MU-NLPC/Calc-aqua_rat huggingface dataset:
ASvennumber is defined as a five-digit number which goes according to the following rules: the leftmost digit is even, any digit to the right of an even digit must be an odd digit, and any digit to the right of an odd digit can only be one of the digits 1 or 7. How many different 4-digit numbers areSvennumbers?	Pick.
A) 20  B) 80  C) 160  D) 220  E) 250

Solution: ASvennumber is defined as a five-digit number which goes according to the following rules: the leftmost digit is even, any digit to the right of an even digit must be an odd digit, and any digit to the right of an odd digit can only be one of the digits 1 or 7. How many different 5-digit numbers areSvennumbers?   4/9*5/10*2/10*2/10*2/10=160/9000   A. 20
Answer: A
Rajan and Rakesh started a business and invested Rs. 20,000 and Rs. 25,000 respectively. After 4 months Rakesh left and Mukesh joined by investing Rs. 15,000. At the end of the year there was a profit of Rs. 4,600. What is the share of Mukesh?	Choose one: A) 900 B) 100 C) 1100 D) 1200 E) 1500

Solution: Ratio of share of Rajan, Rakesh nd Mukesh => 20000:25000:15000   =>4:5:3   =>4*12 : 5*4 : 3*8 [Since Rakesh left after 4 months nd Mukesh joined after 4 months...]   => 12:5:6   Share of Rajan => 4600*12/23= 
4600*12/23 = 2_400
2400   Share of Rakesh=> 4600*5/23= 
4600*5/23 = 1_000
1000   Share of Mukesh=> 4600*6/23= 
4600*6/23 = 1_200
1200   ANSWER:1200
Answer: D
A single discount equivalent to the discount series of 20%, 10% and 5% is?
Choose the correct choice from the following options
A) 31.9	B) 31.7	C) 31.6	D) 31.54	E) 31.1

Solution: 100*(80/100)*(90/100)*(95/100)= 
100*(80/100)*(90/100)*(95/100) = 342/5 = around 68.4
68.4   100 - 68.4= 
100 - 68.4 = 31.6
31.6   Answer:31.6
Answer: C
W, B, C are three consecutive positive integers (W>B>C). What is the value of the expression 2W +B +3C? Select
A) 6A+7.
B) 5A+1.
C) 5A-1.
D) 6A-5.
E) 6W-7.

Solution: => W+W+(W-1)+3(W-2)   Ans E. 6W-7.
Answer: E
Find the compound interest on $ 16,000 at 20% per annum for 9 months, compounded quarterly	Choose the most appropriate option:  A) 2532  B) 2552  C) 2524  D) 2522  E) 2512

Solution: Principal = $ 16000; Time = 9 months =3 quarters;   Rate = 20% per annum = 5% per quarter.   Amount = $ [16000 x (1+(5/100))^3] = $ 18522.   CI. = $ (18522 - 16000)= 
(18522 - 16000) = 2_522
$ 2522.   Answer 2522.
Answer: D
Robert is traveling on his cycle and has calculated to reach point A at 2 p.m. if he travels at 10 km/hr; he will reach there at 12 noon if he travels at 15 km/hr. At what speed must he travel to reach A at 1 p.m.?  Choose the correct choice from the following
A) 109	B) 12	C) 99	D) 81	E) 22

Solution: Let the distance traveled be x km.   Then, x/10 - x/15 = 2   3x - 2x = 60 => x = 60 km.   Time taken to travel 60 km at 10 km/hr = 60/10= 
60/10 = 6
6 hrs.   So, Robert started 6 hours before 2. p.m. i.e., at 8 a.m.   Required speed= 60/5= 
60/5 = 12
12 kmph.   Answer: 12
Answer: B
A man can row 4.8 km/hr in still water. It takes him twice as long to row upstream as to row downstream. What is the rate of the current ?
Select the correct option
A) 1.9	B) 1.7	C) 1.2	D) 1.5	E) 1.6

