MU-NLPC/Calc-aqua_rat huggingface dataset:
If a copier makes 2 copies every 4 seconds, then continues at this rate, how many minutes will it take to make 8,000 copies?  Choose the correct option
A) 266.67	B) 130	C) 140	D) 135	E) 141

Solution: 2 copies 4 seconds   8000 copies = (8000*4)/2= 
(8000*4)/2 = 16_000
16000/60 minutes= 266.67 minutes   266.67nswer : 266.67
Answer: A
There are 32 students in a certain geometry class. If two thirds of the students are boys and three fourths of the boys are under six feet tall, how many boys in the class are under six feet tall?
Choose the correct choice from the following answers:
A) 6
B) 12
C) 16
D) 24
E) 27

Solution: 32*2/3 *3/4= 
32*2/3 *3/4 = 16
16   Answer: 16
Answer: C
Given the equation e=-g^4, which of the following must be true?
I. If g is negative then e is negative.
II. e is negative.
III. g is non-negative.	Choose the correct choice from the following answers.
A) II only	B) I only	C) II and III only	D) III only	E) I and II only

Solution: If e=-g^4, which of the following must be true?   First of all notice g^2 is always non-negative, so -g^2 is non-positive (zero or negative), which means that e is zero when g=0 and e is negative for ANY other value of g.   I. e is negative --> not necessarily true, if g=0 then e=-m^2=0;   II. g is non-negative. g can take ANY value: positive, negative, zero. We don't have any restrictions on its value;   III. If g is negative then e is negative. m is negative means that m is not zero.   Answer: I only (I only).
Answer: B
A group of 10 representatives is to be selected out of 12 seniors and 10 juniors. In how many different ways can the group be selected, if it should have 5 seniors and 5 juniors?
Choose the correct answer.
A) ¹²C₅ * 10
B) ¹²C₇ * 10
C) ¹²C₇ * ¹⁰C₅
D) 12 * ¹⁰C₅
E) None of these

Solution: Here, five seniors out of 12 seniors can be selected in ¹²C₅ ways. Also, five juniors out of ten juniors can be selected ¹⁰C₅ ways. Hence the total number of different ways of selection = ¹²¹²C₇ * ¹⁰C₅₅ * ¹⁰¹²C₇ * ¹⁰C₅₅ = ¹²¹²C₇ * ¹⁰C₅₇ * ¹⁰¹²C₇ * ¹⁰C₅₅   = ¹²¹²C₇ * ¹⁰C₅₅ = ¹²¹²C₇ * ¹⁰C₅₇   ANSWER:¹²C₇ * ¹⁰C₅
Answer: C
The difference between compound interest and simple interest on a certain amount of money at 5% per annum for 2 years is 16. Find the sum : Choose the correct choice:
A) 4500 B) 7500 C) 5000 D) 6400 E) None of these

Solution: Sol.(d) Let the sum be 100.   Therefore, SI = 100×5×2/100=10   and CI = 100(1+5/100)2−100   ∴ =100×21×21/20×20−100=41/4   6400ifference of CI and SI = 41⁄4 - 10 = 1⁄4   If the difference is 1⁄4 , the sum = 100   => If the difference is 16, the sum   = 400 × 16 = 6400 Answer 6400
Answer: D
Stacy has a 12 page history paper due in 12 days. How many pages per day would she have to write to finish on time?  Pick
A) 9	B) 8	C) 10	D) 1	E) 6

Solution: 12/12= 
12/12 = 1
1   Answer : 1
Answer: D
Look at this series: VI, 10, V, 11, __, 12, III, ... What number should fill the blank?
Choose the correct choice:
A) II
B) IV
C) IX
D) 14
E) None

Solution: Explanation: This is an alternating addition and subtraction series. Roman numbers alternate with Arabic numbers. In the Roman numeral pattern, each number decreases by 1. In the Arabic numeral pattern, each number increases by 1.   Answer: Option IV
Answer: B
Two pipes A and B can separately fill a tank in 2 minutes and 15 minutes respectively. Both the pipes are opened together but 4 minutes after the start the pipe A is turned off. How much time will it take to fill the tank? Select the correct option: A) 2 B) 7 C) 8 D) 6 E) 10

