MU-NLPC/Calc-aqua_rat huggingface dataset:
By weight, liquid X makes up 0.8 percent of solution A and 1.8 percent of solution B. If 400 grams of solution A are mixed with 700 grams of solution B, then liquid X accounts for what percent of the weight of the resulting solution?  Options:  A) 1.58%  B) 1.98%  C) 10%  D) 15%  E) 19%

Solution: I think there is a typo in question.   It should have been "By weight Liquid 'X ' makes up..... "   Weight of Liquid X = 0.8 % of Weight of 1.58% + 1.8% of Weight of B   When 400gms of 1.58% and 700gms of B is mixed :   Weight of Liquid X = (0.8 * 400)/100 + (1.8* 700)/100= 
(0.8 * 400)/100 + (1.8* 700)/100 = 15.8
15.8gms   % of Liquid X in resultant mixture= (15.8/1000) *100= 
(15.8/1000) *100 = 1.58
1.58%   1.58%
Answer: A
2 cow’s and 8 goats are brought for Rs.1400. If the average price of a goat be Rs.60. What is the average price of a cow.  Choices:
A) Rs. 480  B) Rs.960  C) Rs.960  D) Rs. 460  E) Rs. 560

Solution: Explanation:   Average price of a goat = Rs.60   total price of 8 goats = 8*60 = Rs.480   But total price of 2 cows and 8 goats = Rs. 1400   Total price of 2 cows is = 1400 - 480   = 980   Average price of a cow = 980/2   = Rs. 460   Answer: Option Rs. 460
Answer: D
A courtyard is 30 meter long and 16 meter board is to be paved with bricks of dimensions 20 cm by 10 cm. The total number of bricks required is? Choose the correct choice from the following answers
A) 22877	B) 24000	C) 20000	D) 27999	E) 17799

Solution: Number of bricks =Courtyard area/1 brick area   =(3000×1600/20×10)=24000   Answer: 24000
Answer: B
Length of train is 130 meters and speed of train is 45 km/hour. This train can pass a bridge in 30
seconds, then find the length of the bridge.
Answers
A) 230 meters
B) 235 meters
C) 240 meters
D) 245 meters
E) None of these

Solution: ExplanaƟon:   Let the length of bridge is X [as always we do :)]   Speed of train is = 45*(5/18) m/sec = 25/2 m/sec   Time = 30 seconds   Total distance = 130+x   We know Speed = distance/Ɵme   so,   130+x30=252=>2(130+x)=750x=245 meters   So length of the bridge is 245 meters   Answer:245 meters
Answer: D
If p/7 = r/2 and r = 0.75s, what is the ratio of p to r to s?  Choose the correct choice:
A) 2 : 3 : 4  B) 8 : 12 : 9  C) 21 : 6 : 8  D) 6 : 4 : 3  E) 12 : 8 : 3

Solution: p/7=r/2, r=0.75s, what is p:r:s?   we get p/r=7/2 and r/s=3/4, so   7/3*3/2 and 2/2*3/4   21/6 and 6/8   21 : 6 : 8
Answer: C
A man sells a horse for Rs.200 and loses something, if he had sold it for Rs.620, his gain would have been double the former loss. Find the cost price of the horse?
Select the correct option:  A) 140  B) 162  C) 160  D) 150  E) 71

Solution: CP = SP + 1CP = SP - g   200 + x = 620 - 2x   3x = 420 => x = 140   140nswer:140
Answer: A
(4300331)-?=2535618
Options.
A) 1865113  B) 1775123  C) 1764713  D) 1675123  E) None of them

Solution: Let 4300331-x=2535618   then x=4300331-2535618= 
4300331-2535618 = 1_764_713
1764713   Answer is 1764713
Answer: C
(2+0.0001)/(0.04+20)
The value of the expression above is closet to which of the following? Choose the correct choice from the following answers:
A) 0.0001 B) 0.001 C) 0.1 D) 1 E) 10