Solution: Speed of boat in still water (b) = 4.8 km/hr. Speed of boat with stream (Down Stream), D = b + u Speed of boat against stream (Up stream), U = b – u It is given upstream time is twice to that of down stream. ⇒ Downstream speed is twice to that of upstream. So b + u = 2(b – u) ⇒ u =b/3 = 1.6 km/hr.   Answer: 1.6
Answer: E
What is the area of an equilateral triangle whose one side length is 40?	Choose the correct choice from the following choices:	A) 100√3	B) 200√3	C) 300√3	D) 350√3	E) 400√3

Solution: -> -> The area of an equilateral triangle with one side length of a is √3a2/4. Thus, √3(40^2)/4=400√3 and the answer is E.   Correct Option:	400√3
Answer: E
Mrs. Rodger got a weekly raise of $145. If she gets paid every other week, write an integer describing how the raise will affect her paycheck.  Choose the correct answer:	A) $ 231	B) $ 545	C) $ 145	D) $ 643	E) $ 112

Solution: Let the 1st paycheck be x (integer).   Mrs. Rodger got a weekly raise of $ 145.   So after completing the 1st week she will get $ (x+145).   Similarly after completing the 2nd week she will get $ (x + 145) + $ 145.   = $ (x + 145 + 145)   = $ (x + 290)   So in this way end of every week her salary will increase by $ 145.   correct answer $ 145
Answer: C
A, B, C are three consecutive positive integers (A>B>C). What is the value of the expression 2A +B - 2C?
Pick one:
A) 6A+7. B) A+3. C) 5A-1. D) 6A-5. E) 6A-7.

Solution: A+3. = A-1   C= A-2   Putting these values in 2A +A+3. -2C we get A +3   A+3. is the answer
Answer: B
ramesh,ram,kareem and Mohan collected coins of different countries. they collected 100 together. none collected less than 10.each collected an even number. each collected a different number. based on these, we can say that the number of coins collected by the boy who collected the most could not have exceeded  Choose the correct choice
A) 54
B) 64
C) 58
D) 60
E) 62

Solution: as other three must have collected atleast 10+12+14= 
10+12+14 = 36
36 coins   the number of coins collected by the boy who collected the most could not have exceeded   100-36= 
100-36 = 64
64   ANSWER:64
Answer: B
64 is divided into two parts in such a way that seventh part of first and ninth part of second are equal. Find the smallest part?  Select:
A) 13.25  B) 28  C) 30  D) 13.2  E) 14

Solution: x/7 = y/9 => x:y = 7:9   7/16 * 64= 
7/16 * 64 = 28
28   ANSWER:28
Answer: B
A woman is 18 years older than her son. In 3 years, her age will be twice the age of her son. The present age of her son is
Choose the correct choice from the following choices:
A) 18	B) 17	C) 15	D) 16	E) 14

Solution: Explanation:   Let the son's present age be x years. Then, woman's present age = (x + 18) years   => (x + 18) + 3 = 2(x + 3)   => x + 21 = 2x + 6   So, x = 15. Answer: 15
Answer: C
Rs.8000 become Rs.9724 in a certain interval of time at the rate of 5% per annum of C.I. Find the time?  Choose the correct choice from the following choices:
A) 6 YEARS	B) 7	C) 5	D) 3	E) 4

Solution: 4xplanation:   9724 = 8000(21/20)N   (21/20)4 = (21/20)N => N = 4   Answer: Option 4
Answer: E
Robert ate 7 chocolates, Nickel ate 5 chocolates. How many more chocolates did Robert ate than nickel?
Choose the correct choice from the following:
A) A)4	B) B)7	C) C)9	D) D)5	E) E)2

Solution: 7-5= 
7-5 = 2
2. Answer is 2
Answer: E
The L.C.M of two numbers is 48. The numbers are in the ratio 2:3. The sum of numbers is? Select.
A) 22	B) 67	C) 40	D) 88	E) 11

