MU-NLPC/Calc-aqua_rat huggingface dataset:
How many words can be formed from the letters of the word ‘EXTRA’ so that the vowels are never together?  Choose the correct choice
A) 72	B) 54	C) 23	D) 68	E) 95

Solution: Sol. The given word contains 5 different letters.   Taking the vowels EA together, we treat them as one letter.   Then, the letters to be arranged are XTR (EA).   These letters can be arranged in 4! = 24 ways.   The vowels EA may be arranged amongst themselves in 2! = 2 ways.   Number of words, each having vowels together = (24x2) = 48 ways.   Total number of words formed by using all the letters of the given words   = 5! = (5x4x3x2x1) = 120.   Number of words, each having vowels never together = (120-48)= 
(120-48) = 72
72.   72ns: 72
Answer: A
Ramesh spends 75% of his income. His income is increased by 20% and he increased his expenditure by 10%.Find the percentage increase in his savings Choose the correct choice from the following answers
A) 30%	B) 35%	C) 40%	D) 45%	E) 50%

Solution: Let the original income=Rs.100 . Then , expenditure=Rs.75 and savings =Rs.25   New income =Rs.120 , New expenditure =   Rs.((110/100)*75)=Rs.165/2   New savings = Rs.(120-(165/2)) = Rs.75/2   Increase in savings = Rs.((75/2)-25)=Rs.25/2   Increase %= ((25/2)*(1/25)*100)= 
((25/2)*(1/25)*100) = 50
50%.   ANSW50%R 50%
Answer: E
A bank issued credit card numbers and the corresponding PIN (Personal Identification Number). Both are 3-digit numbers up to 996. Pinaki was the last to get the credit card and so he had the last possible credit card number.
He was afraid of forgetting his PIN. He wrote down the number 125 in his diary to remember his PIN. He also wrote out the way to calculate 125 : "Multiply the card number by PIN. Divide the product by 997. The remainder is 125".
Once, Prafull saw his diary in which Pinaki wrote this number 125. Prafull did a lot of purchasing, as he now knows Pinaki's PIN. What is Pinaki's PIN?
Choose the correct answer.
A) 874  B) 872  C) 876  D) 875  E) 879

Solution: Explanation :   Let, the PIN is x.   According to the question,   The card number =996 and Remainder =125.   Thus, (996 × x)/997=125.   =>x= 872.   Answer : 872
Answer: B
If the GCD of two distinct numbers (not equal, both integers, greater than 1) is 3, then which of the following can be true?
A. They are prime.
B. They are not even.
C. They do not have a common prime factor.
D. They do not have a common factor other than 3.  Choose the correct choice from the following answers: A) Only A B) Only B C) Only C D) Only D E) Only A and D

Solution: The GCD of two distinct numbers (not equal, both integers, greater than 1) is 3 means that they don't share factors greater than 3. Allowed factors are 1, 2, and 3. Defined factors are 1 and 3. The sequence is (3, 6, 9, 27, 81,...).   A. They are not prime. 3 is the only prime number that is divisible by 3, so one number can be prime but the other number cannot be.   B. They cannot be even. For example: 6 is the only allowed even number in the sequence and has factors of 1, 2, and 3 (1 x 2 x 3), all other numbers divisible by 3 and 2 (to be even) are also divisible by 6.   C. They do have a common prime factor. That prime factor is 3.   D. They have a common factor other than 3. Both numbers have common factors of 3 and 1.   Therefore only (Only B) is correct.
Answer: B
A calculator has a key for squaring and another key for inverting. So if x is the displayed number, then pressing the square key will replace x by x^2 and pressing the invert key will replace x by 1/x. If initially the number displayed is 6 and one alternatively presses the invert and square key 16 times each, then the final number displayed (assuming no roundoff or overflow errors) will be
Pick one.
A) 6/65536
B) 6/65522
C) 6/65288
D) 6/62888
E) 6/65199

Solution: Even number of inverse key has no effect on the number. For example, Initially the given number is 6. Square key makes it 6262 and invert key makes it 162162. Now again square key makes it (162)2=164(162)2=164 and invert key makes it 6464. Now observe clearly, after pressing square key 2 times, the power of 6 became 4.   By pressing the square key, the value got increased like 2, 4, 8, .... Which are in the format of 2n2n. So after the 16 pressings the power becomes 216216   So the final number will be 6216=6/65536   6/65536nswer:6/65536
Answer: A
A boy goes to a playground from the house at 5 km/hr by 10 minute late. If he goes at 6 km/hr. he would be 5 minutes early. What is the distance of the of playground from his house ?  Choices:
A) 7.5 km  B) 8 km  C) 10 km  D) 12 km  E) None of these

