MU-NLPC/Calc-aqua_rat huggingface dataset:
A train running at the speed of 60 km/hr crosses a pole in 12 sec. What is the length of the train?  Choose the correct option
A) 356 B) 200 C) 127 D) 279 E) 150

Solution: Speed = 60 * 5/18 = 50/3 m/sec   Length of the train = speed * time = 50/3 * 12= 
50/3 * 12 = 200
200 m   Answer: 200
Answer: B
A square mirror has exactly half the area of the rectangular wall on which it is hung. If each side of the mirror is 54 inches and the width of the wall is 68 inches, what is the length of the wall, in inches?  Choose the correct choice from the following answers:
A) 25.7  B) 72.7  C) 70.7  D) 85.7  E) 56.7

Solution: Since the mirror is 42 inches in all sides, it must be a square. Area of a square is A=a^2; 54^2=2916.Area of rectangle is double of that 2 *2916= 
2 *2916 = 5_832
5832.Now A=lw and we need find w so A/l=w ; 5832/68= 85.7 Answer!   Answer is 85.7
Answer: D
The proportion of X’s and Y’s ages is 4:5. If the difference between the current age of X and the age of Y 0.5 decades hence is 3, then what is the sum of current ages of X and Y?	Choose the most appropriate option
A) 83 years B) 39 years C) 72 years D) 48 years E) 93 years

Solution: D   72 years   We simplified the most of steps because lack of font prolem.   X = 32 years   and, Y = (5/4) x 32 = 40 years   Therefore X + Y = 40 + 32= 
40 + 32 = 72
72 years.
Answer: D
Insert the missing number
121, 112, ..., 97, 91, 86	Choose one.
A) 102  B) 108  C) 99  D) 104  E) 106

Solution: first and second number difference is starting from 9, and further decresed by 1 by each iteration.   121, 112, ..., 97, 91, 86....   Difference between two numbers Will be as 9, 8, 7, 6, 5,...   ANSWER:104
Answer: D
Tickets numbered from 1 to 20 are mixed and then a ticket is selected randomly. What is the probability that the selected ticket bearsa number which is a multiple of 3?  Pick one.
A) 2/5	B) 3/5	C) 3/10	D) 3/11	E) 4/5

Solution: Here, S = [1, 2, 3, 4, …., 19, 20]   Let E = event of getting a multiple of 3 = [3, 6, 9, 12, 15, 18]   P (E) = n (E) / n (S) = 6 / 20 = 3/10   3/10
Answer: C
How many seconds will a 700 m 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 choice from the following choices
A) 22  B) 42  C) 99  D) 77  E) 12

Solution: Speed of train relative to man = 63 - 3= 
63 - 3 = 60
60 km/hr.= 60 * 5/18 = 50/3 m/sec.   Time taken to pass the man = 700 * 3/50= 
700 * 3/50 = 42
42 sec.   Answer: 42
Answer: B
A positive whole number has factors of 3 and 4. The number MUST be divisible by:
I. 12 II. 24 III. 48	Choose the correct choice from the following
A) I	B) I & III	C) II	D) II & III	E) III

Solution: 12 , 24 is not divisible by 48.But 48 is divisible by 3,4,12,24.   So answer is III   Answer : III
Answer: E
If 500 gm of salt solution has 30% salt in it, how much salt must be added to make the concentration of salt 50% in the solution?  Choose the most appropriate option:  A) 200 gm  B) 280 gm  C) 202 gm  D) 700 gm  E) 206 gm

Solution: Explanation:   Amount of water in solution = 100 % - 30 % = 70 % of total   Amount of water = 70 % x 500 = 350 gm   Amount of water remains same for both the solutions. Therefore, let amount of new solution be x gm.   x = 350 x (100/ 50)   x = 700   Salt added = (700 – 500) = 200 gm   200 gmlternate solution:   Quantity of sugar to be added :   = [Solution (Required % value – Present % value)] / (100 – Required % value)   = [500 (50 – 30)] / 100 – 50   = (500 x 20) / 50   = 200 gm   200 gmNSWER: 200 gm
Answer: A
A person can swim in still water at 4 km/h. If the speed of water 2 km/h, how many hours will the man take to swim back against the current for 6km?
Answers:
A) 5
B) 7
C) 3
D) 1/2
E) 4