Solution: Let the numbers be 2x and 3x.   Then, their L.C.M = 6x. So, 6x = 48 or x = 8.   The numbers are 16 and 24.   Hence, required sum = (16 + 24)= 
(16 + 24) = 40
40.   Answer:40
Answer: C
What is the Positive integer that can be Added by 595 to make it a perfect square? Choose the correct option:
A) 2*3*6
B) 3*2*5
C) 5*3*3
D) 2*3
E) 3*5*4

Solution: 596 is added to a number that gives a perfect square   Nearest perfect square is 625.   so,625-596=30   30=2*3*5   Option 3*2*5 is answer
Answer: B
Two airplanes take off from one airfield at noon. One flies due east at 203 miles per hour while the other flies directly northeast at 283 miles per hour. Approximately how many miles apart are the airplanes at 2 p.m.?	Options:	A) 166	B) 332	C) 406	D) 483	E) 566

Solution: C   In two hours:   the plane flying East will be 406 miles away from airport.   the other plane will be 566 miles away from airport.   566/406= ~1.4 = ~sqrt(2)   This means that planes formed a right isocheles triangle => sides of such triangles relate as 1:1:sqrt(2) => the planes are 406 miles apart.406
Answer: C
A train 110 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going? Choices
A) 5 B) 6 C) 7 D) 9 E) 5

Solution: Speed of train relative to man = 60 + 6= 
60 + 6 = 66
66 km/hr.= 66 * 5/18 = 55/3 m/sec.   Time taken to pass the men = 110 * 3/55= 
110 * 3/55 = 6
6 sec.Answer: 6
Answer: B
A grocer stacked oranges in a pile. The bottom layer was rectangular with 5 rows of 5 oranges each. In the second layer from the bottom, each orange rested on 4 oranges from the bottom layer, and in the third layer, each orange rested on 4 oranges from the second layer. Which of the following is the maximum number of oranges that could have been in the third layer? Select the correct option: A) 2 B) 4 C) 6 D) 7 E) 9

Solution: Bottom Layer = 5 x 5 = 25   IInd Layer = (5-1) x (5-1) = 16   IIIrd Layer = (4-1) x (4-1) = 9   Answer = 9 = 9
Answer: E
If the numerator of a fraction is increased by 20% and its denominator is diminished by 25% value of the fraction is 2/15. Find the original fraction. Choose the correct choice:
A) 1/12
B) 1/8
C) 1/6
D) 1/4
E) 1/2

Solution: X * (120/100)   ---------------- = 2/15   Y * (75/100)   X/Y = 1/12   1/12NSWER:1/12
Answer: A
In Township K, 1/5 of the housing units are equiped with cable Tv. If 1/12 of the housing units, including 1/3 of those that are equiped with cable tv, are equipped with videocassette recorders, what fraction of the housing units have neither cable tv nor videocassette recorders?	Choose the most appropriate option: A) 23/30 B) 11/15 C) 47/60 D) 1/6 E) 2/15

Solution: 1/5 -- cable TV (This includes some data from video cassette recorder)   1/10 -- video cassette recorder including 1/3(equiped with cable tv) i.e. 1/3(1/5) = 1/15   therefore only video cassette recorder = 1/12 - 1/15 = 1/60   Total = 1/5+1/60+neither cable tv nor videocassette recorders   1 =13/60+ neither cable tv nor videocassette recorders   therefore neither cable tv nor videocassette recorders = 1-13/60 = 47/60   Hence 47/60.
Answer: C
Find the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.1792?
Choose the correct choice from the following answers:
A) 1600	B) 2777	C) 2889	D) 27670	E) 2771

Solution: 1792 = P [1 + (5*12/5)/100]   P= 1600.1600nswer:1600
Answer: A
The ratio of ducks and frogs in a pond is 31 : 39 respectively. The average number of ducks and frogs in the pond is 152. What is the number of frogs in the pond ? Pick one:	A) 148	B) 152	C) 156	D) 169	E) None