Solution: Notice that we need approximate value of the fraction.   Now, the nominator is very close to 2 and the denominator is very close to 20, hence the value of the fraction is very close to 2/20=0.1.   Answer: 0.1.
Answer: C
The cost price of 16 articles is the same as the selling price of 12 articles. Find the loss/profit percentages.	Choose the correct choice from the following:
A) 30%
B) 32.50%
C) 33 1/3%
D) 40%
E) 50%

Solution: Explanation:   The gain is 4 out of 12 articles.   Therefore, gain percentage = 4x100/12 = 100/3 = 33 1/3%   Answer: Option 33 1/3%
Answer: C
A borrowed some money at the rate of 5% p.a. for the first four years, 8% p.a.for the next 8 years and 10% p.a.for the period beyond 12 years If the total interest paid by him at the end of 14 years is 41600, how much money did he borrow?	Pick:
A) 40,000
B) 50,000
C) 62,000
D) 45,000
E) None of these

Solution: Let the sum be x. Then,   (x×4×5/100)+(x×8×8/100)+(x×2x10/100)=41600   ⇒ 20x + 64x + 20x = (41600 × 100)   ⇒ 104x = 4160000   ⇒ x = 40000.   40,000nswer 40,000
Answer: A
A batsman makes a score of 85 runs in the 11th inning and thus increases his average by 5. Find his average after 11th inning. Choose the most appropriate option:
A) 40 B) 50 C) 62 D) 45 E) 35

Solution: Let the average after 11th inning = x   Then, average after 10th inning = x-5   10(x-5)+85 = 11x   x = 85-50= 
85-50 = 35
35   Answer is 35
Answer: E
At a loading dock, each worker on the night crew loaded 3/4 as many boxes as each worker on the day crew. If the night crew has 1/2 as many workers as the day crew, what fraction of all the boxes loaded by the two crews did the day crew load?	Choose the correct choice
A) 4/7  B) 5/7  C) 8/11  D) 7/12  E) 11/15

Solution: Let x be the number of workers on the day crew.   Let y be the number of boxes loaded by each member of the day crew.   Then the number of boxes loaded by the day crew is xy.   The number of boxes loaded by the night crew is (x/2)(3y/4) = 3xy/8   The total number of boxes is xy + 3xy/8 = 11xy/8   The fraction loaded by the day crew is xy / (11xy/8) = 8/11   The answer is 8/11.
Answer: C
There are 10 red balls, 10 blue balls, 15 green balls and 9 black balls in a bag. What is the minimum number of balls to be taken out of the bag to assure that you have all the balls of one color?
Choose the correct choice from the following choices:
A) 10	B) 23	C) 43	D) 41	E) 16

Solution: The worst case scenario would be if we pick 9 red balls, 9 blue balls, 14 (?) balls and 8 black balls. In this case we'll have 11+9+14+8=40 balls and still won't have all the balls of one color. The next 41rd ball we pick, no matter which color it'll be, will guarantee that we have all the balls of one color.   Answer: 41.
Answer: D
If 25% of x is 30 less than 15% of 1500, then x is? Pick
A) 872  B) 738  C) 837  D) 780  E) 83

Solution: 25% of x = x/4 ; 15% of 1500   = 15/100 * 1500= 
15/100 * 1500 = 225
225   Given that, x/4= 225 - 30   => x/4 = 195 => x = 780.   Answer:780
Answer: D
If Jesse flips a coin five times in a row, what is the probability that the result will be heads at least 3 times?  Answers.
A) 21/128 B) 29/128 C) 35/128 D) 1/16 E) 1/2