Solution: Explanation:   M = 4   S = 2   US = 4 - 2= 
4 - 2 = 2
2   D= 6   T = 6/2= 
6/2 = 3
3   Answer: 3
Answer: C
A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man? Choose the correct choice from the following.
A) 5.29	B) 5.2	C) 5.76	D) 5.12	E) 5.93

Solution: M = 6   S = 1.2   DS = 7.2   US = 4.8   x/7.2 + x/4.8 = 1   x = 2.88   D = 2.88 * 2= 
2.88 * 2 = 5.76
5.76   Answer:5.76
Answer: C
Equal weights of two alloys containing tin, copper and lead in the ratio 7:4:5 and 5:3:8 are melted and mixed together. What is the ratio of tin, copper and lead in the resultant alloy?
Choose the correct answer:
A) 41:81:37	B) 33:91:81	C) 16:7: 12	D) 12:70: 16	E) 12:7: 16

Solution: Let the weight of the two alloys be w each   Required ratio =   (7w/16 +5w/16): ( 4w/16 +3w/16 ): (5w/16+6w/16)   = 12w/16 : 7w/16 : 11w/16   = 12:7: 16   ANSW12:7: 16R:12:7: 16
Answer: E
Pipe A can fill a tank in 2 hours. Due to a leak at the bottom, it takes 3 hours for the pipe A to fill the tank. In what time can the leak alone empty the full tank? Choose one
A) 10 B) 9 C) 7 D) 6 E) 5

Solution: Let the leak can empty the full tank in x hours 1/2 - 1/x = 1/3   => 1/x = 1/2 - 1/3 = (3 - 2)/6 = 1/6   => x = 6.   Answer: 6
Answer: D
The perimeter of a rectangular yard is completely surrounded by a fence that measures 12 meters. What is the length of the yard if the area of the yard is 9 meters squared?
Choose the correct option:
A) 8 B) 1 C) 3 D) 4 E) 6

Solution: Perimeter of rectangular yard = 2(l + b) = 12 --> l + b = 6   Area = l * b = 9   b = 6 - l   l(6 - l) = 9   6l - l^2 = 9   l^2 - 6l + 9 = 0   Upon simplifying we get l = 3.   Answer: 1
Answer: B
If 5a + 7b = k, where a and b are positive integers, what is the largest possible value of k for which exactly one pair of integers (a, b) makes the equation true?  Choose the correct choice
A) 35 B) 48 C) 69 D) 70 E) 74

Solution: We 'll start putting the values of with a = 10 and b = 1.   Keep decreasing the value of a by 1 and increasing the value of b by 1.   At a = 10 and b = 1, 5a + 7b = 57   At a = 9 and b = 2, 5a + 7b = 59   At a = 8 and b = 3, 5a + 7b = 61   We see a pattern, for every decrease in a and every decrease in b, the result is increasing by 2.   So,   At a = 4 and b = 7, 5a + 7b = 69.   ANSWER:69
Answer: C
Each day a man meets his wife at the train station after work, and then she drives him home. She always arrives exactly on time to pick him up. One day he catches an earlier train and arrives at the station an hour early. He immediately begins walking home along the same route the wife drives. Eventually his wife sees him on her way to the station and drives him the rest of the way home. When they arrive home the man notices that they arrived 16 minutes earlier than usual. How much time did the man spend walking?
Choose the most appropriate option.
A) 45 minutes  B) 50 minutes  C) 40 minutes  D) 55 minutes  E) 52 minutes