Solution: Explanation :   Solution: Let the distance be x km.   Difference in timings = 15 min = 15/60 hr = 1/4 hr.   .'. x/5 - x/6 = 1/4   => 6x-5x = 30/4   => x = 7.5 km.   7.5 kmnswer : 7.5 km
Answer: A
A certain computer manufacturing firm last year produced 82 percent of its computers using parts made by its subsidiary company. If the remaining 10,872 computers were produced using parts purchased from another parts manufacturer, how many computers were produced by the computer manufacturing firm altogether?  Answers
A) 60200
B) 61456
C) 60100
D) 50000
E) 60400

Solution: 82% parts used of subsidary company, so 18% parts used of other companies.   Now, 18% parts = 10,872 computers   So, 1% parts = 10,872/18   Or, 100% parts = 60,400 computers.   Hence answer is (60400)
Answer: E
The class mean score on a test was 60, and the standard deviation was 10. If Jack's score was within 2 standard deviations of the mean, what is the lowest score he could have received?
Choose the correct choice from the following answers.
A) 30	B) 31	C) 45	D) 90	E) 20

Solution: 1 SD from the mean is ADDING and Subtrating the amount if standard deviation from the mean one time. 2 SD from the mean is ADDING and Subtracting TWICE.   1SD from the mean ranges from 70 to 50, where 70 is within SD above the mean and 50 within 1SD below the mean   2SD=10 TWICE=20 from the the mean, which is 80 to 40, where 80 is within 2 SD above the mean AND 20 is within 2 SD below the mean.   Answer = 20
Answer: E
A coin has two sides. One side has the number 1 on it and the other side has the number 2 on it. If the coin is flipped three times what is the probability that the sum of the numbers on the landing side of the coin will be greater than 3? Choose the correct choice from the following options:
A) 7/8
B) 1/16
C) 1/8
D) 1/2
E) 1/4

Solution: One approach to solve the problem is to list the different possibilities for a toss of coin three times. Because there are two outcomes and the coin is tossed three times, the table will have 2*2*2 or 8 rows.   Next add the resulting rows together to find the sum (the fourth column in the table below).   Toss 1 | Toss 2 | Toss 3 | Sum   1 ---------- 1 -------- 1 ------ 3   1 ---------- 1 -------- 2 ------ 4   1 ---------- 2 -------- 1 ------ 4   1 ---------- 2 -------- 2 ------ 5   2 ---------- 1 -------- 1 ------ 4   2 ---------- 1 -------- 2 ------ 5   2 ---------- 2 -------- 1 ------ 5   2 ---------- 2 -------- 2 ------ 6   From the table we see that there are 7 situations where the sum of the tosses will be greater than 3. And there are 8 possible combinations resulting in a probability of   7/8 or a probability of 7/8.   SO the correct answer is 7/8.
Answer: A
A computer system uses alphanumeric case sensitive characters for its passwords. When the system was created it required users to create passwords having 6 characters in length. This year, it added the option of creating passwords having 7 characters in length. Which of the following gives the expression for the total number of passwords the new computer system can accept?
Assume there are 82 unique alphanumeric case sensitive characters. Choose the correct option:
A) 63^4	B) 82^4 * 83	C) 62(62^4)	D) 63(62^4)	E) 63(62^6)

Solution: Total number of passwords = number of 6 character password +number of 7 character password   = 82^4 + 82^5 (Since there is no limitation on repetition , each character can be chosen in 82 ways )   =82^4(1+ 82)   =82^4 * 83   Answer 82^4 * 83
Answer: B
A bad habit milkman to sell his milk at cost price but he mixes it with water and thereby gains 25%. Find the percentage of mixture water ?
Options: A) 20 B) 30 C) 35 D) 40 E) 45

Solution: cp of 1 lr = 1 rs   mix = (100/125*1) = 4/5   ratio of milk to water = 4/5:1/5 = 4:1   =>percentage of mix = (1/5*100)= 
(1/5*100) = 20
20   20NSWER 20
Answer: A
Joe’s average (arithmetic mean) test score across 4 equally weighted tests was 90. He was allowed to drop his lowest score. After doing so, his average test score improved to 85. What is the lowest test score that was dropped?  Choose the correct choice from the following options
A) 20 B) 25 C) 55 D) 75 E) 80

