MU-NLPC/Calc-aqua_rat huggingface dataset:
A train travels from station A to station B. If it travels at a speed of 80 miles per hour, it ends up reaching the station 30 minutes late. If it travels at 120 miles per hour, it reaches the station 15 minutes early. What is the amount of time that the train is scheduled to take for the journey and what is the distance between the stations?
Choose the correct choice from the following options.
A) 2 hours, 225 miles
B) 3 hours, 350 miles
C) 1.75 hours, 180 miles
D) 5 hours, 550 miles
E) 6 hours, 650 miles

Solution: Let t be the usual time and x be the distance between AB. So we need to find t and Distance x. The question gives us 2 combinations of speedtime, but the distance remains the same for both condition.   Equation 1 - x= 80 (t+.5) (converted 30 mins into hr) added .5 hrs because it is late or took more time than usual.   Equation 2 - x= 120 (t-.25) subtracted .25 hrs because it is early or took less time than usual.   Now equating 12 we get 100(t+.5)=120(t-.25)   => 8t +4 = 12t - 3   8  +4= 
8  +4 = 12
12t - 3=> 4t=7 => t= 1.75 hrs.   Hence x= 80(1.75+.5) =>80 X 2.25 => 180 miles.   Hence correct answer 1.75 hours, 180 miles.
Answer: C
Dawson is going with 14 friends on a trip to Washington D.C for spring break. Airfare and hotel costs a total of $13500.00 for the group of 15 friends. How much does each person have to pay for their hotel and airfare? Choose the correct choice from the following answers:
A) $900 B) $800 C) $850 D) $950 E) $920

Solution: $900nswer= $900   The total cost of the trip ($13500.00) divided by 15 equals $900.00.
Answer: A
What is the average of first 21 multiples of 7 ?
Choose the most appropriate option.
A) 70	B) 77	C) 79	D) 81	E) 82

Solution: Required average = 7(1+2+....+21) / 21   (7/21)X ( (21x22) / 2 ) (because sum of first 21 natural numbers)   = 77   77
Answer: B
A train 275 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?	Pick one.
A) 7 sec B) 5 sec C) 15 sec D) 6 sec E) 12 sec

Solution: Speed of train relative to man   = (60 + 6) km/hr   = 66 km/hr   [66 * 5/18] m/sec   = [55/3] m/sec.   Time taken to pass the man   = [275* 3/55= 
275* 3/55 = 15
15 sec   Answer:15 sec
Answer: C
A candidate got 35% of the votes polled and he lost to his rival by 2280 votes. How many votes were cast? Choose the most appropriate option:	A) 7500	B) 3388	C) 2665	D) 2888	E) 7600

Solution: 35%-----------L   65%-----------W   ------------------   30%----------2280   100%---------? => 7600   Answer: 7600
Answer: E
3th/4 of 1th/5 of a number is 60. The number is  Choose the correct choice:	A) 300	B) 400	C) 450	D) 1200	E) None

Solution: Explanation:   Let the number be N. Then   3/4×1/5×N=60⇒3N=1200⇒N=400   Correct Option: 400
Answer: B
A clothing store originally bought 100 jackets at a total cost of j dollars. If each jacket was sold for 60 percent more than its original cost, what was the individual price, in terms of j, of each jacket sold?	Select the correct option:
A) j/62  B) 7j/500  C) 140j  D) j/100+40  E) 140j/100

Solution: lets take j=1000, as decided by you..   now 60% increase makes it 1600..   this is the price for 100 jackets, so selling price for each jacket=1600/100=$16..   j/62   so ans is correct as j/62..
Answer: A
What is the sum of all possible 3-digit numbers that can be constructed using the digits 2, 3, and 5 if each digit can be used only once in each number?	Choose the correct choice from the following.
A) 2210	B) 2220	C) 2230	D) 2240	E) 2250

