MU-NLPC/Calc-aqua_rat huggingface dataset:
Train A leaves the station traveling at 30 miles per hour. Two hours later train В leaves the same station traveling in the same direction at 45 miles per hour. How many miles from the station was train A overtaken by train B? Select the correct option:  A) 100  B) 120  C) 140  D) 160  E) 180

Solution: After two hours, Train A is ahead by 60 miles.   Train B can catch up at a rate of 15 miles per hour.   The time to catch up is 60/15= 
60/15 = 4
4 hours.   In 4 hours, train A travels another  30*4= 
 30*4 = 120
120 miles for a total of 180 miles.   The answer is 180.
Answer: E
The dimensions of an open box are 52, 40 and 29 cms. Its thickness is 2 cms. If 1 cm3 of metal used in the box weighs 0.5 gms, the weight of the box is?	Choose the correct choice
A) 6.892 kg  B) 9.832 kg  C) 6.830 kg  D) 6.832 kg  E) 6.862 kg

Solution: Explanation:   52 * 40 * 29= 
52 * 40 * 29 = 60_320
60320   48 * 36 * 27= 46650   ------------   13664   13664 * 1/2= 
13664 * 1/2 = 6_832
6832=> 6.832 kg   Answer: Option 6.832 kg
Answer: D
How many liters of water must be evaporated from 50 liters of a 4 percent sugar solution to get a 5 percent sugar solution?  Choose the correct choice from the following.
A) 4
B) 6
C) 8
D) 10
E) 12

Solution: Let x be the amount that needs to be evaporated.   0.04(50) = 0.05(50-x)   0.05x = 2.5 - 2= 
2.5 - 2 = 0.5
0.5/0.05= 
0.5/0.05 = 10
10 liters   The answer is 10.
Answer: D
An urn contains 4 white 6 black and 8 red balls . If 3 balls are drawn one by one without replacement, find the probability of getting all white balls.  Choose the correct choice from the following options:
A) 1/209 B) 1/204 C) 1/207 D) 1/202 E) 1/201

Solution: Explanation:   Let A, B, C be the events of getting a white ball in first, second and third draw respectively, then   Required probability =   =   Now, P(A) = Probability of drawing a white ball in first draw = 4/18 = 2/9   When a white ball is drawn in the first draw there are 17 balls left in the urn, out of which 3 are white   Since the ball drawn is not replaced, therefore after drawing a white ball in the second draw there are 16 balls left in the urn, out of which 2 are white.   Hence the required probability   Answer: 1/204) 1/204
Answer: B
The difference between the compound interest compounded annually and simple interest for 2 years at 20% per annum is Rs.144. Find the principal?	Select the correct option.
A) 3629 B) 3608 C) rs.3600 D) 3613 E) 6192

Solution: P = 144( 100 / 5)2 => P   = 3600   Answer:rs.3600
Answer: C
An error 2% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is? Answers
A) 4%  B) 4.04%  C) 4.14%  D) 5%  E) 5.13%

Solution: 100 cm is read as 102 cm.   A1 = (100 x 100) cm2 and A2 (102 x 102) cm2.   (A2 - A1) = [(102)2 - (100)2]   = (102 + 100) x (102 - 100)   = 404 cm2.   Percentage error = 404	x 100	%	= 4.04%   100 x 100   4.04%)
Answer: B
Two equally sized jugs full of water are each emptied into two separate unequally sized empty jugs, X and Y. Now, jug X is 1/3 full, while jug Y is 2/3 full. If water is poured from jug X into jug Y until jug Y is filled, what fraction of jug X then contains water? Choose the most appropriate option
A) 0	B) 1/15	C) 2/15	D) 1/6	E) 2/10

Solution: Suppose the water in each jug is L liters   CX x (1/3) = L   CX = 3L liters   CX is capacity of X   CY x (2/3) = L   CY = 3L/2 liters   CY is capacity of Y   Now, Y is 3L/2 - L empty = L/2 empty   So, we can put only L/2 water in jug Y from Jug X   Jug X's remaining water = L - L/2 = L/2   Fraction of X which contains water = water / CX   = (L/2)/ 3L   = 1/6   Answer will be 1/6
Answer: D
How many integers n greater than and less than 100 are there such that,if the digits of n are reversed, the resulting integer is n+9 ?
Choose the correct choice.
A) 5 B) 6 C) 7 D) 8 E) 9