Solution: Solution:   Ratio of Ducks and Frogs in Pond,   = 31 : 39.   Average of Ducks and Frogs in Pond,   = 152.   So, total number of Ducks and Frogs in the Pond,   = 2* 152= 
2* 152 = 304
304.   Therefore,   Number of Frogs,= (304 *39)/70 = 169.   Answer: Option 169
Answer: D
If n is an integer greater than 7, which of the following must be divisible by 3? Choose the correct choice from the following options
A) 1. n (n+1) (n-4) B) 2. n (n+2) (n-1) C) 3. n (n+3) (n-5) D) 4. n (n+4) (n-2) E) 5. n (n+5) (n-6)

Solution: We need to find out the number which is divisible by three,   In every 3 consecutive integers, there must contain 1 multiple of 3.   So n+4 and n+1 are same if we need to find out the 3's multiple. replace all the numbers which are more than or equal to three   1. n (n+1) (n-4) = > n(n+1)(n-1) = > (n-1)n(n+1)   2. n (n+2) (n-1) = > n(n+2)(n-1) = > (n-1)n(n+1)   3. n (n+3) (n-5) = > n(n+0)(n-2) = > (n-2)n(n)   4. n (n+4) (n-2) = > n(n+1)(n-2) = > (n-2)n(n+1)   5. n (n+5) (n-6) = > n(n+2)(n-0) = > (n)n(n+2)   from the above onlyoption Ais product of consecutive three numbers.   4. n (n+4) (n-2)
Answer: D
A miniature roulette wheel is divided into 9 equal sectors, each bearing a distinct integer from 1 to 9, inclusive. Each time the wheel is spun, a ball randomly determines the winning sector by settling in that sector. If the wheel is spun four times, approximately what is the probability that the product of the four winning sectors’ integers will be even?
Choose the correct option
A) 50%
B) 67%
C) 80%
D) 90%
E) 95%

Solution: The only way to have an odd product is if all 4 integers are odd.   P(odd product) = 5/9*5/9*5/9*5/9 = 625/6561   P(even product) = 1 - 625/6561 = 5936/6561 which is about 90%   The answer is 90%.
Answer: D
The sum of the first 50 positive even integers is 2550. What is the sum of even integers from 102 to 200 inclusive?  Pick: A) 5100 B) 7550 C) 10100 D) 15500 E) 20100

Solution: First 50 even integers:   2   4   6   8   <...>   Integers from 102 to 200   102   104   106   108   <...>   We notice that each integer from the second set is 100 more than the respective integer in the first set. Since we have 50 even integers from 102 to 200, then:   2550+(100*50)= 
2550+(100*50) = 7_550
7550;ANSWER:7550
Answer: B
The product of two numbers is 468 and the sum of their squares is 289. The sum of the number is?
Choose the correct choice from the following answers
A) A)23 B) B)25 C) C)27 D) D)31 E) E)35

Solution: Let the numbers be x and y.   Then, xy = 468 and x2 + y2 = 289.   (x + y)2 = x2 + y2 + 2xy = 289 + (2 x 468) = 1225   x + y = 35.   Option 35
Answer: E
In what time will a train 120 meters long cross an electric pole, if its speed is 184 km/hr	Select the correct option.
A) 5 seconds
B) 4.5 seconds
C) 3 seconds
D) 2.3 seconds
E) None of these

Solution: Explanation:   First convert speed into m/sec   Speed = 184*(5/18) = 51 m/sec   Time = 2.3 secondsistance/speed   = 120/51 = 2.3 seconds   Option 2.3 seconds
Answer: D
A family X went for a vacation. Unfortunately it rained for 13 days when they were there. But whenever it rained in the mornings, they had clear afternoons and vice versa. In all they enjoyed 11 mornings and 12 afternoons. How many days did they stay there totally? Choose the correct choice from the following
A) 15 days B) 16 days C) 17 days D) 18 days E) 19 days