Solution: 4/12 + x/15 = 1   x = 10   Answer: 10
Answer: E
The sum of two numbers is 50. Their difference is 10. The bigger number is  Choose the correct choice
A) 20	B) 25	C) 30	D) 35	E) 45

Solution: X + Y = 50   X - Y = 10   Adding 2X = 60 ==> X = 30 and Y = 50 - 30= 
50 - 30 = 20
20   Bigger number is X= 30   Answer 30.
Answer: C
A bowl was filled with 10 ounces of water, and 0.08 ounce of the water evaporated each day during a 50-day period. What percent of the original amount of water evaporated during this period? Choose one.
A) 0.004%
B) 0.04%
C) 40%
D) 4%
E) 40%

Solution: Total amount of water evaporated each day during a 50-day period = .08 * 50   =.08 * 100/2   = 8/2= 
8/2 = 4
4   percent of the original amount of water evaporated during this period= (4/10) * 100= 
(4/10) * 100 = 40
40 %   Answer 40%
Answer: C
There are 3 department available in XYZ company,namely Finance, Marketing, HR.The total expenditure of the company $69700.the ratio of department expenditure are 11:14:16.Then find out the total expenditure of marketing department? Choose the correct choice.
A) $27560 B) $28900 C) $27250 D) $15600 E) $23800

Solution: Finance:Marketing:HR ratio of expenditure = 11+14+16= 
11+14+16 = 41
41;   Expenditure of marketing department= 14/41 * $69700 = $23800.   Answer 14/41 *  69700= 
14/41 *  69700 = 23_800
$23800.   Answer=$23800
Answer: E
Barbata invests $2400 in the National Bank at 5%. How much additional money must she invest at 8% so that the total annual income will be equal to 6% of her entire investment?
Choose the most appropriate option:  A) 1200  B) 3000  C) 1000  D) 3600  E) 2400

Solution: Let the additional invested amount for 8% interest be x;   Equation will be;   2400+0.05*2400+x+0.08x = 2400+x+0.06(2400+x)   0.05*2400+0.08x = 0.06x+0.06*2400   0.02x = 2400(0.06-0.05)   x = 2400*0.01/0.02= 
2400*0.01/0.02 = 1_200
1200   1200ns: "1200"
Answer: A
Ramu bought an old car for Rs. 45000. He spent Rs. 12000 on repairs and sold it for Rs. 80000. What is his profit percent? Choose the correct answer:
A) 16%  B) 17%  C) 40%  D) 58%  E) 13%

Solution: Total CP = Rs. 45000 + Rs. 12000   = Rs. 57000 and SP = Rs. 80000   Profit(%)   = (80000 - 57000)/57000 * 100   = 40%   Answer: 40%
Answer: C
A man can row his boat with the stream at 6 km/h and against the stream in 4 km/h. The man's rate is? Choose the correct choice from the following.
A) 1 kmph
B) 7 kmph
C) 98 kmph
D) 6 kmph
E) 4 kmph

Solution: DS = 6   US = 4   S = ?   S = (6 - 4)/2= 
(6 - 4)/2 = 1
1 kmph   1 kmphnswer: 1 kmph
Answer: A
A hall 36m long and 15m broad is to be paved with stones, each measuring 5dm by 5 dm. The number of stones required is:
Select:
A) 180
B) 1800
C) 18
D) 2160
E) 1.8

Solution: Area of the hall= 3600*1500   Area of each stone= (50*50)   Therefore, number of stones= (3600*1500/ 50*50)= 2160   ANSWER:2160
Answer: D
Using all the letters of the word "LETTERS", how many words can be formed, which begin with L and end with S?
Select the correct option: A) 50 B) 120 C) 160 D) 100 E) 124

Solution: There are five letters in the given word.   Consider 7 blanks ....   The first blank and last blank must be filled with L and S all the remaining three blanks can be filled with the remaining 5 letters in 5! ways.   The number of words = 5! = 120.   Answer: 120
Answer: B
Find the invalid no.from the following series 2,3,12,37,86,166,288 Answers:
A) 2
B) 3
C) 166
D) 288
E) 37