Solution: (10x+y)=(10y+x)+9   => 9x-9y=9   => x-y=1   and only 8 numbers satisfy this condition and the numbers are 21,32,43,54,65,76,87,98   ANSWER:8
Answer: D
An accurate clock shows 8 o’clock in the morning. Through how many degrees will the hour hand rotate when the clock shows 12 o’clock in the afternoon?	Choose the correct choice:  A) 120°  B) 90°  C) 180°  D) 320°  E) None of these

Solution: Sol.   120°ngle traced by the hour hand in 4 hours = [360/12 * 4= 
360/12 * 4 = 120
120°   120°nswer 120°
Answer: A
Which of the following could be the value of x, if |3x – 9| = 0?	Choose the correct choice from the following:
A) –3 B) 1/9 C) 1/3 D) -1/3 E) 3

Solution: |3x – 9| = 0   => 3x - 9 = 0   or -(3x - 9) = 0   => 3x = 9 or -3x = -9   => x = 3 or x = 3   Answer 3
Answer: E
I. a^2 - 9a + 20 = 0,
II. 2b^2 - 5b - 12 = 0 to solve both the equations to find the values of a and b?
Choose the correct choice from the following answers:
A) If a < b B) If a ≤ b C) If the relationship between a and b cannot be established D) If a > b E) If a ≥ b

Solution: I. (a - 5)(a - 4) = 0   => a = 5, 4   II. (2b + 3)(b - 4) = 0   => b = 4, -3/2 => a ≥ b   Option If a ≥ b
Answer: E
How many ways are there to select a subcommittee of 11 members from among a committee of 17?	Choices
A) 12376  B) 19448  C) 28791  D) 27711  E) 12111

Solution: Explanation:   Since it does not matter what order the committee members are chosen in, the combination formula is used.   Committees are always a combination unless the problem states that someone like a president has higher hierarchy over another person. If the committee is ordered, then it is a permutation.   C(17,11)= 12,376   12376nswer: 12376
Answer: A
What least number should be added to 1053, so that the sum is completely divisible by 23  Choose the correct option
A) A)4  B) B)1  C) C)2  D) D)3  E) E)5

Solution: 5xplanation:   (1053 / 23) gives remainder 18   18 + 5= 
18 + 5 = 23
23, So we need to add 5   Answer: Option 5
Answer: E
The sum of three consecutive even numbers is 93. Find the middle number of the three?	Choose the most appropriate option
A) 14 B) 35 C) 39 D) 31 E) 12

Solution: Middle value =93/3= 
93/3 = 31
31   Ans 31
Answer: D
A boy has 9 trousers and 15 shirts. In how many different ways can he select a trouser and a shirt?  Choices.
A) 100  B) 140  C) 104  D) 135  E) 125

Solution: The boy can select one trouser in nine ways.   The boy can select one shirt in 12 ways.   The number of ways in which he can select one trouser and one shirt is   9 * 15= 
  9 * 15 = 135
135 ways.   135
Answer: D
The average age of husband, wife and their child 3 years ago was 25 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is Pick one.
A) 22
B) 40
C) 34
D) 21
E) 11

Solution: Explanation:   Sum of the present ages of husband, wife and child = (25 x 3 + 3 x 3) years = 84 years.   Sum of the present ages of wife and child (20 x 2 + 5 x 2) years = 50 years.   Husband's present age = (84 - 50)= 
(84 - 50) = 34
34 years.   Answer: 34
Answer: C
The effective annual rate of interest corresponding to a nominal rate of 14% per annum payable half-yearly is? Answers.
A) 16.06%
B) 16.07%
C) 16.08%
D) 14.49%
E) 16.19%