Solution: clearly 11mornings and 12 afternoons = 23 half days   since 13 days raining means 13 half days.   so 23-13= 
23-13 = 10
10 halfdays ( not effecetd by rain )   so 10 halfdays=5 fulldays   total no. of days = 13+5= 
13+5 = 18
18 days   ANSWER:18 days
Answer: D
A honey bee flies for 10 seconds, from a daisy to a rose. It immediately continues to a poppy, flying for 6 additional seconds. The distance the bee passed, flying from the daisy to the rose is 18 meters longer than the distance it passed flying from the rose to the poppy. The bee flies to the poppy at 3 meters per second faster than her speed flying to the rose. The bee flies how many meters per second from the daisy to the rose?
Choose the correct choice from the following answers
A) 1.4
B) 1.5
C) 1.6
D) 1.8
E) 1.0

Solution: Let the speed be 's' and let the distance between rose and poppy be 'x'   The problem boils down to:   Rose to Poppy: s+3=x/6 ------- 1   1.8aisy to Rose: s=(x+18)/10------ 2   so from 1 we can re write x as x=6s+18   substitute the value of x in 2 gives us s=1.8 m/s   1.8
Answer: D
A train 100m long takes 6 sec to cross a man walking at 5kmph in a direction opposite to that of the train. Find the speed of the train?
Choose the correct choice from the following choices:
A) 45kmph  B) 55kmph  C) 32kmph  D) 61kmph  E) 70kmph

Solution: Let the speed of the train be x kmph   Speed of the train relative to man = x+5 = (x+5)*5/18 m/sec   100/[(x+5)*5/18] = 6   30(x+5) = 1800   x = 55kmph   Answer is 55kmph
Answer: B
A, B, C hired a car for Rs.520 and used it for 7,8 and 11 hours respectively. Hire charges paid by B were Pick one
A) Rs.140  B) Rs.160  C) Rs.180  D) Rs.220  E) None

Solution: Solution   A : B : C	= 7 : 8 : 11.   Hire charges paid by B	= Rs(520×8/26)   = Rs.160.   Answer Rs.160
Answer: B
Johnson has a corporate proposal. The probability that vice-president Adams will approve the proposal is 0.6. If VP Adams approves the proposal, then the probability that vice-president Baker will approve the proposal is 0.7. If VP Adams doesn’t approve the proposal, then the probability that vice-president Baker will approve the proposal is 0.3. What is the probability that at least one of the two VPs, approves Johnson’s proposal? Select the correct option.
A) 0.12
B) 0.24
C) 0.28
D) 0.66
E) 0.72

Solution: (1at approves * second rejects ) + (1st rejects * 2nd approves ) + (both approves )   =0.6*0.2+0.4*0.3+0.6*0.7   = 0.12+0.12+0.42= 
0.12+0.12+0.42 = 0.66
0.66   0.66
Answer: D
A painting crew painted 80 houses. They painted the first y houses at a rate of x houses per week. Then more painters arrived and everyone worked together to paint the remaining houses at a rate of 3.25x houses per week. How many weeks did it take to paint all 80 houses, in terms of x and y?  Options
A) (320 - y)/(5x) B) (y +220)/(5x) C) 5(80 - y)/(4x) D) (y + 400)/(4x) E) (4y + 320)/(5x)

Solution: Ans (y +220)/(5x)   Plug some numbers   Let y = 40 houses and x = 20   then they painted 20 houses per week   as painters were added to the group , the rate of the group increased to 3.25 x => 3.25 * 20= 
3.25 * 20 = 65
65 houses per week   total time they took= (40/20) + (40/65) = 2.6 weeks   Putting the values of x and y in equation (y +220)/(5x)   (y +220)/(5x) = (40+220)/5*20 = 260/100= 
260/100 = 13/5 = around 2.6
2.6
Answer: B
In the xy-plane, a line has slope 3 and x-intercept 6. What is the y-intercept of the line?  Answers
A) -18  B) -3  C) 0  D) 3  E) 9

