MU-NLPC/Calc-aqua_rat huggingface dataset:
The public library has exactly 2 floors. It has 2/3 as many shelves on its 2nd floor as it does on its 1st. If the second floor has 1/6 as many books per shelf as the first floor, what fraction of the library's books are on the first floor? Choose the correct choice from the following options.
A) 1/4  B) 9/10  C) 5/9  D) 9/14  E) 5/6

Solution: Let x be the no of shelves and y be the no of books per shelf on first floor.   Now no of shelves on 2nd floor = (2/3)*x   no of books per shelf on 2nd floor = (1/6) * y   So total no books on first floor = xy and total no of books on 2nd floor = (2/3)*x*(1/6)*y = (1/9)*xy   fraction of library books on first floor = (xy)/(xy + (1/9)*xy)   =1 / (1+(1/9))   =9/10   So 9/10
Answer: B
The two lines y = x and x = -4 intersect on the coordinate plane. If z represents the area of the figure formed by the intersecting lines and the x-axis, what is the side length E of a cube whose surface area is equal to 6z? Choose the most appropriate option.
A) E=16 B) E=8√2 C) E=8 D) E=2√2 E) (√2)/3

Solution: 800score Official Solution:   The first step to solving this problem is to actually graph the two lines. The lines intersect at the point (-4, -4) and form a right triangle whose base length and height are both equal to 4. As you know, the area of a triangle is equal to one half the product of its base length and height: A = (1/2)bh = (1/2)(4 × 4) = 8; so z = 8.   The next step requires us to find the length of a side of a cube that has a face area equal to 8. As you know the 6 faces of a cube are squares. So, we can reduce the problem to finding the length of the side of a square that has an area of 8. Since the area of a square is equal to s², where s is the length of one of its side, we can write and solve the equation s² = 8. Clearly s = √8 = 2√2 , oranswer choice (E=2√2).
Answer: D
The area of sector of a circle whose radius is 12 metro and whose angle at the center is 42° is? Choose the correct choice from the following options
A) 52.6	B) 52.9	C) 52.8	D) 52.1	E) 52.2

Solution: 42/360 * 22/7 * 12 * 12= 
42/360 * 22/7 * 12 * 12 = 264/5 = around 52.8
52.8 m2   Answer: 52.8
Answer: C
A straight line in the xy- plane has y-intercept of 79 and slope of 6. On this line the y-coordinate of the point is 14, then what is the X-coordinate of the point? Select.
A) 11	B) -10.83	C) 71	D) 20.83	E) -12

Solution: Eq of line = Y = MX +C   C= 79   M=6   Y=14   Substitute given:   X = (Y - C) / M = (14 - 79) / 6 = -65/6 = -10.83   correct option is -10.83
Answer: B
Find the value of * in the following
(1 5/3) ÷ 3/11 × */11 = (2 2/3 × 7/5 × 6/7)	Select: A) 3 B) 3.2 C) 3.6 D) 3.8 E) 3.5

Solution: 3.6   Option '3.6'
Answer: C
A car covers a distance of 624 km in 4 hours. Find its speed?
Choose the correct choice from the following
A) 104 kmph  B) 126 kmph  C) 156 kmph  D) 174 kmph  E) 101 kmph

Solution: 624/4= 
624/4 = 156
156 kmph   Answer:156 kmph
Answer: C
7500 + (1250 / 50)  Options.
A) 7500	B) 7525	C) 7550	D) 8000	E) None of these

Solution: Explanation:   As per BODMAS rule first we will solve the terms in the bracket then other.   = 7500 + (25)= 
7500 + (25) = 7_525
7525   Option 7525
Answer: B
A driver paid n dollars for auto insurance for the year 1997. This annual premium was raised by p percent for the year 1998; for each of the years 1999 and 2000, the premium was decreased by 1/6 from the previous year’s figure. If the driver’s insurance premium for the year 2000 was again n dollars, what is the value of p? Pick:
A) 12 B) 33 1/3 C) 36 D) 44 E) 50