Solution: As they arrived 16 minutes earlier than usual, they saved 16 minutes on round trip from home to station (home-station-home) --> 8 minutes in each direction (home-station) --> wife meets husband 8 minutes earlier the usual meeting time --> husband arrived an hour earlier the usual meeting time, so he must have spent waking the rest of the time before their meeting, which is hour-8 minutes=52 minutes.   Answer: 52 minutes
Answer: E
Two perpendicular line segments divide a large rectangle
into 4 small rectangles. The areas of 3 of these 4 small
rectangles are shown. What is the area of the other small
rectangle?  Choose one: A) 12 B) 13 C) 14 D) 15 E) 16

Solution: Label the 4 small rectangles R1, R2, R3, and R4 so that the areas of R1, R2,   and R3 are 8, 6, and 9 respectively and R4 is the rectangle whose area we want to find.   Denote the area of R4 by x. Then 8 · 9 = 6 · x. (Note that R1 and R2 have the same   base and so do R3 and R4. 12lso, R1 and R4 have the same height and so do R2 and   R3.)   correct answer 12
Answer: A
A person purchased a TV set for Rs. 16000 and a DVD player for Rs. 6250. He sold both the items together for Rs. 31750. What percentage of profit did he make? Choose the correct choice from the following choices
A) 42.7	B) 27	C) 40	D) 26	E) 11

Solution: The total CP = Rs. 16000 + Rs. 6250 = Rs. 22250 and SP = Rs. 31750   Profit(%) = (31750 - 22250)/22250 * 100 = 42.7%.42.7nswer:42.7
Answer: A
A certain list consists of 21 different numbers. If n is in the list and n is 5 times the average (arithmetic mean) of the other 20 numbers in the list, then n is what fraction of the sum of the 21 numbers in the list?
Choices.
A) 1/20
B) 1/6
C) 1/5
D) 4/21
E) 5/21

Solution: series : a1, a2....a20,n   sum of a1+a2+...+a20 = 20*x (x = average)   so, n = 5*x   Hence, a1+a2+..+a20+n = 25x   So, the fraction asked = 5x/25x = 1/5   Answer 1/5
Answer: C
A sum of Rs.96000 is divided into three parts such that the simple interests accrued on them for Eight, two and four years respectively may be equal. Find the amount deposited for 8 years. Choose the correct choice from the following.
A) 14000 B) 16000 C) 12000 D) 20000 E) 13000

Solution: Let the amounts be x, y, z in ascending order of value. As the interest rate and interest accrued are same for 2 years 4 years and 8 years i.e. 2x = 4y = 8z = k.   L.C.M. of 2,4,8 = 8 So x:y:z: = 48000 : 24000 :12000   The amount deposited for 11 years = 12000   ANSWER:12000
Answer: C
Three cars A,B and C started at same point and time. After A reach 50 km, B and C are backward by 10km and 20 km. When B reach 200km, find the position of A and C?  Choose the correct choice from the following answers
A) 240 and 160km B) 170 and 230 km C) 180 and 240 km D) 235 and 165 km E) 250 and 150 km

Solution: 250 and 150 kmxplanation:   A:B = 50 : 40 = 5 : 4   A:C = 50 : 30 = 5 : 3   =>B:C = 4:3   When B covers 40 km , C Covers 30 km   When B covers 200 km , C Covers   => 150 km   When B covers 40 km , A Covers 50 km   When B covers 200 km , A Covers   => 250 km   Answer: 250 and 150 km
Answer: E
In an examination, 30% of total students failed in Hindi, 42% failed in English and 28% in both. The percentage of these who passed in both the subjects is :	Choose the correct choice from the following answers:
A) 23 B) 37 C) 56 D) 40 E) 81

Solution: Explanation:   Formula n(aâˆªb) = n(a) + n(b) âˆ’ n(aâˆ©b)   Fail in Hindi or English = 30 + 42 â€“ 28 = 44   Therefore students who passed = 100 â€“ 44 = 56.   Answer: 56
Answer: C
The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?
Choose the correct choice from the following options.
A) 85 kg	B) 87 kg	C) 90 kg	D) 91 kg	E) 93 kg