Solution: Let the line be represented by a general equation y=mx+b, where m = slope (3) and b=y intercept. We are also given the value of x-intercept 6.   Theory : y intercept represents the point on the line where the x=0, and x intercept represents the point on the line where the y=0.   Putting these values in the equation : 0 = 3*6 + b => b = -18. Hence -18.
Answer: A
On a purchase of $110, a store offered a payment plan consisting of a $10 down payment and 12 monthly payments of $10 each. What percent of the purchase price, to the nearest tenth of a percent, did the customer pay in interest by using this plan? Options.
A) 9.5%
B) 10.5%
C) 11.5%
D) 9.1%
E) 12.5%

Solution: 12*10 + 10= 
12*10 + 10 = 130
130   (10/110)* 100= 9.1   Answer : 9.1%
Answer: D
If the price of an article went up by 50%, then by what percent should it be brought down to bring it back to its original price?  Pick one.
A) 2/3%  B) 2/8%  C) 2/1%  D) 33.3%  E) 2/7%

Solution: Let the price of the article be Rs. 100.   50% of 100 = 50.   New price = 100 + 50 = Rs. 150   Required percentage = (150 - 100)/150 * 100   = 50/150 * 100= 33.33%.   Answer:33.3%
Answer: D
A man 24 years older than his son. In two year his age will be twice of his son. what is the present age of his son?
Choose the correct choice from the following answers:
A) 23 B) 22 C) 21 D) 20 E) 32

Solution: Correct Answer : B   present age of son = x years   present age of man = ( x +24 )years   In two year his age will be twice of his son.   (x +24)+2=2(x+2)   x=22
Answer: B
The total of the ages of Jayant, Prem and Saransh is 75 years. Ten years ago, the ratio of their ages was 2 : 3 : 4. What is the present age of Prem?
Choose one
A) 25 years B) 32 years C) 34 years D) 38 years E) None

Solution: Solution   Let the ages of Jayant, Prem and Saransh 10 years ago be 2x, 3x and 4x years respectively. Then,   (2x + 10)+(3x + 10)+(4x + 10)	= 75.   ‹=›9x = 45   x = 5.   ∴ Prem's present age = 3x + 10 = 25 years.   25 yearsnswer 25 years
Answer: A
A chemical is composed of hydrogen, oxygen and nitrogen. If 20 moles of the chemical is to be made containing twice as much hydrogen as oxygen and three times as much oxygen as nitrogen how many moles of oxygen is required?	Choose the correct choice.
A) 5 moles  B) 6 moles  C) 8moles  D) 2 moles  E) 1.5 moles

Solution: Amount of chemical=20 moles   hydrogen=2 oxygen   oxygen=3 nitrogen   hydrogen+oxygen+nitrogen=20   2 oxygen+oxygen+1/3 oxygen=20   10 oxygen=20   oxygen=2   Answer is 2 moles
Answer: D
3889 + 12.597 - ? = 3854.002 Select the correct option
A) A)47.095  B) B)47.595  C) C)47.932  D) D)47.95  E) of the above

Solution: Let 3889 + 12.597 - x = 3854.002.   Then x = (3889 + 12.597) - 3854.002   = 3901.597 - 3854.002   = 47.595.   Answer = 47.595
Answer: B
A cricketer has a certain average for 10 innings. In the eleventh inning, he scored 108 runs, there by increasing his average by 8 runs. His new average is:	Choose the correct choice from the following choices:
A) 22 runs
B) 24 runs
C) 26 runs
D) 28 runs
E) 30 runs

Solution: Let average for 10 innings be x. Then,   (10x + 108)/11 = x + 8   = 11x + 88 = 10x + 108   = x = 20.   New average = (x + 8) = 28 runs.   Answer:28 runs
Answer: D
If 1 added to the age of the elder sister, then the ratio of the ages of two sisters becomes 0.5:1, but if 2 is subtracted from the age of the younger one, the ratio becomes 1:3, the age of the younger sister will be?
Select the correct option
A) 7 years
B) 5 years
C) 8 years
D) 10 years
E) 4 years