Solution: 3-2= 
3-2 = 1
1   12-3= 
12-3 = 9
9   37-12= 
37-12 = 25
25   86-37= 
86-37 = 49
49   166-86= 
166-86 = 80
80(this must be 81=167-86= 
167-86 = 81
81)   so wrong number in the sequence is 166   difference between two sucessive numbers sequence would be   1,9,25,49,81,121(square of 1,3,5,7,9,11)   166
Answer: C
How many numbers amongst the numbers 8 to 52 are there which are exactly divisible by 5 but not by 3? Choose the correct choice from the following choices:
A) Nil B) 1 C) 2 D) 3 E) More than 3

Solution: 10,15,20,25,30,35,40,45,50 are divisible by 5.   15,30,45 are divisible by 3 also.   So there are 6 numbers exactly divisible by 5 but not by 3   ANSWMore than 3R:More than 3
Answer: E
In one hour a boat goes 14 km long the stream and 6 km against the stream.The speed of the boat in still water is?  Choose one.
A) 7	B) 10	C) 12	D) 11	E) 13

Solution: Speed in still water A = ½ ( 14+6) km/hr A= 10 kmph   Answer: 10
Answer: B
In the infinite sequence 27, 36, 45, 54, 63, . . . , where each term is 9 greater than the previous term, the 55th term is Choose the correct choice from the following.
A) 783	B) 513	C) 198	D) 963	E) 741

Solution: T(n) = a + (n-1) d   Here d =9, a=27, n=55   Solving we get T(n) = 513.   Answer: 513
Answer: B
If the positive integer y is divisible by 3, 8, and 16, then which of the following must y be divisible by?
I. 21
II. 32
III. 48	Choose the correct choice from the following answers
A) III only	B) II only	C) I and II only	D) II and III only	E) I, II, and III

Solution: III onlynswer = III only   LCM of 3, 8, 16 = 48   III onlynswer = 48   III onlynswer : III only
Answer: A
An article is bought for Rs.700 and sold for Rs.900, find the gain percent? Choose the correct option:	A) 33 1/8%	B) 33 8/3%	C) 28 4/7%	D) 35 1/3%	E) 32 1/3%

Solution: 700 ---- 200   100 ---- ? => 28 4/7%   Answer: 28 4/7%
Answer: C
What will be the cost of building a fence around a square plot with area equal to 289 sq ft, if the price per foot of building the fence is Rs. 57?  Choose the correct choice from the following.
A) s.3876
B) s.3948
C) s.3942
D) s.3965
E) s.3929

Solution: Let the side of the square plot be a ft.   a2 = 289 => a = 17   Length of the fence = Perimeter of the plot = 4a = 68 ft.   Cost of building the fence = 68 * 57   = Rs.3876.   s.3876nswer: s.3876
Answer: A
The paragraph can start only with the sentence E. The opening words of the sentence of ‘B’ – ‘these two parties’ is a continuation of the last words of the sentence E– ‘two parties’. There are only two options with EB; in the option 4, D follows B; but whom the opening pronoun ‘he’ of D does refer to? F is the further explanation of B. Hence EBFCAD. Choose the correct answer:
A) 11
B) 77
C) 26
D) 99
E) 171

Solution: Answer:	77
Answer: B
1604 x 1604 = ?  Pick:
A) A)2572816
B) B)3624216
C) C)3624316
D) D)3625116
E) E)3625216

Solution: 1604 x 1604 = (1604)2   = (1600 + 4)2   = (1600)2 + (4)2 + (2 x 1600 x 4)   = 2560000 + 16 + 12800.= 
2560000 + 16 + 12800. = 2_572_816
2572816.   2572816)
Answer: A
Arrange 4boys and 4girls in a row such that all the 4 girls are together.  Answers:  A) 1240  B) 1440  C) 2880  D) 3200  E) 3260

Solution: Treat all the 4 girls as G   4boys and G can be arranged in 5!ways   G can be arranged among them in 4!ways   total = 5!*4! = 2880   correct option is 2880
Answer: C
If s and t are positive integers such that s/t = 43.18, which of the following could be the remainder when s is divided by t ? Pick one
A) 44
B) 17
C) 54
D) 20
E) 47