Solution: Amount of Rs. 100 for 1 year when compounded half-yearly = [100 * (1 + 7/100)2] = Rs. 14.49 Effective rate = (114.49 - 100)= 
(114.49 - 100) = 14.49
14.49%   ANSWER:14.49%
Answer: D
The circumferences of two circles are 264 meters and 352 meters. Find the difference between the areas of the larger and the smaller circles?	Answers
A) 1877 sq m	B) 1976 sq m	C) 4312 sq m	D) 1987 sq m	E) 1678 sq m

Solution: Let the radii of the smaller and the larger circles be s m and l m respectively.   2∏s = 264 and 2∏l = 352   s = 264/2∏ and l = 352/2∏   Difference between the areas = ∏l2 - ∏s2   = ∏{1762/∏2 - 1322/∏2}   = 1762/∏ - 1322/∏   = (176 - 132)(176 + 132)/∏   = (44)(308)/(22/7) = (2)(308)(7) = 4312 sq m   Answer:4312 sq m
Answer: C
In a certain province in France there are 13 cities. If a single road segment connects only two cities, how many road segments are required in order to connect the cities so that each city is connected to all other cities with a single road segment?  Pick one:
A) 76	B) 78	C) 75	D) 98	E) 72

Solution: 1 city needs 12 roads to connect directly to the rest => 13 city needs 13*12 roads.   One road is counted twice => the number of road needed is 13*12/2= 
13*12/2 = 78
78   Answer 78
Answer: B
At 1:00 PM, Train X departed from Station A on the road to Station B. At 1:40 PM, Train Y departed Station B on the same road for Station A. If Station A and Station B are p miles apart, Train X’s speed is r miles per hour, and Train Y’s speed is s miles per hour, how many hours after 1:00 PM, in terms of p, r, and s, do the two trains pass each other?  Pick:
A) 0.5 + (p - 0.5s)/(r + s)
B) (p - 0.5s)/(r + s)
C) 0.5 + (p - 0.5r)/r
D) (p - 0.5r)/(r + s)
E) 0.5 + (p - 0.5r)/(r + s)

Solution: The distance A is going to cover between 1:00 and 1:30   = .5r   now the distance between the two trains = (p-.5r)   the relative velocity = (r-(-s)) = r+s   From 1:30, time is going to take when they meet = (p-.5r)/(r+s)   so the ans is .5+((p-.5r)/(r+s)) [.5 is added for the time from 1:00 to 1:30]   ans is (p - 0.5r)/(r + s)
Answer: D
The cost price of 30 articles is the same as the selling price of x articles. If the profit is 20%, what is x?
Choose the correct option.
A) 20 B) 21 C) 23 D) 25 E) 27

Solution: Let the cost price = y   The cost price of 30 articles = 30y   The selling price of x articles = 1.20y*x   1.20y*x = 30y   x = 30 / 1.2= 
30 / 1.2 = 25
25   The answer is 25.
Answer: D
A certain psychologist charges $20 more for the first hour of therapy than for each additional hour. If the total charge to a patient who receives 5 hours of therapy is $300, what is the total charge to a patient who receives only 3 hours of therapy ?	Select:
A) $120  B) $135  C) $150  D) $165  E) $188

Solution: Let the charge for first hour = x+20   then charge for each additional hour = x   x+20 + 4x = 300   => 5x = 280   => x = 56   Total charge for patient for 3 hours of therapy = x+20 + 2x = 3x+20   = 188 $   Answer $188
Answer: E
A man can row 5 kmph in still water. When the river is running at 2.3 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man?
Select.
A) 2.91  B) 3.48  C) 2.98  D) 3.78  E) 4.21

Solution: M = 5   S = 2.3   3.78S = 6.3   US = 2.7   x/6.3 + x/2.7 = 1   x = 1.89   3.78 = 1.89* 2= 
1.89* 2 = 3.78
3.78   Answer: 3.78
Answer: D
D is the set of all the multiples of 3 between 30 and 100. E is the set of all the factors of 400. Set D and Set E have how many numbers in common?
Select
A) 1  B) 0  C) 3  D) 5  E) 12