Solution: The arithmetic mean of 4 equally weighted tests was 90. So what we can assume is that we have 4 test scores, each 90.   He dropped his lowest score and the avg went to 95. This means that the lowest score was not 90 and other three scores had given the lowest score 5 each to make it up to 90 too. When the lowest score was removed, the other 3 scores got their 5 back. So the lowest score was  3 *5= 
 3 *5 = 15
15 less than 90.   So the lowest score= 90 - 15= 
90 - 15 = 75
75   Answer (75)
Answer: D
Find the value of m 62519 x 9999 = m?	Select the correct option:	A) 724533811	B) 353654655	C) 545463251	D) 625127481	E) 477899932

Solution: 62519 x 9999 = 62519 x (10000 - 1)   = 62519 x 10000 - 62519 x 1   = 625190000 - 62519= 
625190000 - 62519 = 625_127_481
625127481   625127481
Answer: D
A baseball card decreased in value 30% in its first year and 10% in its second year. What was the total percent decrease of the card's value over the two years?	Answers
A) 28%	B) 37%	C) 32%	D) 36%	E) 72%

Solution: consider the initial value of the baseball card as $100   After first year price = 100*0.7= 
100*0.7 = 70
70   After second year price= 70 *0.9= 
70 *0.9 = 63
63   final decrease= [(100 - 63)/100] * 100 = 37%   correct answer - 37%(100 - 63)/100  * 100= 
(100 - 63)/100  * 100 = 37
37%   correct answer - 37%
Answer: B
An investment of $10000 was made in a certain account and earned interest that was compounded annually. The annual interest rate was fixed for the duration of the investment, and after 12 years the $10000 increased to $40000 by earning interest. In how many years after the initial investment was made the $10000 have increased to $80000 by earning interest at that rate?  Pick one:  A) 16  B) 22  C) 20  D) 21  E) 18

Solution: In 12 years the investment quadrupled (from $10,000 to $40,000).   Thus, at the same rate compounded annually, it would need additional   12/2= 
  12/2 = 6
6 years to double (from $40,000 to $80,000).   Therefore, 12+6=18 years are needed $10,000 to increase to $80,000.   Answer: 18.
Answer: E
Find the value of 72519 x 9999 = m? Choose the correct choice: A) 456578972 B) 436567874 C) 653658791 D) 725117481 E) 357889964

Solution: 72519 x 9999 = 72519 x (10000 - 1)   = 72519 x 10000 - 72519 x 1   = 725190000 - 72519= 
725190000 - 72519 = 725_117_481
725117481   725117481
Answer: D
What is the equation of a circle of radius 6 units centered at (3, 2)? Choose the most appropriate option:
A) x2 + y2 + 6x - 4y = 23 B) x2 + y2 - 6x + 4y = 23 C) x2 + y2 + 6x + 4y = 23 D) x2 + y2 - 6x - 4y = -23 E) x2 + y2 - 6x - 4y = 23

Solution: x2 + y2 - 6x - 4y = 23xplanatory Answer   x2 + y2 - 6x - 4y = 23quation of a circle with center (a, b) and radius 'r' units is (x - a)2 + (y - b)2 = r2   Therefore, the equation of this circle = (x - 3)2 + (y - 2)2 = 62   i.e., x2 - 6x + 9 + y2 - 4y + 4 = 36   or x2 + y2 - 6x - 4y = 23   The correct choice is (x2 + y2 - 6x - 4y = 23)
Answer: E
The 19th of September 1987 was a Saturday. If 1988 was a leap-year, what day of the week was the 23rd of September 1990? Choose the correct choice from the following answers:	A) Sunday	B) Monday	C) Wednesday	D) Thursday	E) Friday

Solution: 19th September   1987: Saturday   1988: Monday (due to leap year)   1989: Tuesday   1990: Wednesday   Hence 23rd September was a Sunday.   The answer is Sunday.
Answer: A
A company purchased raw material worth 1/4 of it capital, 1/10 of the remaining is spent on machinery. How much fraction of the capital was left with the company after its expenditures on raw material and machinery?  Choose the correct choice from the following options:  A) 1/5  B) 2/8  C) 5/9  D) 27/40  E) 15/30