Solution: s/t= 43.18   s = 43.18t   s = (43 + 0.18)t   s = 43t + (18/100)t   s = 43t + (9/50)t   So remainder will be multiple of 9. The only multiple of 9 is 54.   Ans. 54
Answer: C
he number of sequences in which 8 players can throw a ball, so that the youngest player may not be the last is?	Choose the correct option.
A) 43288  B) 23770  C) 43200  D) 35280  E) 27820

Solution: x Not younger_______ ↑   The last ball can be thrown by any of the remaining 7 players. The first 7 players can throw the ball in 7p7₆ ways.   The required number of ways = 7(7!) = 35280   Answer:35280
Answer: D
Find the number of square tiles to cover the floor of a room measuring 6 m * 11 m leaving 0.50 m space around the room. A side of square tile is given to be 50 cms? Answers:
A) 187
B) 476
C) 200
D) 208
E) 276

Solution: Area of the room =5 * 10= 
5 * 10 = 50
50   Area of the tile= 0.5 *0.5= 
0.5 *0.5 = 0.25
0.25   No. of tiles=50/0.25= 
50/0.25 = 200
200   Answer : 200
Answer: C
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:
Select:
A) 276	B) 299	C) 322	D) 345	E) 354

Solution: Clearly, the numbers are (23 x 13) and (23 x 14).   Larger number = (23 x 14) = 322.   Answer: Option 322
Answer: C
The sector of a circle has radius of 14 cm and central angle 108o. Find its perimeter?
Choose the correct choice from the following answers.
A) 52cm
B) 54.4cm
C) 60cm
D) 65cm
E) 70cm

Solution: Perimeter of the sector = length of the arc + 2(radius)   = (108/360 * 2 * 22/7 * 14) + 2(14)   = 26.4 + 28= 
26.4 + 28 = 54.4
54.4 cm   Answer:54.4cm
Answer: B
A number increased by 25% gives 520. The number is?  Choose the correct choice.
A) 216  B) 316  C) 616  D) 516  E) 416

Solution: Formula = TOTAL=100% ,INCR416AS416 = "+" D416CR416AS416= "-"   A number means = 100 %   That same number increased by 25 % = 125 %   125 % -------> 520 (120 Ã— 4.16 = 520)   100 % -------> 416 (100 Ã— 4.16 = 416)   Option '416'
Answer: E
What percent is 520 gm of 1 kg? Choose the correct choice:
A) 25%
B) 40%
C) 52%
D) 8%
E) 12%

Solution: 1 kg = 1000 gm   520/1000 Ã— 100 = 52000/1000= 
52000/1000 = 52
52 %   Answer is 52%
Answer: C
In 10 years, A will be twice as old as B was 10 years ago. If A is now 9 years older than B, the present age of B is :  Choose the correct choice from the following answers.
A) 19  B) 29  C) 39  D) 49  E) None of these

Solution: Explanation:   Let B's present age = x years. Then, A's present age = (x + 9) years.   (x + 9) + 10 = 2(x - 10)   => x + 19 = 2x - 20   => x =39. Answer: 39
Answer: C
Ramu bought an old car for Rs. 42000. He spent Rs. 13000 on repairs and sold it for Rs. 64900. What is his profit percent?  Choose the correct choice from the following choices.
A) 33	B) 12	C) 18	D) 19	E) 11

Solution: Total CP = Rs. 42000 + Rs. 13000 = Rs. 55000 and SP = Rs. 64900   Profit(%) = (64900 - 55000)/55000 * 100= 
(64900 - 55000)/55000 * 100 = 18
18%   Answer: 18
Answer: C
An amount of Rs. 85000 is invested in two types of shares. The first yields an interest of 9% p.a and the second, 11% p.a. If the total interest at the end of one year is 9 3/4 %, then the amount invested in each share was?  Choices
A) s. 53125; Rs. 31875 B) s. 62500; Rs. 37500 C) s. 72500; Rs. 27500 D) s. 82500; Rs. 17500 E) s. 72500; Rs. 17500