Solution: D is a set of multiples of 3.   400 is NOT a multiple of 3, hence none of its factors is a multiple of 3.   Therefore, those two sets won't have any overlap.   Answer: 0
Answer: B
Train X crosses a stationary train Y in 60 seconds and a pole in 25 seconds with the same speed. The length of the train X is 300 m. What is the length of the stationary train Y?	Options
A) 267 m
B) 420 m
C) 167 m
D) 287 m
E) 265 m

Solution: Let the length of the stationary train Y be LY   Given that length of train X, LX = 300 m   Let the speed of Train X be V.   Since the train X crosses train Y and a pole in 60 seconds and 25 seconds respectively.   => 300/V = 25 ---> ( 1 )   (300 + LY) / V = 60 ---> ( 2 )   From (1) V = 300/25= 
300/25 = 12
12 m/sec.   From (2) (300 + LY)/12= 60   => 300 + LY = 60 (12) = 720   => LY = 720 - 300= 
720 - 300 = 420
420 m   Length of the stationary train= 420 m   Answer:420 m
Answer: B
Two men A and B start from place X walking at 4 ½ kmph and 5 ¾ kmph respectively. How many km apart they are at the end of 3 ½ hours if they are walking in the same direction?  Options:
A) 4 1/8 km B) 5 4/8 km C) 6 1/8 km D) 4 3/8 km E) 3 2/8 km

Solution: D   4 3/8 km   RS = 5 ¾ - 4 ½ = 1 ¼   T = 3 ½ h.   4 3/8 km = 5/4 * 7/2 = 35/8 = 4 3/8 km
Answer: D
Rasik walked 20 m towards north. Then he turned right and walks 30 m. Then he turns right and walks 35 m. Then he turns left and walks 15 m. Finally he turns left and walks 15 m. In which direction and how many metres is he from the starting position? Select:
A) 23	B) 38	C) 37	D) 45	E) 92

Solution: 45 m East   Answer: 45
Answer: D
A chair is bought for Rs.900/- and sold at Rs.810/- find the loss percentage? Pick one.
A) 10% Loss
B) 20% Loss
C) 30% Loss
D) 40% Loss
E) 50% Loss

Solution: Formula = (Selling price ~ Cost price)/Cost price * 100   = (810 ~ 900)/900 = 10% Loss   10% Loss)
Answer: A
At 1:00, Annie starts to bicycle along a 84 mile road at a constant speed of 14 miles per hour. Thirty minutes earlier, Scott started bicycling towards Annie on the same road at a constant speed of 12 miles per hour. At what time will they meet?  Answers: A) 2:30 B) 3:00 C) 4:00 D) 5:00 E) 6:00

Solution: In the first 30 minutes, Scott can travel 6 miles, so there are 78 miles left.   Together Annie and Scott can complete 26 miles.   78/26= 
78/26 = 3
3, so they will meet 3 hours after 1:00.   The answer is 4:00.
Answer: C
How many integers from 20 to 150, inclusive, are divisible by 3 but not divisible by 7?
Pick one:
A) 37	B) 40	C) 42	D) 45	E) 55

Solution: We should find # of integers divisible by 3 but not by 3*7= 
3*7 = 21
21.   # of multiples of 21 in the range from 20 to 150, inclusive is   (147-21)/21+1= 
  (147-21)/21+1 = 7
7;    44-7= 
 44-7 = 37
37.   37nswer: 37.
Answer: A
The product of all the prime numbers less than 12 is closest to which of the following powers of 10 ?
Choose the correct choice from the following answers:
A) 10^7	B) 10^4	C) 10^8	D) 10^5	E) 10^9

Solution: Product of Prime numbers less than 12 is 2*3*5*7*11   2*5= 
2*5 = 10
10 .   10*11*3*7= 10*10*3*10 (approximately) ~ Product will be >10^3 <10^5 i.e. 10^4   10^4 is the answer
Answer: B
A restaurant meal cost $40 and there was no tax. If the tip was more than 5 percent but less than 15 percent of the cost of the meal, then total amount paid must have been between:
Choose the most appropriate option
A) $40 and $42 B) $41 and $46 C) $41 and 45 D) $43 and $46 E) $41 and $47