Solution: There are 6 possible arrangements of the three numbers.   Then each number will be in the hundreds, tens, and ones place two times each.   The sum is 2(222) + 2(333) + 2(555) = 2220   The answer is 2220.
Answer: B
At a certain organisation, the number of male members went up by 13% in the year 2001 from year 2000, and the number of females members went down by 6% in the same time period. If the total membership at the organisation went up by 1.2% from the year 2000 to 2001, what was the ratio of male members to female members in the year 2000?
Answers
A) 1:2 B) 1:3 C) 2:3 D) 3:5 E) 2:1

Solution: men increase by 13% ==> 1.13M = males in 2001   women decrease by 6% ==> 0.94F = women in 2001   total employees increase by 1.2% ==> 1.012*(M + F) = total number of employees in 2001   Obviously   (males in 2001) + (females in 2001) = total number of employees in 2001   1.13M + 0.94F = 1.012*(M + F)   1.13M + 0.94F = 1.012M + 1.012F   1.13M - 1.012M = 1.012F - 0.94F   0.108M = 0.072F   M/F = (0.072)/(0.118) = 72/118 = 3/5   Answer =(3:5)
Answer: D
A train running at a speed of 36 kmph crosses an electric pole in 12 seconds. In how much time will it cross a 320 m long platform?
Options:
A) 44 min  B) 55 min  C) 47 min  D) 67 min  E) 45 min

Solution: A   44 min   Let the length of the train be x m.   When a train crosses an electric pole, the distance covered is its own length.   So, x = 12 * 36 * 5 /18= 
12 * 36 * 5 /18 = 120
120 m.   Time taken to cross the platform= (120 +320)/ 36 * 5/18 = 44 min.
Answer: A
Two goods trains each 400 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?	Choose the correct choice from the following.
A) 38.4	B) 32.6	C) 48	D) 27.4	E) 21

Solution: Relative speed = 45 + 30= 
45 + 30 = 75
75 km/hr.   75 * 5/18= 125/6 m/sec.   Distance covered = 400 + 400= 
400 + 400 = 800
800 m.   Required time= 800 * 6/125= 
800 * 6/125 = 192/5 = around 38.4
38.40 sec.   38.4nswer:38.4
Answer: A
The banker's gain of a certain sum due 2 years hence at 10% per annum is Rs. 24. The present worth is: Pick one:	A) 480	B) 520	C) 600	D) 960	E) 840

Solution: T.D. = B.G. x 100 / Rate x Time   = Rs.(24 x 100/10 x 2)= Rs. 120.   P.W. =(100 x T.D./Rate x Time)   = Rs.(100 x 120/10 x 2)= Rs. 600.   600orrect answer is 600.
Answer: C
In the rectangular coordinate system, what is the area of triangle CDE with points
C=(5,8)
D=(4,2)
E=(8,0)
Choose one: A) 13 B) 12 C) 12.8 D) 14 E) 20

Solution: Use the formula of the distance formula   square root (x2-x1)^2+(y2-y1)^2   Do this for each of the sides and then the value is given as 13.
Answer: A
A distributor sells a product through an on-line store, which take a commission of 20% of the price set by the distributor. The distributor obtains the product from a producer at the price of $15 per item. What is the price that the buyer observers on-line if the distributor wants to maintain a 25% profit on the cost of the item?
Choose the correct choice from the following.
A) 18	B) 21.6	C) 22	D) 22.5	E) 24

Solution: Producer price = $15;   The distributor wants to maintain a 20% profit on the cost of the item, thus he must get $ 15*1.2= 
 15*1.2 = 18
$18 after the store takes a commission of 25% of the final price --> (final price)*0.75= $18 --> (final price) = $24.   Answer: 24.
Answer: E
Which symbol would be exactly at the middle of the fifth symbol from the right and ninth symbol from the left end of the following sequence of symbols ?
& * ∧ % $ # @ + - ! ∼ μ Ω Δ ± ∈ ≈ ∫ → √ ∞ ∧ @ ↓ ≥ ∈ $ + @  Select.
A) +  B) _  C) ≈  D) "  E) ?