Solution: Let the sum invested at 9% be Rs. x and that invested at 11% be Rs. (85000 - x). Then,   (x * 9 * 1)/100 + [(85000 - x) * 11 * 1]/100 = (85000 * 39/4 * 1/100)   (9x + 935000 - 11x)/100 = 39000/4 = 16575/2   x = 53125   Sum invested at 9% = Rs. 53125   Sum invested at 11% = Rs. (85000 - 53125) = Rs. 31875.   s. 53125; Rs. 31875NSWER:s. 53125; Rs. 31875
Answer: A
Of the three numbers, the sum of the sum of the first two is 45; the sum of the second and the third is 55 and the sum of the third and thrice the first is 90. the third number is :  Options:  A) 20  B) 25  C) 30  D) 3  E) None of these

Solution: Solution   Let the numbers be x,y, and z. then, x + y = 45, y + x = 55 and 3 x + z = 90   ⇒ y = 45 - x, z = 55 - y = 55 - (45 - x) = 10 + x.   ∴ 3 x + 10 + x = 90 or x = 20.   y = (45 - 20)= 
(45 - 20) = 25
25 and z= (10 + 20)= 
(10 + 20) = 30
30.   ∴ third number= 30   Answer 30
Answer: C
In a two digit number, the digit in the units place is three times the digit in ten's place and sum of the digits is equal to 8. What is the number?  Select.
A) 26  B) 28  C) 32  D) 36  E) 38

Solution: Solution   Let the ten digits be x. Then,units digit=3x   Therefore x + 3x = 8   ‹=›4x = 8   ‹=›x= 2.   So, ten's digit = 2, unit's digit = 6.   Hence, the required number is 26.   26nswer 26
Answer: A
If 8m − n = p, then which of the following represents the average (arithmetic mean) of m, n, and p, in terms of m?  Choose the correct choice from the following.
A) 2m −1  B) 3m  C) 6m  D) m/5  E) 6m/5

Solution: 8m - n = p   Add n to both sides:   8m = n + p   Add m to both sides:   9m = n + p + m   Now, divide both sides by 3   3m = (n + p + m)/3 = the average of n, p, and m   3m
Answer: B
Given 2 negative numbers, the greater of the two is quadrupled, the difference between it and the lesser number is 14. what is the greater number if the product of both numbers is 30?	Choices:  A) -9  B) -8  C) -4  D) -1  E) -5

Solution: Test the options. The options give you the greater number. Start from the middle option.   (C) - 4   quadruple of -4 is -16 and 14 less is -2.   -2 * -4= 
-2 * -4 = 8
8 (Not correct)   ...   (E) - 5   quadruple of -5 is -20 and 14 less is -6.   -6 * -5= 
-6 * -5 = 30
30   Correct   Answer (-5)
Answer: E
A merchant marks goods up by 75% and then offers a discount on the marked price. The profit that the merchant makes after offering the discount is 22.5%. What % discount did the merchant offer?
Choose one:
A) 20%	B) 25%	C) 30%	D) 35%	E) 40%

Solution: Let P be the original price of the goods and let x be the rate after the markup.   (1.75P)*x = 1.225P   x = 1.225/1.75= 
1.225/1.75 = 0.7
0.7 which is a discount of 30%.   The answer is 30%.
Answer: C
A cube with its sides numbered 1 through 6 is rolled twice, first landing on a and then landing on b. If any roll of the cube yields an equal chance of landing on any of the numbers 1 through 6, what is the probability W that a + b is prime? Choose the correct choice from the following answers:
A) 0	B) 1/12	C) 5/12	D) 7/18	E) 4/9

