: 20%
Answer: E
a man owns 2/3 of market reserch beauro buzness,and sells 3/4 of his shares for 45000rs,what is the value of buzness? Choose the correct choice from the following answers:
A) 150000	B) 90000	C) 85000	D) 190000	E) 250000

Solution: If value of business=x   Total sell (2x/3)(3/4)=45000   ->x=150000   ANSWER:90000
Answer: B
here's an easy question of averages, but let's try to see innovative ways of solving this.
A class has 12 boys and x girls. Average score of boys and girls is 84 and 92 respectively. the average of the whole class is 86, what is the value of x?  Choose the correct option.
A) a) 6
B) b) 4
C) c) 8
D) d) 10
E) e) 12

Solution: 12(84)+92x/12+x=86   1008+92x/12+x=86   1008+92x=86(12+x)   1008+92x=1032+86x   X's one side, numbers one side we get,   92x - 86x=1032-1008   6x=24   hence, x=4   Answer b) 4
Answer: B
In the quadratic equation ax2 - 11x + 40 = 0, if the sum of two roots is 1.1, what is the product of the two roots? Choices.
A) 7 B) 6 C) 5 D) 4 E) 3

Solution: Explanation:   The sum of the roots of the quadratic equation ax2 - bx + c = 0 are (-b/a) and the product of the roots are (c/a).   Thus, in the equation ax2 - 11x + 40 = 0, where a = a, b = - 11 and c = 40.   we get, sum of the roots = - (- 11) / a = 1.1   a = 11 / 1.1= 
11 / 1.1 = 10
10   Product of the roots= 40 / 10= 
40 / 10 = 4
4   ANSWER: 4
Answer: D
How many different positive integers exist between 106 and 107, the sum of whose digits is equal to 2? Choices:	A) 6	B) 7	C) 5	D) 8	E) 18

Solution: Explanatory Answer   Find the number of such integers existing for a lower power of 10 and extrapolate the results.   Between 10 and 100, that is 101 and 102, we have 2 numbers, 11 and 20.   Similarly, between 100 and 1000, that is 102 and 103, we have 3 numbers, 101, 110 and 200.   Therefore, between 106 and 107, one will have 7 integers whose sum will be equal to 2.   Alternative approach   All numbers between 106 and 107 will be 7 digit numbers.   There are two possibilities if the sum of the digits has to be '2'.   Possibility 1: Two of the 7 digits are 1s and the remaining 5 are 0s.   The left most digit has to be one of the 1s. That leaves us with 6 places where the second 1 can appear.   So, a total of six 7-digit numbers comprising two 1s exist, sum of whose digits is '2'.   Possibility 2: One digit is 2 and the remaining are 0s.   The only possibility is 2000000.   Total count is the sum of the counts from these two possibilities = 6 + 1= 
6 + 1 = 7
7   Choice 7 is the correct answer.
Answer: B
Rashmi walks to her bus stop at 5 kmph and reaches there late by 10 minutes. On the next day,she increases her speed to 6 kmph and reaches the bus stop 10 minutes early.How far is the bus stop ?	Options: A) 13 B) 12 C) 11 D) 10 E) 9

Solution: Let the distance to the bus stop is "d"km   Time taken by her(at 5kmph)=d/5hour, and   Time taken by her(at 6kmph)=d/6 hour   As per given condition,   d/5 - d/6 = 20/60   d= 10 kms   ANSWER:10
Answer: D
Two angles of a triangle have ratio 5:3, and the third angle is the difference of the other two. Find the smallest angle of such a triangle in degrees. Pick one.
A) 16	B) 18	C) 20	D) 24	E) 36

Solution: The angles are 5x, 3x, and (5x-3x) = 2x [note that 2x is the smallest angle]   the angles of a triangle add up to 180, so   5x+3x+2x  (5 -3 )= 
  (5 -3 ) = 2
2x [note that 2x is the smallest angle]   the angles of a triangle add up to 180, so   5x+3x+2x=180   10x = 180   x = 18   2x is the smallest angle, so  2*18= 
 2*18 = 36
36 is the smallest angle   36
Answer: E
There are two sticks of which the longer one is 10 cm longer than the short stick. Find the length of the shorter stick if the total length of both the sticks is 24 cm? Choose the correct choice from the following answers.
A) 6 B) 7 C) 8 D) 12 E) 14

Solution: Since, 24 is the total length. Shorter is any one from answers.   Try Back solving from first answer, i.e. 6. 6+(6+10) = 22<24   Hence, Select next greater no. : 7 +(7+10)= 
7 +(7+10) = 24
24. So, 7 is the answer
Answer: B