Solution: Explanation:   & * ∧ % $ # @ + - ! ∼ μ Ω Δ ± ∈ ≈ ∫ → √ ∞ ∧ @ ↓ ≥ ∈ $ + @   The fifth symbol from the right end of the given sequence is “≥”, while the ninth symbol from the left end of the sequence is “-”.   The symbol at the middle of “≥” and “-” is “ ≈ ”.   ANSWER:≈
Answer: C
In a 1000 m race Usha beats Shiny by 50 m. In the same race, by what time margin Shiny beat Mercy.
who runs at 4 m/s ?  Choose the correct option.
A) 100 sec.
B) 50 sec
C) 25 sec
D) Data not sufficient
E) None of these

Solution: Explanation:   Speed of Shiny = 50/ 10= 
50/ 10 = 5
5m/s   Time taken by shiny to complete the race is B= 1000/5= 
1000/5 = 200
200 sec.   Time taken by Baley to complete the race is D= 1000/4= 
1000/4 = 250
250 sec.   Hence, D-50 sec= 50 sec   Answer : 50 sec
Answer: B
The perimeter of a rhombus is 68 cm and one of its diagonals is 16 cm. Find its area?
Choose the correct choice from the following
A) 299	B) 240	C) 277	D) 266	E) 121

Solution: 4a = 68 => a = 17   172 – 82 = 152   1/2 * 16 * 30= 
1/2 * 16 * 30 = 240
240   Answer: 240
Answer: B
One fourth of one third of two fifth of a number is 20. What will be40% of that number Select the correct option:
A) A)140
B) B)150
C) C)180
D) D)240
E) E)220

Solution: Explanation:   (1/4) * (1/3) * (2/5) * x = 20   then x = 20 * 30= 
20 * 30 = 600
600   40% of 600= 240   Answer: Option 240
Answer: D
Find the area of a parallelogram with base 24 cm and height 16 cm. Pick:
A) 200 B) 384 C) 345 D) 244 E) 242

Solution: Area of a parallelogram = base * height = 24 * 16= 
24 * 16 = 384
384 cm2   Answer: Option 384
Answer: B
18 litres of mixture contains 20% alcohol and the rest water. If 3litres of water be mixed with it, the percentage of alcohol in the new mixture would be?
Pick:
A) 16.67%  B) 17.14%  C) 18.3%  D) 19.75%  E) 21.23%

Solution: Alcohol in the 18litres of mix. = 20% of 18litres = (20*18/100)= 
(20*18/100) = 18/5 = around 3.6
3.6litres   water in it= 18-3.6= 
18-3.6 = 14.4
14.4litres   new quantity of mix.= 18+3= 
18+3 = 21
21 litres   Quantity of alcohol in it= 3.6litres   Percentage of alcohol in new mix. = 3.6*100/21 = 17.14%   Answer is 17.14%
Answer: B
a, b, and c are integers and a<b<c. S is the set of all integers from a to b, inclusive. Q is the set of all integers from b to c, inclusive. The median of set S is (3/4)*b. The median of set Q is (6/8)*c. If R is the set of all integers from a to c, inclusive, what fraction of c is the median of set R?	Choose the correct choice from the following options:
A) 3/8  B) 1/2  C) 11/16  D) 5/8  E) 3/4