Solution: Total # of outcomes is 6*6= 
6*6 = 36
36;   Favorable outcomes:   a-b --> prime   1-1 --> 2;   1-2 --> 3;   2-1 --> 3;   1-4 --> 5;   4-1 --> 5;   2-3 --> 5;   3-2 --> 5;   1-6 --> 7;   6-1 --> 7;   2-5 --> 7;   5-2 --> 7;   3-4 --> 7;   4-3 --> 7;   6-5 --> 11;   5-6 --> 11.   Total of 15 favorable outcomes   W=15/36.   Answer: 5/12.
Answer: C
A string of 30 light bulbs is wired in such a way that if any individual light bulb fails, the entire string fails. If for each individual light bulb the probability of failing during time period T is 0.1, what is the probability that the string of light bulbs will fail during the time period T?  Choose the correct answer:
A) 0.1
B) (0.1)^30
C) 1 - (0.1)^30
D) (0.93)^30
E) 1 - (0.90)^30

Solution: The string of light bulbs will fail if at least one light bulb fails. So, let's find the probability of the opposite event and subtract that value from 1.   The opposite event is when none of the 30 light bulbs fails, since the probability of each light bulb not to fail is 1-0.1= 
1-0.1 = 0.9
0.90 the the probability that none of the 30 light bulbs fails is 0.90^30.   Hence, the probability that at least one light bulb fails is 1-0.90^30.   Answer: E.   Now, you should have spotted that your reasoning was not right because of one simple thing, consider the case when we have 100 light bulbs instead of 30, then according to your logic the probability that the string of light bulbs will fail would be 100*0.1= 
100*0.1 = 10
10, which is not possible since the probability of an event cannot be more than 1 (100%).
Answer: E
In a class of 70 students, 10 did not opt for math. 5 did not opt for science and 3 did not opt for either. How many students of the class opted for both math and science?  Choose the correct choice from the following choices.
A) 23  B) 25  C) 27  D) 37  E) 38

Solution: 70 students total   10 did not opt for math   5 did not opt for science   3 did not opt for either   Total of 40 students in math and 2 did not opt for sci but did for math    40-2= 
 40-2 = 38
38   38 students of the class opted for both math and science   Answer:38
Answer: E
A coin is tossed live times. What is the probability that there is at the least one tail?	Choices
A) 31/32	B) 31/38	C) 31/31	D) 61/38	E) 31/35

Solution: Let P(T) be the probability of getting least one tail when the coin is tossed five times.   = There is not even a single tail.   i.e. all the outcomes are heads.   = 1/32 ; P(T) = 1 - 1/32 = 31/32   31/32nswer: 31/32
Answer: A
John bought a shirt on sale for 25% off the original price and another 25 % off the discounted price. If the final price was $19, what was the price before the first discount?	Choose the most appropriate option:
A) $45.10
B) $34.31
C) $28.44
D) $67.54
E) $33.77

Solution: let x be the price before the first discount. The price after the first discount is   x - 25%x (price after first discount)   A second discount of 25% of the discounted price after which the final price is 19   (x - 25%x) - 25%(x - 25%x) = 19   Solve for x   x = $33.77   correct answer $33.77
Answer: E
What will be the ratio of simple interest earned by certain amount at the same rate of interest for 2 years and that for 12 years?
Select
A) 3 : 2	B) 1 : 3	C) 1 : 6	D) 3 : 1	E) 2 : 1

Solution: Explanation :   Simple Interest = PRT/100   Here Principal(P) and Rate of Interest (R) are constants   Hence, Simple Interest ∝ T   Required Ratio = Simple Interest for 2 years/Simple Interest for 12 years   =T1/T2   =2/12   =1/6   =1:6   Answer : Option 1 : 6
Answer: C
The sale price of an article including the sales tax is Rs. 616. The rate of sales tax is 10%. If the shopkeeper has made a profit of 18%, then the cost price of the article is:	Select.
A) 500 B) 474.6 C) 222 D) 297 E) 111

Solution: Explanation:   110% of S.P. = 616   S.P. = (616 * 100)/110 = Rs. 560   C.P = (100 * 560)/118 = Rs. 474.6   Answer:474.6
Answer: B
A certain car traveled twice as many miles from Town A to Town B as it did from Town B to Town C. From Town A to Town B, the car averaged 40 miles per gallon, and from Town B to Town C, the car averaged 50 miles per gallon. What is the average miles per gallon that the car achieved on its trip from Town A through Town B to Town C?  Choose one
A) 42.85
B) 40
C) 35
D) 41
E) 39