Solution: Premium in 1997 = n;   Premium in 1998 = n(1+p/100);   Premium in 1999 = 5/6*n(1+p/100);   Premium in 2000 = 5/6*5/6*n(1+p/100).   Given that premium in 2000 = 5/6*5/6*n(1+p/100)=n --> 5/6*5/6*(1+p/100)=1 --> 1+p/100=36/25 --> p/100=11/25=44/100 --> p=44.   Answer: 44.
Answer: D
Which of the following is equal to the cube of a non-integer?  Choices:
A) –64
B) –1
C) 8
D) 9
E) 27

Solution: All except 9 is cube of non integer as it is square of 3.   A. –64 = -4*-4*-4-- OUT   B. –1 = -1*-1*-1 -- OUT   C. 8 = 2*2*2 -- OUT   D. 9 -- Left One. Hence the answer   E. 27 = 3*3*3 -- OUT   ANSWER:9
Answer: D
Two sides of a triangle have lengths x and e and meet at a right angle. If the perimeter of the triangle is 4x, what is the ratio of x to e ?  Pick:
A) a) 2 : 3
B) b) 3 : 4
C) c) 4 : 3
D) d) 3 : 2
E) e) 2 : 1

Solution: Ahhhh....my bad. Thank you, you're correct. 8x = 6e --> x/e = 3/4.   Actually b) 3 : 4 is the right answer.
Answer: B
Sebastian bought a meal at a restaurant
and left a 15% tip. With the tip, he paid
exactly $36.11. How much did the meal cost without the tip?
Options
A) $28.98	B) $29.91	C) $30.40	D) $30.60	E) $30.85

Solution: The tip is a percent increase of 15%, which is 115%. Let x equal the price before the tip.   Thus, 115% of this price equals $36.11:   1.15x = 36.11   Divide both sides by 1.15:=>x=36.11/1.15= 
36.11/1.15 = 31.4
31.40   correct answer $30.40)$31.40
Answer: C
A amount doubles itself in 15 years. what is the rate of interest?  Choose the correct option
A) 20/3 % B) 10/3 % C) 40/3 % D) 50/3 % E) 70/3 %

Solution: let amount be x & rate of interest be r% annual then   (2x-x)=(x*15*r)/100   => 15r = 100   => r=20/3 %   20/3 %NSWER:20/3 %
Answer: A
In a certain appliance store, each model of television is uniquely designated by a code made up of a particular ordered pair of letters. If the store has 15 different models of televisions, what is the minimum number of letters that must be used to make the codes?  Choose the correct choice from the following answers:
A) 6	B) 7	C) 4	D) 9	E) 10

Solution: If n is the number of distinct letters used to create the two lettered codes, then a total of n∗n=n^2 different codes can be created. We need n2≥15. The smallest n which fulfills this condition is n = 4.   Answer 4
Answer: C
The number of stamps that P and Q had were in the ratio of 7:3 respectively. After P gave Q 13 stamps, the ratio of the number of P's stamps to the number of Q's stamps was 5:4. As a result of the gift, P had how many more stamps than Q?	Select the correct option: A) 10 B) 25 C) 40 D) 65 E) 90

Solution: P started with 7k stamps and Q started with 3k stamps.   (7k-13)/(3k+13) = 5/4   28k - 15k = 117   k = 9   P has 7(9) - 13 = 50 stamps and Q has 3(9)+13 = 40 stamps.   The answer is 10.
Answer: A
Solution Y is 30 percent liquid X and 70 percent water. If 3 kilograms of water evaporate from 8 kilograms of solution Y and 3 kilograms of solution Y are added to the remaining 6 kilograms of liquid, what percent of this new solution is liquid X?	Choose the correct choice from the following choices.
A) 35%	B) 37%	C) 41.3%	D) 42%	E) 45%