Solution: The answer isC: 11/16.   The key to this problem is remembering that the median for a consecutive set of numbers is equivalent to its mean. For example, the mean and median of a set consisting of x, x+1, x+2, ... ,y will always be (x+y)/2.   For set S, consisting of numbers (a, a+1,...,b), the median is given to be 3/4*b:   (a+b)/2 = (3/4)*b   a = b/2   For set Q, consisting of numbers (b, b+1,...,c), the median is given to be 6/8*c:   (b+c)/2 = (6/8)*c   b = (1/2)*c   For set R, consisting of numbers (a, a+1,...c), the median needs to be found:   a = b/2 = (1/2*c)/2 = (1/4)*c   Median = (a + c)/2 = (1/4*c + c)/2 = (5/4)*c/2 = (5/8)*c (ANSWER 5/8)
Answer: D
A jogger running at 9 kmph along side a railway track is 240 metres ahead of the engine of a 120 metre long train running at 45 kmph in the same direction. In how much time will the train pass the jogger? Pick one.
A) 3.6 sec B) 18 sec C) 36 sec D) 72 sec E) None of these

Solution: Speed of train relative to jogger   = (45 – 9) km/h = 36 km/h   = (36 × 5⁄18) m/sec = 10 m/sec   Distance to be covered = (240 + 120)= 
(240 + 120) = 360
360 m.   ∴ Time taken= (360⁄10) sec = 36 sec.   Answer 36 sec
Answer: C
A monkey ascends a greased pole 20 meters high. He ascends 2 meters in the first minute and then slips down 1 meter in the alternate minute. If this pattern continues until he climbs the pole , in how many minutes would he reach at the top of the pole ? Select:
A) 30th minute	B) 31st minute	C) 37th minute	D) 32nd minute	E) 33th minute

Solution: The money is climbing 1meter in 2min. This pattern will go on till he reaches 10meters. I mean this will continue for first  18*2= 
 18*2 = 36
36mins. he would have reached 18meters. After that he will climb 2meters and he will reach the pole. So total time taken= 36 + 1= 
36 + 1 = 37
37mins.   So, asnwer will be 37th minute
Answer: C
The area of the square formed on the diagonal of a rectangle as its side is 108 1/3 % more than the area of the rectangle. If the perimeter of the rectangle is 28 units, find the difference between the sides of the rectangle?	Select:
A) 1m	B) 5m	C) 8m	D) 2m	E) 9m

Solution: Let the sides of the rectangle be l and b respectively.   From the given data,   (√l2 + b2) = (1 + 108 1/3 %)lb   => l2 + b2 = (1 + 325/3 * 1/100)lb   = (1 + 13/12)lb   = 25/12 lb   => (l2 + b2)/lb = 25/12   12(l2 + b2) = 25lb   Adding 24lb on both sides   12l2 + 12b2 + 24lb = 49lb   12(l2 + b2 + 2lb) = 49lb   but 2(l + b) = 28 => l + b = 14   12(l + b)2 = 49lb   => 12(14)2 = 49lb   => lb = 48   Since l + b = 14, l = 8 and b = 6   l - b = 8 - 6= 
8 - 6 = 2
2m.   Answer: 2m
Answer: D
There are 9 baskets numbered from 1 to 9 and filled with apples. 10 children are asked to pick apples one by one from each basket such that the number of apples picked by each child from each basket is equal to the number marked on the basket. If there were 1000 apples in total and the baskets were filled in such a way that none of the basket became empty in the process, how many apples were left in the end?
Choose the correct choice from the following answers.
A) 440	B) 550	C) 660	D) 770	E) 880

Solution: Each child takes a total of 1+2+3+4+5+6+7+8+9 = 9*10/2= 
9*10/2 = 45
45 apples.   The total number of apples taken by 10 children is  10*45= 
 10*45 = 450
450   The number of apples left in the end is  1000 - 450= 
 1000 - 450 = 550
550 apples.   The answer is 550.
Answer: B
A man sells an article at a gain 15%. If he had bought it at 10% less and sold it for 5 less, he would have gained 25%. Find the cost price of the article.
Pick one.
A) 150	B) 160	C) 170	D) 180	E) 200