Solution: let tip=t   meal cost=40   range of tip = from 5% of 40 to 15% of 40 = 2 to 6   hence range of amount paid= 40+T= 42 to 46 i.e. $41 and $47
Answer: E
The value of a 10.5% stock, in which an income of Rs.756 is derived by investing Rs.9000, brokerage being% is?
Choose the correct choice:
A) Rs. 112.75	B) Rs. 121.75	C) Rs. 124.75	D) Rs. 118.75	E) Rs. 234.75

Solution: For an income of Rs.756, investment = Rs.9000   For an income of Rs., investment = = Rs.125   For a Rs.100 stock, investment = Rs.125.   Market value of Rs. 100 stock = = Rs. 124.75   Rs. 124.75
Answer: C
If money is invested at r percent interest, compounded annually, the amount of the investment will double in approximately 70/r years. If Pat's parents invested $5,000 in a long-term bond that pays 8 percent interest, compounded annually, what will be the approximate total amount of the investment 18 years later, when Pat is ready for college?
Pick one.
A) $20000  B) $15000  C) $12000  D) $10000  E) $9000

Solution: Since investment doubles in 70/r years, then for r=8 it'll double in 70/8=~9 years (we are not asked about the exact amount so such an approximation will do). Thus in 18 years investment will double twice and become ($5,000*2)*2=$20,000 (after 9 years investment will become $5,000*2=$10,000 and in another 9 years it'll become $10,000*2=$20,000).   $20000nswer: $20000.
Answer: A
In an intercollegiate competition that lasted for 3 days, 115 students took part on day 1, 80 on day 2 and 100 on day 3. If 50 took part on day 1 and day 2 and 70 took part on day 2 and day 3 and 40 took part on all three days, how many students took part only on day 3?  Choose the correct choice from the following options:
A) 20
B) 35
C) 40
D) 55
E) 60

Solution: Day 1&2 = 50; Only Day 1&2 (50-40) = 10,   Day 2&3 = 70; Only Day 2&3 (70-40) = 30,   Only Day 3 = 100 - (10+30+40)= 
100 - (10+30+40) = 20
20   20nswer:20
Answer: A
A train covers a distance of 12 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is? Choose the correct choice from the following answers:	A) 227	B) 177	C) 120	D) 288	E) 271

Solution: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec.   Length of the train = 20 * 6= 
20 * 6 = 120
120 m.Answer:120
Answer: C
If d is a positive integer, and if the units' digit of d^2 is 4 and the units' digit of (d + 1)^2 is 1, what is the units' digit of (d + 2)^2 ?  Choose the correct choice.
A) 0  B) 2  C) 4  D) 6  E) 8

Solution: A for me.   _1² = _1   _2² = _4   _3² = _9   _4² = _6   _5² = _5   _6² = _6   _7² = _9   _8² = _4   _9² = _1   _0² = _0   On the list, the only number that squared has the units digit = 4 preceding a number that squared has the units digit = 1 is the _8.   So, d = _8, that has square 4. The next square is 1 andnext nextsquare is 0.
Answer: A
Find the number of square tiles to cover the floor of a room measuring 10.5 m * 9.5 m leaving 0.25 m space around the room. A side of square tile is given to be 25 cms? Choose the correct choice from the following:
A) 422	B) 476	C) 1440	D) 428	E) 413

Solution: Floor area to be covered by tiles = 10 * 9= 
10 * 9 = 90
90   tiles area= 0.25 * 0.25= 
0.25 * 0.25 = 0.0625
0.0625   No. of tiles= 90/0.0625= 
90/0.0625 = 1_440
1440   Answer : 1440
Answer: C
If p=25*343*9/1575, how many digits are in p?  Choose the correct choice from the following choices:
A) 7
B) 2
C) 1
D) 4
E) 3