Solution: In 8 kilograms of solution Y there are   0.3*8= 
  0.3*8 = 2.4
2.4 kilograms of solution X;   After 3 kilograms of water are replaced by 3 kilograms of solution Y, to the existing 2.4 kilograms of solution X, 0.3*3=0.9 kilograms of solution X are added, so in the new solution of 8 kilograms there are 2.4+0.9= 
2.4+0.9 = 3.3
3.3 kilograms of solution X, which is 3.3/8*100=41.3% of this new solution.   Answer: 41.3%.
Answer: C
40% of a number is added to 120, the result is the same number. Find the number?
Choices:
A) 400	B) 288	C) 1687	D) 997	E) 121

Solution: (40/100) * X + 120 = X   2X = 400   X = 200   400nswer:400
Answer: A
The average of first 22 natural numbers is? Select the correct option:	A) 11.6	B) 11.5	C) 12.9	D) 15.4	E) 15.1

Solution: Sum of 22 natural no. = 506/2= 
506/2 = 253
253   Average= 253/22= 
253/22 = 23/2 = around 11.5
11.5   Answer:11.5
Answer: B
A person was asked to state his age in years. His reply was, "Take my age three years hence, multiply it by 3 and then subtract three times my age three years ago and you will know how old I am." What was the age of the person?
Choose the correct option:
A) 18 years	B) 20 years	C) 24 years	D) 32 years	E) 34 years

Solution: Explanation:   Let the present age of the person be x years.   Then, 3(x + 3) - 3(x - 3) = x   3x + 9 - 3x + 9 = x => x = 18   18 yearsNSWER IS 18 years
Answer: A
Pointing to a photograph, a lady tells Pramod, "I am the only daughter of this lady and her son is your maternal uncle." How is the speaker related to Pramod's father Choose one
A) Sister-in-law	B) Wife	C) Either (a) or (b)	D) Neither (a) nor (b)	E) Either B) or (A)

Solution: Explanation:   Clearly, the speaker's brother is Pramod's maternal uncle. So, the speaker is Pramod's mother or his father's wife   Answer: Wife
Answer: B
Listed below are the mean temperatures measured in the Tokharian desert in a certain month. What is the median temperature E in that particular month?
Mean Temp (C°) No. of days
29 --------------------> 5
30 --------------------> 11
31 --------------------> 8
32 --------------------> 6
Pick: A) 29 B) 30 C) 30.5 D) 31 E) 32

Solution: to find out median===>they must be arranged in ascending order.   29 29 29...(5 times)30 30 30 30.....(11 times)31 31 31.....(8 times)32 32 32 .....(6 times)   total days=5+11+8+6= 
5+11+8+6 = 30
30   therefore 30 numbers ...median E will be==>mean of 15 and 16 th place temperature===>(30+30)/2= 
(30+30)/2 = 30
30   hence 30
Answer: B
If two letters are chosen at random (without replacement) from the word HORSEBACK, what is the probability that none of the letters are vowels?  Choose the most appropriate option.
A) 4/9 B) 5/9 C) 5/12 D) 7/24 E) 11/36

Solution: The number of ways to choose two letters is 9C2 = 36   The number of ways to choose two consonants is 6C2 = 15.   P(no vowels) = 15/36 = 5/12   The answer is 5/12.
Answer: C
You collect baseball cards. Suppose you start out with 11. Maria takes half of one more than the number of baseball cards you have. Since you're nice, you give Peter 1 baseball card. Since his father makes baseball cards, Paul decides to triple your baseball cards. How many baseball cards do you have at the end? Choose the most appropriate option
A) 12 B) 18 C) 19 D) 20 E) 21

Solution: Solution   Start with 11 baseball cards.   Maria takes half of one more than the number of baseball cards you have. So Maria takes half of 11 + 1 which is 6,   so you're left with   11 - 6= 
  11 - 6 = 5
5.   Peter takes 1 baseball card from you:  5 - 1= 
 5 - 1 = 4
4 baseball cards.   Paul triples the number of baseball cards you have: 4 Ã— 3= 12 baseball cards.   So you have 12 at the end.   Correct answer : 12
Answer: A
Find the smallest number which when divided by 11 and 12 leaves respective remainders of 2 and 3.	Answers
A) 131
B) 197
C) 207
D) 219
E) 227