Solution: Total weight increased = (8 x 2.5) kg = 20 kg.   Weight of new person = (65 + 20)= 
(65 + 20) = 85
85 kg.   85 kgnswer is 85 kg
Answer: A
At a certain university, 66% of the professors are women, and 70% of the professors are tenured. If 90% of the professors are women, tenured, or both, then what percent of the men are tenured? Choose the correct option.
A) 25
B) 37.5
C) 60
D) 62.5
E) 75

Solution: answer is 75%   total women = 66%   total men = 40%   total tenured = 70% (both men and women)   therefore, women tenured + women professors + men tenured = 90%   men tenured = 24%   but question wants to know the percent of men that are tenured   24%/40% = 60%   60
Answer: C
There are 4 copies of 5 different pencils. In how many ways can they be arranged on a shelf?
Choose the correct option:
A) 20!/4! B) 20!/5(4!) C) 20!/(4!)^5 D) 20! E) 5!

Solution: There are 4 copies of 5 different pencils.20!/((4!)^5)   Answer - 20!/(4!)^5
Answer: C
25 liters of a mixture is created by mixing Liquid P and Liquid Q in the ratio 3:2. How many liters of Liquid Q must be added to make the ratio 5:4?  Choose the most appropriate option.
A) 1 B) 2 C) 3 D) 4 E) 5

Solution: Let x be the amount of liquid Q to be added.   (2/5)*25 + x = (4/9)*(25+x)   450 + 45x = 500 + 20x   25x = 50   x = 2   The answer is 2.
Answer: B
What is the place value of 7 in the numeral 2734?	Choose the correct choice from the following options:
A) 600	B) 650	C) 700	D) 800	E) 850

Solution: Option '700'    7 * 100= 
 7 * 100 = 700
700
Answer: C
A rope of which a calf is tied is increased from 12 m to 18 m, how much additional grassy ground shall it graze?
Select:  A) 1217  B) 1219  C) 1210  D) 565.7  E) 1312

Solution: π (182 – 122) = 565.7   Answer:565.7
Answer: D
Lali builds a tower using only red, green, and blue toy bricks in a ratio of 4:3:1. She then removes 1/2 of the green bricks and adds 1/3 more blue bricks, reducing the size of the tower by 14 bricks. How many red bricks will she need to add in order to double the total number of bricks used to build the original tower?
Choose the correct answer
A) 82
B) 96
C) 110
D) 120
E) 192

Solution: Lali want to double the original amount of blocks, not just the red blocks   the original tower had 96 bricks, the new tower has 82 bricks and the question is asking how many extra red blocks are needed to build a tower of 192 bricks (double the original: 96*2).   192-82= 
192-82 = 110
110   so 110 bricks need to be added to the new 82 brick tower to double the original.   They worded the question ashow many red bricks need to be addedbut really it could be any colour just that 110 more bricks need to be there to equal 192=192
Answer: E
The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is: Choose the correct choice:  A) 276  B) 299  C) 322  D) 345  E) 390

Solution: the numbers are (23 x 13) and (23 x 14).   Larger number = (23 x 14) = 322.   Answer: Option 322
Answer: C
In a recent election, Ms. Robbins received 7,000 votes cast by independent voters, that is, voters not registered with a specific political party. She also received 20 percent of the votes cast by those voters registered with a political party. If N is the total number of votes cast in the election and 50 percent of the votes cast were cast by independent voters, which of the following represents the number of votes that Ms. Robbins received?
Choose the correct choice from the following answers:  A) 0.06N + 3,200  B) 0.1N + 7,000  C) 0.4N + 7,200  D) 0.1N + 8,000  E) 0.06N + 8,000