Solution: p = 25 * 343 * 9 / 1575   p = 5^2 * 7^3 * 3^2 / (5^2 * 3^2 * 7)   p = 7 ^ 2   p = 49   Ans: 2
Answer: B
Ayesha's father was 38 years of age when she was born while her mother was 36 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?	Choose the correct answer
A) 8
B) 7
C) 6
D) 5
E) 1

Solution: Mother's age when Ayesha's brother was born = 36 years.   Father's age when Ayesha's brother was born = (38 + 4)= 
(38 + 4) = 42
42 years.   Required difference= (42 - 36)= 
(42 - 36) = 6
6 years.   Answer: 6
Answer: C
How many four digit even numbers do not use any digit more than once  Choose the correct option.
A) 1720
B) 2160
C) None of these
D) 2460
E) 2520

Solution: The Way i solved it is   A B None of these D ( thousand , hundreds, tens, units)   D can be 0 2 4 6 8 ( any of the 5 digits )   A can be anything except (D or 0) so 8 possibilities   None of these can be anything execpt A and B so 8 possibilities   B can be anything execpt ( A D None of these ) so 7 possibilities   total ways are   8 * 7 * 8 * 5= 
  8 * 7 * 8 * 5 = 2_240
2240   Ans : None of these
Answer: C
Given that 0 < a < b < c < d, which of the following the largest ?	Pick one
A) (c+d) / (a+b)
B) (a+d) / (b+c)
C) (b+c) / (a+d)
D) (b+d) / (a+c)
E) None of these

Solution: Explanation :   For the fraction to be largest, denominator should be minimum and numerator should be maximium.   Here a and b is minimum which is in denominator of option 1. and c and d is maximum which is also in the numerator of option 1.   Hence 1.) (c+d) / (a+b   (c+d) / (a+b)nswer : (c+d) / (a+b)
Answer: A
Find the expenditure on digging a well 14m deep and of 3m diameter at Rs.15 per cubic meter? Choose the correct option.
A) 1979	B) 1456	C) 1699	D) 1485	E) 1689

Solution: 22/7 * 14 * 3/2 * 3/2= 
22/7 * 14 * 3/2 * 3/2 = 99
99 m2   99 * 15= 
99 * 15 = 1_485
1485   Answer:1485
Answer: D
If a new town has 350 residents, and the population doubles every 10 years, what will be its population after 75 years?	Select the correct option:
A) 63357 residents
B) 9051 residents
C) 12068 residents
D) 15075 residents
E) 18102 residents

Solution: 350*2^(75/10)=350*2^7.5=100*181.02=63357   The answer is 63357 residents.
Answer: A
If 4f^4 − 41f^2 + 100 = 0, then what is the sum of the two greatest possible values of f ?
Select
A) 4
B) 9/2
C) 7
D) 41/4
E) 25

Solution: just forget about the value of f^4 for the moment and let f^2= X. (its better to work with power of 2 than 4)   now we have equation as 4x^2 -41x +100 =0, factoring them gives us 4X^2 -16x -25x +100 =0. which can be solved as (4x-25)(x-4) , so x= 4 and 25/4.   so f^2 = 4 and 25/4   so f= +2 and minus 2 and +5/2 and minus 5/2   The two greatest values are +2 and +5/2. so their sum 2+5/2 =9/2 = 9/2
Answer: B
3 candidates in an election and received 1136, 7636 and 11628 votes respectively. What % of the total votes did the winningcandidate got in that election?
Choose one.
A) 45%	B) 54%	C) 57%	D) 60%	E) 65%

Solution: Total number of votes polled = (1136 + 7636 + 11628)= 
(1136 + 7636 + 11628) = 20_400
20400   So, Required percentage= 11628/20400 * 100= 
11628/20400 * 100 = 57
57%   57%
Answer: C
If X and Y are consecutive integers (Y>X), which of the following statements could be false?
1. The multiplication XY is an even number.
2. (Y/X) > 1.
3. (X + Y) is always an odd number.  Choices:
A) 1 only B) 2 only. C) 1 and 2 only. D) 1 and 3 only. E) 1, 2 and 3