Solution: The amount spent by the company on raw material is 1/4, so remaining is 3/4.   1/10 of the remaining is spent on machinery, 1/10*3/4=3/40   Total amount spent on raw material and machinery is 1/4+3/40   To make the denominator common we use 40, so 1/4 is 10/40   10/40+3/40=13/40 is spent on raw material and machinery   Remaining 27/40 is left with the company   Answer is 27/40
Answer: D
A train covers a distance of 12 km in 10 min. If it takes 8 sec to pass a telegraph post, then the length of the train is? Choose one.
A) 298	B) 288	C) 120	D) 160	E) 991

Solution: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec.   Length of the train = 20 * 8= 
20 * 8 = 160
160 m.   Answer:160
Answer: D
Find the perimeter of a triangle with sides measuring 5 centimeters,20 centimeters and 30 centimeters.  Choices:
A) 30cm
B) 40cm
C) 50cm
D) 55cm
E) 60cm

Solution: perimeter of triangle=a+b+c   Perimeter = 5 cm + 20 cm + 30 cm = 55 cm   Answer: 55cm.
Answer: D
Eight people went to a restaurant for dinner. Seven of them spent $10 each on their meals and the eighth spent $7 more than the average expenditure of all eight people. What was the total amount of money that the eight people spent?
Choose the correct choice:	A) $85	B) $88	C) $91	D) $94	E) $97

Solution: Let T be the total amount of money spent.   7*10 + (T/8 + 7) = T   77 = 7T/8   T = (8*77)/7= 
(8*77)/7 = 88
88   The answer is $88.
Answer: B
John and Ingrid pay 30% and 40% tax annually, respectively. If John makes $60000 and Ingrid makes $72000, what is their combined tax rate? Choose the most appropriate option
A) 32%
B) 34.4%
C) 35%
D) 35.6%
E) 36.4%

Solution: (1) When 30 and 40 has equal weight or weight = 1/2, the answer would be 35.   (2) When 40 has larger weight than 30, the answer would be in between 35 and 40. Unfortunately, we have 2 answer choices D and E that fit that condition so we need to narrow down our range.   (3) Get 72000/132000 = 6/11. 6/11 is a little above 6/12= 1/2. Thus, our answer is just a little above 35.   Answer: 35.6%
Answer: D
A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn. If the area of the lawn is 2109 sq. m, then what is the width of the road? Select.
A) 2.91 m  B) 3 m  C) 5.82 m  D) 4 m  E) None of these

Solution: Explanation:   Area of the park = (60 x 40) m2= 2400 m2.   Area of the lawn = 2109 m2.   Area of the crossroads = (2400 - 2109) m2= 291 m2.   Let the width of the road be x metres. Then,   60x + 40x - x2 = 291   x2 - 100x + 291 = 0   (x - 97)(x - 3) = 0   x = 3.   Answer: 3 m
Answer: B
The speed of a boat in upstream is 50 kmph and the speed of the boat downstream is 80 kmph. Find the speed of the boat in still water and the speed of the stream? Choose the correct choice from the following choices.
A) 15 kmph B) 23 kmph C) 65 kmph D) 55 kmph E) 14 kmph

Solution: Speed of the boat in still water   = (50+80)/2= 
(50+80)/2 = 65
65 kmph. Speed of the stream= (80-50)/2= 
(80-50)/2 = 15
15 kmph.   15 kmphnswer: 15 kmph
Answer: A
An article is bought for Rs.655 and sold for Rs.900, find the gain percent?	Choose the correct choice
A) 37 53/131%	B) 33 1/3%	C) 23 1/3%	D) 35 1/3%	E) 29 1/3%

Solution: 37 53/131%   37 53/131%   655 ---- 245   100 ---- ? => 37 53/131%
Answer: A
Arun got 30% of the maximum marks in an examination and failed by 10 marks. However, Sujith who took the same examination got 40% of the total marks and got 15 marks more than the passing marks. What were the passing marks in the examination?	Choose the correct choice from the following answers: A) 90 B) 250 C) 75 D) 85 E) 95

Solution: Explanation :   Let x is the maximum marks of the examination   Marks that Arun got = 30 % of x = 30x/100   Given that Arun failed by 10 marks   ⇒Minimum Pass Mark = (30x/100) + 10......(Equation 1)=85   ANSWER IS 85
Answer: D
Water is leaking out from a cylinder container at the rate of 0.31 m^3 per minute. After 10 minutes, the water level decreases 4 meters. What is value of the radius? Choose the most appropriate option:
A) 0.5  B) 1.0  C) 1.5  D) 2.0  E) 2.5