Solution: Let 'N' is the smallest number which divided by 11 and 12 leaves respective remainders of 2 and 3.   Required number = (LCM of 11 and 12) - (common difference of divisors and remainders) = (132) - (1)= 
(132) - (1) = 131
131.   131NSWER:131
Answer: A
A two-digit number is seven times the sum of its digits. If each digit is increased by 2, the number thus obtained is 4 more than six times the sum of its digits. Find the number. Select the correct option
A) 42 B) 24 C) 48 D) Data inadequate E) None of these

Solution: Let the two-digit number be l0 x + y.   10x + y = 7(x + y) Þ x = 2y...(i)   10(x + 2) + y + 2 = 6(x + y + 4) +4   or 10x + y + 22 = 6x + 6y + 28 Þ 4x – 5y = 6 ... (ii)   Solving equations (i) and (ii), we get x = 4 and y = 2   42nswer 42
Answer: A
Ross has 20 shirts, 3/4 of the shirts are green and 1/10 is without buttons. Therefore Ross has between ___ and ___ shirts with buttons that are not green.  Pick:
A) 3 ; 5.  B) 3 ; 6.  C) 3 ; 7.  D) 3 ; 8.  E) 3 ; 9.

Solution: Total shirts = 20   Green shirts = 3/4*20= 
3/4*20 = 15
15, Non green shirts= 5   Shirts without button = 1/10*20= 
1/10*20 = 2
2, shirts with button= 18   Required: Range of shirts with buttons that are not green.   Maximum non green shirts with buttons = number of non green shirts = 5   Minimum non green shirts with buttons (3 ; 5.ll without button shirts are non green) = Non green shirts - shirts without button = 5 - 2= 
5 - 2 = 3
3   Hence the range would be (3, 5)   Correct Option: 3 ; 5.
Answer: A
Consider an equilateral triangle 4ABC with unit side length. Let M be the midpoint of side
AB. A ball is released in a straight line from M and bounces o the side BC at a point D.
Then, it bounces o the side CA at a point E and lands exactly at B. By the law of re
ection,
we have \BDM = \CDE and \CED = \AEB. Calculate MD + DE + EB, the distance
that the ball travels before reaching B. Choose the correct choice from the following answers:
A) √12/2
B) √11/2
C) √13/2
D) √14/2
E) √17/2

Solution: The solution can be obtained by re   ecting the triangle across edge CB to obtain   another equilateral triangle 4A0CB, and then across A0C to get 4A0B0C. The length of the   line MB0 is the minimum distance from M to the vertex B that hits both sides BC and CA0.   The length of the line segment BB0 is   √3/2   Thus, the length of MB =√1+3/4=√13/2   correct answer √13/2
Answer: C
A firm has 4 senior partners and 6 junior partners. How many different groups D of 3 partners can be formed in which at least one member of the group is a senior partner. (2 groups are considered different if at least one group member is different)
Select the correct option
A) 48 B) 100 C) 120 D) 288 E) 600

Solution: What seems to work as well, though its tougher to come up with this solution:     (10*9*8) * 2/3 + (10*9*4)*1/3= 
  (10*9*8) * 2/3 + (10*9*4)*1/3 = 600
600. Divided by all possible permutations (=3!) yields 100.   Explanation: For the first spot you have 10 possible canditates, for the 2nd 9. For the 3rd spot you need to differentiate if a senior partner has been picked for one of the first 2 spots or not. If yes, then you can pick one of the 8 remaining guys, so 10*9*8. If no senior partner has been picked yet, you need 10*9*4.   Now you need to weight the 2 cases with the corresponding probabilities: probability of no senior partner being picked in the first 2 draws = 6/10*5/9=1/3, so you weight 10*9*4 with 1/3. For the complementary case (senior partner was picked in the first 2 draws) you just take the complementary prob (1-1/3)= 2/3 and weight 10*9*8 with it.   Now you just need to divide the answer (600) by the number of different positions (=3!) and get D=600/6=100100
Answer: B
A man's speed with the current is 30km/hr and the speed of the current is 5 km/hr. The man's speed against the current is
Choose the correct choice from the following options:  A) 10 km/hr  B) 20 km/hr  C) 25 km/hr  D) 30 km/hr  E) 35 km/hr