Solution: I will go with option B   According to question 50 percent of total votes (N) cas were cast by independent voters. This implies 50 percent of N are voters that belong to political party. And she received 7000 votes from independent voters and 20 percent from registered voters (i.e 0.2 * 0.5 * N = 0.1N). Hence total votes = 7000 + 0.1N ....option 0.1N + 7,000
Answer: B
A and B enter into partnership with capital as 7:9. At the end of 8 months, A withdraws. If they receive the profits in the ratio of 8:9 find how long B's capital was used?
Choose the most appropriate option:  A) 5  B) 4  C) 6  D) 7  E) 9

Solution: 7 * 8 : 9 * x = 8:9 => x= 7   Answer: 7
Answer: D
Calculate the amount that an investor needs to be invest to earn $460 in interest in 12 months if the investor plans to invest x dollars in a savings account that pays interest at an annual rate of 9% compounded semi-annually?	Choose one.
A) 7,000	B) 4,000	C) 6,000	D) 5,000	E) 8,000

Solution: the approach is substitution,   our interest requirement is 460 after 12 months, 2 compounding period.   calculate the compound interest on each option and find out the one that yields 460 in 12 months   5,000 yielded $460   using the formula   A = P(1 + r/n)nt   hence answer is 5,000
Answer: D
A man can row with a speed of 15 kmph in still water. If the stream flows at 15 kmph, then the speed in downstream is?	Choose the most appropriate option
A) 30 kmph
B) 5 kmph
C) 20 kmph
D) 22 kmph
E) 25 kmph

Solution: M = 15   S = 15   DS = 15 + 15= 
15 + 15 = 30
30   30 kmphNSWER:30 kmph
Answer: A
Divide Rs.116000 among three persons A, B and C such that the ratio of the shares of A and B is 3:4 and that of B:C is 5:6.find the share of A?	Choose the correct choice from the following answers.
A) 29491	B) 28491	C) 39491	D) 49491	E) 59491

Solution: Compound ratio of A:B:C   A:B = 3:4   B:C = 5:6   ----------   A:B:C = 15:20:24   We can divide Rs.116000 in this ratio.   Share of 29491 = 15/59 * 116000 = 29491   29491NSWER:29491
Answer: A
What will be the CI on a sum of Rs. 25,000 after 3 years at the rate of 12 per year?
Select the correct option
A) Rs. 10110.20	B) Rs. 10120	C) Rs. 10123.20	D) Rs. 10124	E) Rs. 10125.12

Solution: Amount   = Rs. 25000 x 1 +	12 3   100   = Rs. 25000 x	28	x	28	x	28   25	25	25   = Rs. 35123.20   C.I. = Rs. (35123.20 - 25000) = Rs. 10123.20   Rs. 10123.20
Answer: C
The average age of 12 men is increased by years when two of them whose ages are 21 years and 23 years are replaced by two new men. The average age of the two new men is Choose the correct choice: A) 22 B) 30 C) 34 D) 38 E) 27

Solution: total age increased = (12 * 2)= 
(12 * 2) = 24
24 years.   Sum of ages of two new men= (21 + 23 + 24)= 
(21 + 23 + 24) = 68
68 years   Average age of two new men= (68/2)= 
(68/2) = 34
34 years.   Answer: 34
Answer: C
If a survey shows that 50 citizens out of a sample of 200 support a particular Senate bill, what percent of the sample does not support the bill?
Choose the correct answer
A) 56%  B) 64%  C) 75%  D) 82%  E) 86%

Solution: Those who support = 50.   % of those who don't support it is (200-50)/ 200 = 75%   Answer 75%
Answer: C
What percent is 2 gm of 1 kg?	Choose the correct choice from the following options
A) 0.5 %  B) 0.2%  C) 1.5%  D) 2%  E) 3%

Solution: 1 kg = 1000 gm   2/1000 × 100 = 200/1000   =1/5= 
1/5 = 1/5 = around 0.2
0.2 %   0.2%)
Answer: B
what is the value of (2)^-3?  Pick one
A) 1/6 B) 1/5 C) 1/8 D) 1/9 E) 1/7