Solution: Let the C.P. be 100   First S.P. = 115   Second C.P. = 90   Second S.P = 125% of 90 = 112.50   Difference of two selling prices is 115 – 112.50 = 2.50 and C.P. of the article is 100   But actual difference is 5.   ∴ C.P. = 100⁄2.50 × 5 = 200.   Answer 200
Answer: E
A certain plant was 11 feet long on the day it was plantedthe length grows by a constant amount everyday(inc. the first day it was planted).
if this plant grew by 60% b/w the 4th day and 10 th day after it was planted ,how many feet per day does the plant grow	Options
A) a) 2  B) b) 4.5  C) c) 1.83  D) d) 5.5  E) e) 3

Solution: If the plant is 11 feet tall when it is planted, it will be 11 + k feet tall at the end of the day (where k is the constant length it grows by every day).   Similarly, at the end of the 4th day the plant must be 11 + 4k feet tall and at the end of the 10th day it must be 11 + 10k feet tall.   Therefore 6k = 0.6 (11 + 4k)   => k = 1.83   Therefore the plant grows by 1.83 feet every day.   Option (c) 1.83)
Answer: C
The equation y = ax*b* + c produces the
following (x, y) coordinate pairs: (0, 2),
(1, 7), and (2, 42). What is the value of abc? Choices:
A) 10  B) 20  C) 30  D) 40  E) 60

Solution: To begin, plug x = 0 and y = 2 into the equation y = axb + c. Note that the first term   drops out:   2 = a(0)b + c   2 = c   Now you can substitute 2 for c in the original equation, giving you y = axb + 2. Next, plug in   x = 1 and y = 7. Notice that everything drops out except for the coefficient of the first term:   7 = a(1)b + 2   5 = a   You can now substitute 5 for a in the equation, giving you y = 5xb + 2.= 
+ 2. = 2
2   and y= 42:   42 = 5(2)b + 2   40 = 5(2)b   8 = 2b   23 = 2b   3 = b   Finally, you can see that abc = (5)(3)(2) = 30.   correct answer 30)30
Answer: C
Sheela deposits Rs. 3800 in bank savings account. If this is 22% of her monthly income. What is her monthly income in?  Choose the correct choice from the following answers
A) 22000
B) 20000
C) 25123
D) 17272
E) None of these

Solution: Explanation :   22% of income = Rs. 3800   100% of income = 3800 X 100/22 = Rs. 17272   Answer : 17272
Answer: D
Three distinct single digit no A,B and c are in G.M ,if abs(x) for real x is the absolute value of x(x , if x is positive or zero,and -x if x is negative), then the number of different possible values of abs (A+B -C) is;
Answers.
A) 3
B) 6
C) 5
D) 4
E) 1

Solution: 1,2,4   2,4,8   4,2,1   8,4,2   1,3,9   9,3,1   total=6   ANSWER:6
Answer: B
A person starts walking at a speed of 5km/hr through half the distance, rest of the distance he
covers with aspeed 4km/hr. Total time of travel is 36 hours. What is the maximum distance he
can cover?
Choose the correct choice
A) 20km	B) 40km	C) 60km	D) 80km	E) 160km

Solution: t=d/s, so   36=x/2*1/5+x/2*1/4(because half distance with 5 km/ph, and remaining half with 4km/hr)   36=x(18/80)   x=160km   ANSW160kmR:160km
Answer: E
The average age of three boys is 120 years and their ages are in proportion 2:6:12. What is the age in years of the youngest boy?
Choose the correct answer:
A) 8
B) 9
C) 7
D) 12
E) 5

Solution: 2x + 6x + 12x = 120   x =6   2x = 12   Answer:12
Answer: D
Village X has a population of 76000, which is decreasing at the rate of 1200 per year. Village Y has a population of 42000, which is increasing at the rate of 800 per year .in how many years will the population of the two villages be equal?
Choices:
A) 15
B) 17
C) 11
D) 18
E) 13