Solution: Explanation:   Speed of man with the current = 30 km/hr   Speed of current = 5   Since, Speed of current + speed of man = 30   5 + speed of man = 30   Speed of man = 25 km/hr   man's speed against the current is = speed of man - speed of current = 25 - 5= 
25 - 5 = 20
20 km/hr   Answer: Option 20 km/hr
Answer: B
A store’s selling price of $2240 for a certain computer would yield a profit of 40 percent of the store’s cost for the computer. What selling price would yield a profit of 60 percent of the computer’s cost?
Choose the correct choice from the following options.
A) $2400 B) $2464 C) $2560 D) $2732 E) $2800

Solution: 1.4x = 2240   x=2240/1.4   so, 1.6X = 2240*1.6/1.4= 
2240*1.6/1.4 = 2_560
2560   Answer:- $2560
Answer: C
Using all the letters of the word "NOKIASE", how many words can be formed, which begin with N and end with A?
Choose the most appropriate option:
A) 8
B) 120
C) 9
D) 3
E) 1

Solution: There are five letters in the given word.   Consider 7 blanks ....   The first blank and last blank must be filled with N and A all the remaining three blanks can be filled with the remaining 3 letters in 5! ways.   The number of words = 5! = 120.   Answer:120
Answer: B
A cistern of capacity 8000 litres measures externally 3.3 m by 2.6 m by 1.6 m and its walls are 5 cm thick. The thickness of the bottom is:
Pick one:
A) 90 cm
B) 6 dm
C) 1 m
D) 1.1 cm
E) None of these

Solution: Explanation:   Let the thickness of the bottom be x cm.   Then , [(330 - 10) × (260 - 10) × (160 - x)] = 8000 × 1000   => 320 × 250 × (160 - x) = 8000 × 1000   => (160 - x) = 8000×1000/320=   100   => x = 60 cm = 6 dm.   Answer: 6 dm
Answer: B
The parameter of a square is double the perimeter of a rectangle. The area of the rectangle is 480 sq cm. Find the area of the square.	Choose the correct choice:
A) 290 sq cm	B) 800 sq cm	C) 209 sq cm	D) Cannot be determined	E) 200 sq cm

Solution: Explanation:   Let the side of the square be a cm. Let the length and the breadth of the rectangle be l cm and b cm respectively.   4a = 2(l + b)   2a = l + b   l . b = 480   We cannot find ( l + b) only with the help of l . b. Therefore a cannot be found .   Area of the square cannot be found.   Answer: Option Cannot be determined
Answer: D
what is the integer among the following that represents a sum of 3 consecutive even integers?  Choose the correct choice from the following
A) 200 B) 303 C) 400 D) 554 E) 588

Solution: Sum of three consecutive Even Integers must be a multiple of 2 as well as a multiple of 3 because such a sum is always 3 times the middle number (applicable to all equally spaced numbers)   Divisibility of 3: Sum of the digits of the number must be divisible by 3   Divisibility of 2: Unit digit of the number must be divisible by 2   A. 200NOT A MULTIPLE OF 3 SO RULED OUT   B. 303NOT A MULTIPLE OF 2 SO RULED OUT   C. 400NOT A MULTIPLE OF 3 SO RULED OUT   D. 554NOT A MULTIPLE OF 3 SO RULED OUT   E. 588A MULTIPL588 OF BOTH 2 AND 3 SO TH588 CORR588CT ANSW588R!!!
Answer: E
Two printing presses begin printing currency at the same time and at constant speeds. Press F produces 5-dollar bills at the rate of 1,000 bills per minute. Press T produces 20-dollar bills at the rate of 200 bills per minute. Once the machines have begun printing, how many seconds does it take for Press F to produce 50 dollars more currency than Press T? Choose the correct choice from the following choices.
A) 2  B) 3  C) 4  D) 5  E) 6