Solution: 2^-3= 1/(2)^3= 1/8   ANSWER:1/8
Answer: C
A man can row upstream at 6km/hr and down stream at 11km/hr find mans rate in still water ?  Choose the correct choice from the following options:
A) 2.9km/hr
B) 8.5km/hr
C) 7.8km/hr
D) 85.4km/hr
E) 6.6km/hr

Solution: given upstream(u) =6km/hr   down stream (v)= 11km/hr rate in still water =1/2(u+v)=1/2(6+11)=8.5km/hr Answer is (8.5km/hr)
Answer: B
If a card is drawn from a well shuffled deck of cards, what is the probability of drawing a black card or a face card?	Choose the most appropriate option:	A) 7/13	B) 15/26	C) 9/12	D) 8/13	E) 29/52

Solution: P(Bá´œF) = P(B) + P(F) - P(Bâˆ©F), where B denotes black cards and F denotes face cards.   P(Bá´œF) = 26/52 + 12/52 - 6/52   = 8/13   Answer: 8/13
Answer: D
The sum of 3 consecutive numbers is definitely
Select the correct option:
A) Positive.
B) Divisible by 3.
C) Divisible by 2.
D) Divisible by 4.
E) Divisible by 5.

Solution: If 1st term is x:   x+(x+1)+(x+2)=3x+3--->Always divisible by 3   If 2nd term is x:   (x-1)+x+(x+1)  +( +1)+( +2)= 
  +( +1)+( +2) = 3
3x+3--->Always divisible by 3   If 2nd term is x:   (x-1)+x+(x+1)=3x--->Always divisible by 3   If 3rd term is x:   (x-2)+(x-1)+x=3x-3--->Always divisible by 3   Answer: Divisible by 3.
Answer: B
If w, x, and y are consecutive even positive integers and w < x < y, which of the following could be equal to y - x - w ?	Choose the correct choice from the following answers
A) -4
B) -2
C) -1
D) 0
E) 3

Solution: Since W, X and Y are CONSECUTIVE EVEN POSITIVE INTEGERS and W < X < Y, we can start with the easiest set of values that comes to mind:   W = 2   X = 4   Y = 6   The question asks for what COULD be the value of Y - X - W.   In this case, the value would be...   6 - 4 - 2= 
6 - 4 - 2 = 0
0   0 IS among the answer choices, so we're done.   0
Answer: D
If C.P. of 24 books is equal to S.P of 30 books , then your gain or loss is ? Choose one:
A) 23 1/3 gain %  B) 30 10/23 loss %  C) 20% loss %  D) 30 1/3 loss %  E) 40 1/3 loss %

Solution: Say the cost price of 24 books is $24 so $1 for a book.   The cost of 30 books would be $30, and the selling price of 30 books would be 24$, hence the loss = ($30 - $24)/$30 = 20%.   Answer: 20% loss %.
Answer: C
75% of a number when added to 75 is equal to the number. The number is ?  Pick
A) 150  B) 200  C) 225  D) 300  E) None

Solution: Answer   75 + 75% of N = N   ⇒ N -3N/4 = 75   ⇒ N/4 = 75   ∴ N = (75 x 4) = 300   Correct Option: 300
Answer: D
Given two sets A = {1,1,6,6,7,7} and B = {0,1}, if one number is chosen from each set at random, what is the probability that the sum of both numbers is an even number Choose the correct choice from the following options.
A) 1/4
B) 1/6
C) 1/2
D) 1/3
E) 1/5