Solution: 10*0.31= 
10*0.31 = 3.1
3.1 m^3= pi*R^2*h   R^2 = 3.1 / (pi*4) which is about 1/4   R = 1/2   The answer is 0.5.
Answer: A
Bruno and Sacha are running in the same direction around a stadium. Sacha runs at a constant speed of 6 meters per second, and Bruno runs at a constant speed of 5 meters per second. At a certain point Sacha overtakes Bruno. If six minute afterward, Sacha stops and waits for Bruno to reach him, then how many seconds does he have to wait?	Select the correct option
A) 12  B) 24  C) 36  D) 60  E) 72

Solution: the difference of the speed is 1m per second so in six minute Sacha will be 360 m ahead of Bruno..   Bruno will cover this in  360/5= 
 360/5 = 72
72 secs..   72
Answer: E
In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?  Pick one
A) 63 B) 67 C) 70 D) 74 E) 80

Solution: We need to select 5 men from 7 men and 2 women from 3 women.   Number of ways to do this   = 7C5 × 3C2   = 7C2 × 3C1 [∵ nCr = nC(n-r)]   =   7   ×   6   2   ×   1   ×   3   =   21   ×   3   =   63   63)
Answer: A
A man buys s cycle for $100 and sells it at a loss of 18%. What is the selling price of the cycle? Choose the correct choice from the following answers:
A) $50
B) $60
C) $70
D) $82
E) $90

Solution: S.P. = 82% of the $100 = 82/100 * 100= 
82/100 * 100 = 82
$82   Answer is $82
Answer: D
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?  Answers
A) 56 kg	B) 90 kg	C) 85 kg	D) Data inadequate	E) None of these

Solution: C   85 kg   Total weight increased = (8 x 2.5) kg = 20 kg.   Weight of new person = (65 + 20)= 
(65 + 20) = 85
85 kg.
Answer: C
If x^2 – 4x = 5, then one possible value of x – 2 =  Choose the correct choice from the following options:  A) -9  B) -5  C) -3  D) -1  E) 5

Solution: x^2 – 4x = 5   i.e. x^2 – 4x - 5 = 0   i.e. x^2 – 5x + x - 5 = 0   i.e. (x-5)(x+1) = 0   i.e. x = 5 or -1   i.e. x-2 = 5-2 or -1-2   i.e. x-2 = 3 or -3   Answer: Option -3
Answer: C
Of the 5 numbers, whose average is 80, the first is one-fourth of the sum of the last 4. The first number is?	Answers.
A) 83	B) 80	C) 78	D) 56	E) 67

Solution: Total of 5 numbers = 5 * 80= 
5 * 80 = 400
400   Let total of last 4 numbers= x   1st number = x/4   x+ x/4 = 400   5x = 1600 => x =320   1st number = 320/ 4= 
320/ 4 = 80
80   Answer :80
Answer: B
Mrs. Rodger got a weekly raise of $125. If she gets paid every other week, write an integer describing how the raise will affect her paycheck.  Choose the correct choice from the following:
A) $ 145. B) $ 146 C) $ 125 D) $ 148 E) None

Solution: Solution:   Let the 1st paycheck be x (integer).   Mrs. Rodger got a weekly raise of $ 125.   So after completing the 1st week she will get $ (x+125).   Similarly after completing the 2nd week she will get $ (x + 125) + $ 125.   = $ (x + 125 + 125)   = $ (x + 250)   So in this way end of every week her salary will increase by $ 125.   Answer $ 125
Answer: C
A bus started from bus stand at 8.00a m and after 30 min staying at destination, it returned back to the bus stand. The destination is 27 miles from the bus stand. The speed of the bus 50 percent fast speed. At what time it returns to the bus stand. Choose the correct choice.
A) 11a.m B) 12a.m C) 10a.m D) 10.30p.m E) 11.30p.m

Solution: bus started after 30min ie .5hrs   Now,   Time=distance/speed ie Time=27/18 during going ie 1.5 hrs   now during the return journey speed increasd by 50% so new speed 27mph   Time=27/27 ie 1(RETURN journey)   so total time=1+.5+1.5= 
1+.5+1.5 = 3
3hrs   so the bus will reach at 11am   11a.mNSWER:11a.m
Answer: A
Pipe P can fill a tank in 2 hours, pipe Q in 4 hours and pipe R in 12 hours. If all the pipes are open, in how many hours will the tank be filled?  Pick one:  A) 2 hours  B) 1.2 hours  C) 3 hours  D) 1.5 hours  E) 2.5 hours