Solution: Press F produces $5 bills @1000 per minute(60 sec) so $500 in 6 secs   Press T produces $20 bills200per minute(60 sec) so $400 in 6 secs..   so we can see F produces $ 100 in 6 secs or will print $50 in 3 secs..   ans 3 secs..   3
Answer: B
There is an increase of 30% in the production of milk chocolates in Amul Dairy in one month. If now it is 5,200 milk chocolates per month, what was it one month ago?	Choices:  A) 10,000 chocolates  B) 9000 chocolates  C) 4000 chocolates  D) 7000 chocolates  E) None of these

Solution: Let one month ago, production be x chocolates.   Then, 130 % of x = 5200   ⇒ x = 5200×100/130=4000 chocolates   Answer 4000 chocolates
Answer: C
If the numerator of a fraction Q is tripled, and the denominator of a fraction is doubled, the resulting fraction will reflect an increase of what percent?	Choose the correct choice:
A) 16 1⁄6%	B) 25%	C) 33 1⁄3%	D) 50%	E) 66 2⁄3%

Solution: This question can be dealt with conceptually or by TESTing VALUES.   We're told that the numerator of a fraction Q is tripled and the denominator of that same fraction is doubled. We're asked for the resulting increase, in percentage terms, of that fraction.   Let's TEST 2/1   If we triple the numerator and double the denominator, we end up with....   (2x3)/(1x2) = 6/2= 
6/2 = 3
3   Since we're increasing 2 to 3, we're increasing that fraction by (3-2)/2= 1/2 of itself = 50%   50%
Answer: D
The price of pulses has fallen by 22%. How many quintals can be bought for the same amount which was sufficient to buy 20 quintals at the higher price?	Choose the most appropriate option:
A) 20	B) 22.5	C) 25.6	D) 27.8	E) 32.5

Solution: 80% of original price can buy = 18 quintals.   Therefore, he can buy ( 20 x 100 )/ 78 = 25.6 quintals at the lower price.   ANSWER:25.6
Answer: C
A man purchased 3 blankets @ Rs.100 each, 5 blankets @ Rs.150 each and two blankets at a certain rate which is now slipped off from his memory. But he remembers that the average price of the blankets was Rs.150. Find the unknown rate of two blankets?
Choose the correct choice from the following answers
A) 450
B) 200
C) 250
D) 300
E) 350

Solution: 10 * 150= 
10 * 150 = 1_500
1500   3 * 100 + 5 * 150= 
3 * 100 + 5 * 150 = 1_050
1050   1500 â€“ 1050= 450   450NSWER 450
Answer: A
A certain series is defined by the following recursive rule: Sp=K(Sp-1) , where k is a constant. If the 1st term of this series is 64 and the 25th term is 192, wha is the 9th term?	Choose the correct choice from the following
A) ROOT 2	B) ROOT 3	C) 64*ROOT 3	D) 64*3^1/3	E) 64*3^24

Solution: Ans...D   No need for any GP formula here   The rule is that pth term is K times the (p-1)th term.   1st = 64   2nd = k.64   3rd = k^2.64   .   .   .   9th term = k^8 *64   .   .   .   so 25th = k^24*64   Using this solve for k and substitute k in the equation for the 9th term
Answer: D
The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling alongthe oundary of the park at the speed of 12 km/hr completes one round in 8 min, then the area of the park (in sq. m) is?	Choose the correct choice from the following:
A) 123600 m B) 112600 m C) 153600 m D) 153500 m E) 154300 m