Solution: One way to look at it:   The number from set A can be ANYTHING.   The number selected from set B will determine whether the sum is odd or even.   For example, if a 6 is selected from set A, we need a 0 from set B to get an even sum.   If a 7 is selected from set A, we need a 1 from set B to get an even sum.   And so on.   So, P(sum is even) = P(select ANY number from set AANDselect the number from set B that makes the sum even)   = P(select ANY number from set A)xP(select the number from set B that makes the sum even)   = 1x1/2   = 1/2   = 1/2
Answer: C
A, B and C invests Rs.2000, Rs.3000 and Rs.4000 in a business. After one year A removed his money; B and C continued the business for one more year. If the net profit after 2 years be Rs.3200, then A's share in the profit is?	Choose the most appropriate option.
A) 238
B) 288
C) 237
D) 400
E) 281

Solution: Explanation:   2*12 : 3*12 : 4*24   1: 3: 4   1/8 * 3200= 
1/8 * 3200 = 400
400   Answer: 400
Answer: D
An outlet pipe empties a tank which is full in 5 hours. If the inlet pipe is kept open, which lets water in at the rate of 4 litres/min then outlet pipe would take 3 hours longer. Find the capacity of the tank.	Choose the correct choice from the following answers.
A) 8600 litres
B) 3200 litres
C) 12800 litres
D) 11200 litres
E) 13200 litres

Solution: Let the rate of outlet pipe be x liters/hour;   Rate of inlet pipe is 8 litres/min, or  4*60= 
 4*60 = 240
240 liters/hour;   Net outflow rate when both pipes operate would be x-240 liters/hour.   Capacity of the tank= x*5 hours = (x-240)*(5+3) hours   5x=(x-240)*8 --> x=640 --> capacity = 5x = 3200 liters.   Answer: 3200 litres.
Answer: B
Some persons can do a piece of work in 20 days. Two times the number of these people will do half of that work in?
Choose the most appropriate option:
A) 3	B) 4	C) 5	D) 6	E) 8

Solution: 20/ (2 * 2)= 
20/ (2 * 2) = 5
5 days   Answer:5
Answer: C
If log	(a/b)+log(b/a)	= log (a + b), then:
Choose one.
A) a=b	B) a+b=0	C) a-b=1	D) a+b=1	E) a-b = 0

Solution: log(a/b)+ log(b/a)	= log (a + b)   log (a + b) = log{(a/b)x(b/a)}	= log 1.   So, a + b = 1.   Answer is a+b=1
Answer: D
1. Internet: $90, with no sales tax, plus $10 shipping fee
2. Store X: $90, a 10% discount, plus 30% tax on discounted price
3. Store Y: $100, no tax
4. Store Z: $90, a 20% sales tax, and $10 rebate after tax
Isaac can purchase a certain item in four different ways, as shown in the table. What is the lowest price for which he can purchase this item?
Choose the correct choice from the following answers.
A) 88.1
B) 89.0
C) 89.1
D) 89.5
E) 98.0

Solution: Option 2 = (90 - 9) + 0.3 * 81= 
(90 - 9) + 0.3 * 81 = 105.3
105.3   Option 4= 90 + 0.2 * 90 - 10= 
90 + 0.2 * 90 - 10 = 98
98   So the OA is correct - 98.0
Answer: E
A man can row with a speed of 15 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is?  Pick one
A) 27
B) 27
C) 20
D) 99
E) 2

Solution: M = 15   S = 5   DS = 15 + 5= 
15 + 5 = 20
20'   Answer:20
Answer: C
Aishwarya was first to board to her flight to delhi.
She forgot her seat number and picks a random seat for herself.
After this, every single person who get to the flight sits on his seat if its available else chooses any available seat at random.
Abhishek is last to enter the flight and at that moment 99/100 seats were occupied.
Whats the probability what Abhishek gets to sit in his own seat ?
Options:
A) 1/2
B) 1/5
C) 2/9
D) 4/7
E) 3/6

Solution: A   1/2   one of two is the possibility   1. If any of the first 99 people sit in Abhishek seat, Abhishek will not get to sit in his own seat.   2. If any of the first 99 people sit in 1/2ishwarya's seat, 1/2bhishek will get to sit in his seat.
Answer: A