Solution: Explanation :   Let, the age of the elder sister be x year, and younger sister be y year.   Now, according to the question,   y/(x+1)=0.5/1.   =>y/(x+1)=1/2.   =>2y= x + 1   =>x−2y =−1 -------(i)   And,   =>(y−2)/x=1/3.   =>x−3y =−6 -------(ii)   On solving these equations, we get :-   x=9 and y=5   Hence, the age of the younger sister is 5 years.   Answer : 5 years
Answer: B
The current of a stream runs at the rate of 4 kmph. A boat goes 6 km and back to the starting point in 2 hours, then find the speed of the boat in still water? Choose the correct choice from the following answers.
A) 7 B) 6 C) 8 D) 5 E) 3

Solution: S = 4   M = x   DS = x + 4   US = x - 4   6/(x + 4) + 6/(x - 4) = 2   x = 8   Answer:8
Answer: C
There are 10 children in a company's day-care center, and a pair of children is to be selected to play a game. At most, how many different pairs are possible? Choices.
A) 100  B) 90  C) 50  D) 45  E) 25

Solution: 1. first child out of 10 - 10 possibilities   2. second child out of 9 - 9 possibilities. the total number of pairs = 9*10= 
9*10 = 90
90   3. exclude xy yx cases:  90/2= 
 90/2 = 45
45   Second way   N=10C2=10!/(8!2!)=10*9/2= 
10*9/2 = 45
45   ANS:45
Answer: D
Ramesh can finish a work in 20 days and Sushil in 25 days. They both work together for 5 days and then Sushil goes away. In how many days will Ramesh complete the remaining work?
Choices:  A) 11  B) 10  C) 9  D) 8  E) 7

Solution: (5 + x)/20 + 5/25 = 1 => x = 11 days   11NSWER 11
Answer: A
Of the three-digit integers greater than 900, how many have two digits that are equal to each other and the remaining digit different from the other two? Choose one: A) 94 B) 82 C) 80 D) 45 E) 36

Solution: To satify the given condition,   required no. of cases = total numbers - numbers with all digits different - numbers when all three digits are same,   number greater than 700;   total numbers = 1*10*10= 
1*10*10 = 100
100   numbers with all digits different= 1*9*8= 
1*9*8 = 72
72   numbers when all three digits are same (777)= 1   req. = 100- 72 - 1= 
100- 72 - 1 = 27
27   considering the numbers between 700999= 27*3=95   94nswer is 94 ('cause 700 can't be included)   94nswer (94).
Answer: A
The distance between a gym and a pharmacy is approximately 1.2 x 10^5 inches. Which of the following is closest to the distance between the gym and a pharmacy, in kilometers? (1 kilometer is approximately 3.9 x 10^4 inches.)	Choose the correct choice from the following answers
A) 3.1
B) 3.9
C) 3.7
D) 4.2
E) 4.8

Solution: We know that 1 kilometer = 3.9x10^4 inches. Therefore, we now have a ratio of (1 kilometer/3.9x10^4 inches).   We also know that the distance between the gym and a pharmacy is approximately 1.2 x 10^5 inches. To convert inches to kilometers, we need to multiply 1.2 x 10^5 inches by the ratio we just found out.   kilometers = 1.2 x 10^5 inches x (1 kilometer/3.9x10^4 inches) [note: "inches" cancel out, leaving us with just km]   km = 1.2 x 10^5/3.9x10^4 km   km = 3.08 = 3.1 km   Therefore, we can see that the closest answer is 3.1.
Answer: A
I. x2 + 5x + 6 = 0,
II. y2 + 9y +14 = 0 to solve both the equations to find the values of x and y? Choose the correct choice from the following answers
A) If x < y B) If x > y C) If x ≤ y D) If x ≥ y E) If x = y or the relationship between x and y cannot be established.

Solution: I. x2 + 3x + 2x + 6 = 0   => (x + 3)(x + 2) = 0 => x = -3 or -2   II. y2 + 7y + 2y + 14 = 0   => (y + 7)(y + 2) = 0 => y = -7 or -2   No relationship can be established between x and y.   ANSWIf x = y or the relationship between x and y cannot be established.R:If x = y or the relationship between x and y cannot be established.
Answer: E