Solution: Explanation:   Part filled by (P + Q + R) in 1 hour = (1/2 + 1/4 + 1/12) = 5/6   All the three pipes together will fill the tank = 6/5= 
6/5 = 6/5 = around 1.2
1.2 hours   ANSWER 1.2 hours
Answer: B
In a partnership between A, B and C. A's capital is Rs.6000. If his share of a profit of Rs.800 is Rs.200 and C's share is Rs.130, what is B's capital?	Choose the most appropriate option
A) 23676	B) 19766	C) 29172	D) 14100	E) 11267

Solution: Explanation:   200 + 130= 
200 + 130 = 330
330   800 - 330= 
800 - 330 = 470
470   200 ---- 6000   470 ---- ?=> 14100   Answer:14100
Answer: D
total 63 matches are conducted in Knockout match type. How many players will be participated in that tournament?  Choose the most appropriate option.
A) 60
B) 61
C) 62
D) 63
E) 64

Solution: 64 players   ANSW64R:64
Answer: E
A money lender finds that due to a fall in the annual rate of interest from 8% to 7 3/4 % his yearly income diminishes by Rs. 60.50, his capital is? Choose the correct choice from the following answers:
A) 24,200
B) 28,888
C) 24,600
D) 24,628
E) 24,6012

Solution: Let the capital be Rs. x. Then,   (x * 8 * 1)/100 - (x * 31/4 * 1/100) = 60.50   32x - 31x = 6050 * 4   x = 24,200.   24,200nswer: 24,200
Answer: A
Martin bought 10 concert tickets, some at the full price of $2.00 per ticket, and some at a discounted price of $1.60 per ticket. If he spent a total of $18.80, how many discounted tickets did he buy?
Choices:	A) 3	B) 4	C) 5	D) 6	E) 7

Solution: Let x be the number of tickets he bought at $2 per ticket.   then 2 x + (10-x)1.6 = 18.8   0.4x = 2.8 => x = 7   discounted tickets = 10 -x = 3   3ns : 3
Answer: A
A clock is set right at 8 a.m. The clock gains 10 minutes in 24 hours will be the true time when the clock indicates 1 p.m. on the following day?  Choose one:
A) 48 min. past 12  B) 48 min. past 32  C) 48 min. past 19  D) 48 min. past 11  E) 48 min. past 16

Solution: Time from 8 a.m. on a day to 1 p.m. on the following day = 29 hours.   24 hours 10 min. of this clock = 24 hours of the correct clock.   hrs of this clock = 24 hours of the correct clock.   29 hours of this clock = hrs of the correct clock   = 28 hrs 48 min of the correct clock.   Therefore, the correct time is 28 hrs 48 min. after 8 a.m.   This is 48 min. past 12.   48 min. past 12nswer: 48 min. past 12
Answer: A
If 2/w + 2/x = 2/y and wx = y, then the average (arithmetic mean) of w and x is Choose the correct choice:
A) 1/2
B) 1
C) 2
D) 4
E) 8

Solution: Given: 2/w + 2/x = 2/ywx=y   Find: (w+x)/2 = ?   2(1/w + 1/x) = 2(1/y) - divide both sides by 2   (1/w + 1/x) = 1/y   (x+w)/wx = 1/wx - sub'd in y=wx   x+w - 1 = 0   x+w = 1   Therefore (w+x)/2 = 1/2   1/2ns: 1/2
Answer: A
A father said to his son, "I was as old as you are at present at the time of your birth." If the father's age is 52 years now, the son's age 10 years back was?
Answers:
A) 16yr	B) 15yr	C) 14yr	D) 10yr	E) 20yr

Solution: Let the son's present age be x years   Then, 52-x = x   x = 26   Son's age 10 years back = 26-10= 
26-10 = 16
16 years   16yrnswer is 16yr
Answer: A
Rice weighing 33/4 pounds was divided equally and placed in 4 containers. How many ounces of rice were in each?
Choose the correct choice from the following choices.
A) 18 ounces  B) 15 ounces  C) 19 ounces  D) 17 ounces  E) 14 ounces

Solution: 33/4 ÷ 4 pounds.   = (4 × 3 + 3)/4 ÷ 4 pounds.   = 15/4 ÷ 4 pounds.   = 15/4 × 1/4 pounds.   = 15/16 pounds.   Now we know that, 1 pound = 16 ounces.   Therefore, 15/16 pounds = 15/16 × 16 ounces.   = 15 ounces.   Answer: (15 ounces)15 ounces.
Answer: B