Solution: Let the population of two villages be equal after p years   Then, 76000-1200p=42000+800p   2000p=34000   p=17   Answer is 17.
Answer: B
In year Y imported machine tools accounted for 25 percent of total machine-tools sales in the United States, and Japanese imports accounted for 65 percent of the sales of imported machine tools. If the total sales of machine tools imported from Japan that year was x billion dollars, then the total sales of all machine tools in the United States was how many billion dollars?  Choose the correct choice:  A) 9x/80  B) 13x/20  C) 80/9x  D) 20x/13  E) 80x/13

Solution: Sales of imported tools = 25% of the total sales = 0.25*{total} = {total}/4;   Sales of Japanese tools = 65% of the sales of imported tools = 0.65*{total}/4 = 13/20*{total}/4 = 13*{total}/80.   Since the sales of of Japanese tools was x, then 13*{total}/80 = x --> {total} = 80x/13.   Answer: 80x/13.
Answer: E
Tough and Tricky questions: Combinations.
Six students - 3 Girls and 3 boys - are to sit side by side for a makeup exam. How many ways could they arrange themselves given that no two boys and no two girls can sit next to one another? Choose the correct choice:
A) 12
B) 72
C) 34
D) 240
E) 520

Solution: Six students - 3 boys and 3 girls - are to sit side by side for a makeup exam. How many ways could they arrange themselves given that no two boys and no two girls can sit next to one another?   A) 12   B) 36   C) 72   D) 240   E) 720   The boys (B) and girls(G) can either be arranged as BGBGBG or GBGBGB.   Within the arrangement BGBGBG or GBGBGB, the boys can be arranged 3! ways and girls can be arranged 3! ways.   Therefore total number of ways boys and girls can be arranged = 2*3!*3!= 72 ways   Answer:72
Answer: B
If in a $150 mln portfolio of stock, twice as much is invested in stock A as is invested in all the other stocks, how much is invested in all the other stocks?
Options.
A) 50mln  B) 60mln  C) 70mln  D) 80mln  E) 90mln

Solution: Let x denote the amount invested in all the other stocks. Then the amount invested in stock A is 2x. As we have the $150 mln portfolio, x+2x=3x=150 mln from where x=50 mln.   50mlnnswer: 50mln
Answer: A
On a sum of money, the S.I. for 2 years is Rs. 660, while the C.I. is Rs. 696.30, the rate of interest being the same in both the cases. The rate of interest is?	Choose the correct answer
A) 12% B) 32% C) 72% D) 11% E) 82%

Solution: Difference in C.I. and S.I for 2 years = (696.30 - 660) = Rs. 36.30.   S.I for one year = Rs. 330.   S.I. on Rs. 330 for 1 year = Rs. 36.30   Rate = (100 * 36.30)/(330 * 1)= 
(100 * 36.30)/(330 * 1) = 11
11%   Answer:11%
Answer: D
All the water in container A which was filled to its brim was poured into two containers B and C. The quantity of water in container B was 62.5% less than the capacity of container A. If 148 liters was now transferred from C to B, then both the containers would have equal quantities of water. What was the initial quantity of water in container A?	Answers
A) 1289	B) 1198	C) 281	D) 1184	E) 282

Solution: Explanation:   B has 62.5% or (5/8) of the water in A. Therefore, let the quantity of water in container A(initially) be 8k.   Quantity of water in B = 8k - 5k = 3k.   Quantity of water in container C 8  - 5= 
8  - 5 = 3
3k.   Quantity of water in container C= 8k - 3k = 5k   Container: A B C   Quantity of water: 8k 3k 5k   It is given that if 148 liters was transferred from container C to container B, then both the containers would have equal quantities of water.   5k - 148 8  - 3= 
8  - 3 = 5
5k   Container: A B C   Quantity of water: 8k 3k 5k   It is given that if 148 liters was transferred from container C to container B, then both the containers would have equal quantities of water.   5k - 148= 3k + 148 => 2k = 296 => k = 148   The initial quantity of water in A = 8k = 8 * 148= 
8 * 148 = 1_184
1184 liters.   Answer: Option 1184
Answer: D
How many different pairs of numbers (s, t) such that s = 3t can be obtained if s and t are selected from the set of number {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
Choose the correct option.
A) 1
B) 2
C) 3
D) 4
E) 5