Solution: step 1) took LCM of 40 and 50.. came as 200.   step 2) 200 distance between B to C... do 200/50 hence 4 gallons used   step 3) twice distance.. hence 200*2= 400... do as above.. 400/40= 10 gallons used   step 4) total gallons.. 4+10= 14 gallons   step ) total miles= 200+400= 
200+400 = 600
600 miles   hence.. average of whole journey= 600/14 which comes to 42.85   42.85nswer : 42.85
Answer: A
The cost price of a Rs. 100 stock at 4 discount, when brokerage is 15% is  Choose the correct option.
A) Rs. 96.25 B) Rs. 96.2 C) Rs. 97.25 D) Rs. 97.5 E) Rs. 97.75

Solution: Explanation :   Cost Price = 100−4+1/5=96.2   Answer : Option Rs. 96.2
Answer: B
If a+b+c=13, a2+b2+c2=69, then find ab+bc+ca  Choose the correct choice from the following:	A) -50	B) 50	C) 69	D) 75	E) 89

Solution: (a+b+c)2= a2+b2+c2+2(ab+bc+ca)   2(ab+bc+ca)= (a+b+c)2- a2+b2+c2   =169-69= 
169-69 = 100
100   ab+bc+ca=50   ANSWER 50 50
Answer: B
Set S consists of integers {1,3,5,7}. If two numbers are chosen from set S at random, what is the probability that the product of 2 numbers is more than 15? Select:  A) 1/2  B) 1/3  C) 1/5  D) 1/6  E) 2/3

Solution: Number of ways you can choose 2 from 4 = 4C2 = 6   E = event of getting the 2 numbers product is more than 15 = (3,7),(5,7) = 2   probability = 2/6 = 1/3   Answer is 1/3
Answer: B
Which of the numbers below is the odd one out
1,65,190,406,749,950,1261.
Choose the correct answer
A) 190	B) 406	C) 950	D) 749	E) 1261

Solution: 950 is the odd man.. diff between sucessive are 950ube Numbers   ANSWER:950
Answer: C
At a florist shop on a certain day, all corsages sold for either $25 or $40. If 8 of the corsages that sold for $30 had instead sold for $20, then the store's revenue from corsages that day would have been reduced by 40 percent. What was the store's actual revenue from corsages that day?  Choose the correct answer:
A) $200
B) $400
C) $600
D) $800
E) $300

Solution: I am doing it elaborately, hope it will help you.   Let, No. of corsages @ $25 = x, no. of corsages @ $40 = y and revenue= r   so, 25x+40y=r.........(1)   Now,   Given the situation, 25(x+8) + 40(y-8)= r-.4r   => 25x+200+40y-320 = .6r   => 25x+40y = .8r+120............(2)   so, r = .6r+120   => r = 300   The answer is $300.
Answer: E
Pipe A can fill a tank in 45 hrs and pipe B can fill it in 36 hrs. If both the pipes are opened in the empty tank. In how many hours will it be full?
Choose the correct choice from the following:
A) 10 hr B) 15 hr C) 20 hr D) 25 hr E) 28 hr

Solution: Part filled A in 1 hr= (1/45)   Part filled B in 1 hr= (1/36)   Part filled by (A+B) together in 1 hr=(1/45)+(1/36)=1/20   So, The tank will be full in 20 hr.   Answer : 20 hr
Answer: C
Find a sum for first 6 prime numbers?  Choose the correct choice: A) 22 B) 28 C) 29 D) 32 E) 41

Solution: Required sum = (2 + 3 + 5 + 7 + 11+ 13)= 
(2 + 3 + 5 + 7 + 11+ 13) = 41
41   Note: 1 is not a prime number   Option 41
Answer: E
f(x) is a function such that f(2x + 1) = 2f(x) + 1 for all real numbers x and f(0) = 2. Find the value of f(3). Options
A) 9  B) 10  C) 11  D) 12  E) 15

Solution: f(2x + 1) = 2f(x) + 1 : given   f(3) = 2f(1) + 1 : x = 1 in A   f(1) = 2f(0) + 1 : x = 0 in A   f(3) = 11 : substitute   correct answer is 11) 11
Answer: C