Solution: Perimeter = Distance covered in 8 min. = 12000 x 8 m = 1600 m.   60   Let length = 3x metres and breadth = 2x metres.   Then, 2(3x + 2x) = 1600 or x = 160.   Length = 480 m and Breadth = 320 m.   Area = (480 x 320) m2 = 153600 m   153600 m
Answer: C
The difference between the place value and the face value of 6 in the numeral 856973 is
Answers.
A) 5994	B) 6973	C) 973	D) 1000	E) 7000

Solution: (Place value of 6) - (Face value of 6) = (6000 - 6)= 
(6000 - 6) = 5_994
5994   5994NSWER 5994
Answer: A
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 1/16 meters. What is value of the radius in meters? Choose the most appropriate option:  A) 1/4  B) 2  C) 4  D) 8  E) 12

Solution: 10*0.31= 
10*0.31 = 3.1
3.1= pi*R^2*h   R^2 = 3.1 / (pi*1/16) which is about 16   R = 4   The answer is 4.
Answer: C
Find the smallest number that should be multiplied with 54000 to make it a perfect cube.  Choose the correct option: A) 4 B) 5 C) 6 D) 3 E) 7

Solution: 54000 = 2^1 * 3^3 * 10^3   to make it ps * 2^2 or 4   4NSWER:4
Answer: A
A factory produces 4340 toys per week. If the workers at this factory work 2 days a week and if these workers make the same number of toys everyday, how many toys are produced each day?
Choose the correct choice from the following options:
A) 1375 toys  B) 2170 toys  C) 2375 toys  D) 2175 toys  E) 5375 toys

Solution: To find the number of toys produced every day, we divide the total number of toys produced in one week (of 2 days) by 2.   4340 / 2= 
4340 / 2 = 2_170
2170 toys   correct answer 2170 toys
Answer: B
If the terms of a series are either2or24and the sum of all the terms S of the series is 124, then which of the following could be the number of2sin the series?
Select the correct option:
A) 26  B) 29  C) 35  D) 40  E) 48

Solution: Ans: A   Solution: we are not certain how many 2 or 24 are there. but as given sum of all the terms is 124 means  24*5= 
 24*5 = 120
120 so number of 24 can't be more than 5   so S=24x +2y = 124   24*5 + 2y =124 then y=2   24*4 + 2y = 124 then y=14   24*3 +2y = 124 then y= 26   24*2 +2y =124 then y = 38   24 +2y = 124 then y= 50   26 is the ans.
Answer: A
Two pipes A&B can fill a tank in 24 min and 32 min respectively. If both the pipes are opened simultaneously, after how much time B should be closed so that the tank is full in 18 min.
Pick one
A) 8 min B) 3 min C) 21 min D) 23 min E) 24 min

Solution: 3/4 tank is filled by A in 18 mins.   then balance 1/4 tank is filled by B in 32*1/4= 
32*1/4 = 8
8 mins.   8 minNSWER:8 min
Answer: A
If x≠7 and (x^2 - 49)/(2y) = (x - 7)/4, then in terms of y, x = ? Options:
A) (y - 6)/2  B) (y - 3)/2  C) y - 3  D) y - 6  E) (y - 14)/2

Solution: Since (x^2 – 49)=(x-7)(x+7) the original equation can be changed into 4*(x-7)(x+7) = 2y *(x-7).   By cancelling 2(x-7) (we can do it because x≠7) we get :   2*(x+7)=y.   So x=(y-14)/2. So the answer is (y - 14)/2).
Answer: E
The speed of a car is 50 km in the first hour and 60 km in the second hour. What is the average speed of the car? Choose the correct answer.
A) 79 kmph
B) 85 kmph
C) 55 kmph
D) 23 kmph
E) 14 kmph

Solution: S = (55 + 60)/2   = 55 kmph   Answer:55 kmph
Answer: C