Solution: Given s=3t   t can take 0,1,2,3, 4   and so s = 0,3,6,9, 12   4 such pairs can be formed.   answer 5
Answer: E
A and B can do a piece of work in 8 days. B and C can do it in 12 days and A and C in 16 days. Working together they will complete the work in how many days? Options:
A) 3.33 days
B) 8.33 days
C) 3.99 days
D) 7.38 days
E) 2.88 days

Solution: A + B = 1/8   B + C = 1/12   C + A = 1/16   -------------------------------   2(A + B +C) = 1/8 + 1/12 + 1/16 = 13/48   A + B +C = 13/96   96/13 = 7.38 days   Answer:7.38 days
Answer: D
A gives B as many as rupees B has and C as many as rupees C has.Similarly B gives A as many as rupees A has and C as many as rupees C has, C similarly gives B as many as rupees B has and A as many as rupees A has..Now finally each of them has 32 rupees.how much rupees does A has initially?
Choose the correct choice from the following answers.
A) 52
B) 56
C) 60
D) 62
E) 45

Solution: initially   52   B   C   after 52 gives   52 has ->52-B-C   B has ->2B   C has ->2C   after B gives   52 has ->252-2B-2C   B has ->-52+3B-C   C has ->4C   52FTER C gives   52 has ->452-4B-4C=32---------1   B has ->-252+6B-2C=32----------2   C has ->-52-B-7C=32-----------3   ON solving 1,2,3 52=52   52NSWER:52
Answer: A
What least no. must be subtracted from 50248 so that remaining no.is divisible by 20?
Choose the correct choice from the following answers:
A) 3
B) 2
C) 4
D) 8
E) 6

Solution: Explanation:   On dividing 50248 by 20 we get the remainder 8, so 8 should be subtracted   Option 8
Answer: D
If x^2−2ax+a^2=0 get value of x/a  Answers:
A) 8 B) 9 C) 7 D) 5 E) 1

Solution: a is obviously non-zero. We divide the equation by   a^2   we get (x/a-1)^2=0   x/a=1   Ans: 1
Answer: E
Find the area of a rhombus whose side is 25 cm and one of the diagonals is 30 cm?  Answers
A) 287
B) 2766
C) 188
D) 261
E) 600

Solution: Consider the rhombus ABCD. Let the diagonals intersect at E. Since diagonals bisect at right angles in a rhombus.   BE2 + AE2 = AB2   252 = 152 + AE2 AE = √(625 - 225)= 
(625 - 225) = 400
√400= 20,   AC = 20 + 20= 
20 + 20 = 40
40 cm.   Area of a rhombus= 1/2 * d1d2   = 1/2 * 40 * 30= 
1/2 * 40 * 30 = 600
600 sq.cm.   Answer: 600
Answer: E
On the shelf, there are four books of poetry, four novels, and four reference works. Suppose we picked two books at random. What is the probability that we pick one novel and one reference work?  Choose the correct answer:	A) 2/15	B) 4/21	C) 6/25	D) 8/33	E) 10/37

Solution: We could pick one novel and then one reference work, or, we could choose one reference work and then one novel.   P(one novel and one reference work) = 4/12*4/11 + 4/12*4/11 = 8/33   The answer is 8/33.
Answer: D
A, B and C can do a piece of work in 7 days, 14 days and 28 days respectively. How long will they taken, if all the three work together?
Choose the correct choice from the following answers
A) 4 days	B) 3 days	C) 6 days	D) 8 days	E) 9 days

Solution: 4 days   4 days   1/7 + 1/14 + 1/28 = 7/28 = 1/4 => 4 days
Answer: A