Solution: Consecutive numbers means that one will be even and one will be odd.   1. The multiplication XY is an even number. Odd*even= even. True   2. (Y/X) > 1.   If Y= 1 and X=0   Y/X= Undefined   Or if Y =-1 and X=-2   Y/X= 1/2 <1   Could be False   3. (X + Y) is always an odd number.   Even+ Odd= Odd. True   2 only. is the answer
Answer: B
Of the 100 employees at company X, 80 are full-time, and 100 have worked at company X for at least a year. There are 20 employees at company X who aren’t full-time and haven’t worked at company X for at least a year. How many full-time employees of company X have worked at the company for at least a year?	Choices:
A) 20 B) 30 C) 50 D) 80 E) 100

Solution: Full time employee who have NOT worked for at least one year = a   Full time employee who have worked for at least one year = b   NON Full time employee who have worked for at least one year = c   NON Full time employee who have NOT worked for at least one year = d   a+b+c+d = 150   a+b = 80   i.e. c+d = 70   b+c = 100   i.e. a+d = 50   d = 20   i.e. c = 70-20= 
70-20 = 50
50   i.e. b= 100-50= 
100-50 = 50
50   i.e. a= 80-50= 
80-50 = 30
30   b= 20   20nswer: Option 20
Answer: A
An alloy weighing 26 ounces is 70 percent gold. How many ounces of pure gold must be added to create an alloy that is 90 percent gold?
Choose the correct choice from the following options.
A) 6 B) 9 C) 12 D) 34 E) 48

Solution: In 24 ounces, gold is 26 * (70/100)= 
26 * (70/100) = 91/5 = around 18.2
18.2 ounces. Now we add x ounces of pure gold to make it 90% gold.   So 18.2 + x= (24 + x)* 90/100 => x =34.   Answer is 34.
Answer: D
By approximately what percent is x greater than 1/3 if (2/3)(x) = 1?  Choose the most appropriate option:
A) 173%
B) 516%
C) 461%
D) 350%
E) 290%

Solution: what percent is x greater than 1/3 if (2/3)(x) = 1?   => x = 3/2   % change =[(3/2 -1/3) /(1/3) ] * 100   = 350   Ans 350%, 350%
Answer: D
By travelling at 50 kmph, a person reaches his destination on time. He covered two-third the total distance in one-third of the total time. What speed should he maintain for the remaining distance to reach his destination on time?  Choose the correct choice from the following choices.
A) 23 kmph
B) 24 kmph
C) 25 kmph
D) 26 kmph
E) 27 kmph

Solution: Let the time taken to reach the destination be 3x hours. Total distance = 50 * 3= 
50 * 3 = 150
150x km   He covered 2/3 * 150= 
2/3 * 150 = 100
100x km in 1/3 * 3x= x hours So, the remaining 50x km, he has to cover in 2x hours. Required speed = 50x/2x   =25 kmph.   Answer: 25 kmph50 /2= 
50 /2 = 25
25 kmph.   Answer: 25 kmph
Answer: C
If e = (x – 5)^2 + (x + 1)^2 – 6, then y is least when x =  Select the correct option
A) -2 B) -1 C) 0 D) 2 E) None of the above

Solution: Let us transform the formula:   e = (x – 5)² + (x +1)² – 6 =   x² – 10x + 25 + x² + 2x + 1 – 6 =   2x² – 8x + 20 = 2 × (x² – 4x + 10) =   2 × ((x² – 4x + 4) + 6) =   2 × ((x – 2)² + 6)   Any square is greater or equal 0. Therefore the formula possess the least value when (x – 2)² = 0.   x – 2 = 0   x = 2   The correct answer is choice (2).
Answer: D
Three times the first of three consecutive odd integers is 4 more than twice the third. The third integer is:  Choose the correct option.
A) 9	B) 11	C) 13	D) 16	E) 17

Solution: Let the three integers be x, x + 2 and x+ 4.   Then,   3x = 2(x + 4) + 4   x = 12   Third integer = x + 4 = 16.   ANSWER:16
Answer: D