Solution: Question : Atleast 3 heads in 5 flip.   The total outcome of flip is = 2^5 = 32   For any Coins problem write the ask in the shown format.   HHHTT   HHHHT   HHHHH   Once you have written in the above mentioned format the answer is pretty straight.   HHHTT = [5!]/3!*2! = 10   HHHHT = [5!]/4! = 5   HHHHH = [5!]/[5!] = 1   Sum 5  / 5= 
5  / 5 = 1
1   Sum= 10+5+1= 
10+5+1 = 16
16/32= 1/2   Answer - 1/2
Answer: E
How many 3 digits number are there which sum of digits is equal to 16.
Answers.
A) 63	B) 64	C) 65	D) 66	E) 67

Solution: 100-200=4;   200-300=5;   ---------   ---------   700-800=10;   800-900=9;   900-999=8;   Total= 66   ANSWER:66
Answer: D
The cost price of a radio is Rs.1500 and it was sold for Rs.1230, find the loss %?  Choices: A) 18% B) 12% C) 22% D) 24% E) 21

Solution: 1500 ---- 270   100 ---- ? => 18%   18%nswer:18%
Answer: A
Two trains running in opposite directions cross a man standing on the platform in 47 seconds and 38 seconds respectively and they cross each other in 40 seconds. The ratio of their speeds is:
Choices:
A) 3 : 1
B) 3 : 2
C) 2 : 7
D) 3 : 25
E) 3 : 4

Solution: Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 47 x meters, and length of the second train = 38 y meters. (47 x + 37 y) / (x + y) = 40 ==>   47 x + 38 y = 40x + 40 y ==> 7x = 2 y ==> x/y = 2/7   Answer: Option 2 : 7
Answer: C
In 1998 the profits of company N were 10 percent of revenues. In 1999, the revenues of company N fell by 20 percent, but profits were 14 percent of revenues. The profits in 1999 were what percent of the profits in 1998?  Answers.
A) 80%  B) 105%  C) 120%  D) 112%  E) 138%

Solution: 0,112R = x/100*0.1R   Answer 112%
Answer: D
What is the largest integer n such that
n2- 38/n + 1
is an integer?	Pick:
A) 36 B) 38 C) 72 D) 76 E) None of these

Solution: Doing the long division algebraically, we get a quotient of n-1 with a remainder of   -37. In order for the division to give an integer, n+1 must divide -37 evenly. So n+1 = 37,   and n = 36.   correct answer 36
Answer: A
If 135*s is a perfect square then s can be which of the following numbers? Choose one:
A) 15 B) 35 C) 54 D) 105 E) 150

Solution: My solution:   For a number to be a perfect square all the prime factors must be in pairs. So,   Prime factors of 135 are 3 *3 *3 *5   1)15 = 3 * 5   2) 35 = 5 * 7   3) 54 = 2 * 3 * 3 * 3   4) 105 = 3 * 5 * 7   5) 150 = 2 * 3 * 5 * 5   So only answer choice A completes the pairing of 3, 5 . It adds a3, a5, and a7to the prime factors of 135 (3*3*3*5) and makes it a perfect square. 15
Answer: A
Solution X is 30% chemical A and 70% chemical B by volume. Solution Y is 40% chemical A and 60% chemical B by volume. If a mixture of X and Y is 36% chemical A, what percent of the mixture is Solution X? Choose the correct choice from the following choices.
A) 30%
B) 35%
C) 40%
D) 45%
E) 50%

Solution: The volume of the mixture be X+Y.   0.3X +0.4Y=0.36(X+Y)   X=2Y/3   X/(X+Y)=(2Y/3) / (5Y/3)=2/5=40%.   The answer is 40%.
Answer: C
Grace has 18 jellybeans in her pocket. She has 10 red ones, 4 green ones, and 4 blue ones. What is the minimum number of jellybeans she must take out of her pocket to ensure that she has one of each color?  Answers.
A) 4
B) 8
C) 12
D) 13
E) 15

Solution: The worst scenario is when she takes 10 red and 4 green, total of 14 jellybeans, and still doesn't have 3 distinct colors. But the next draw (15th) will surely be the third color jellybean (blue) as there is no other color jellybeans left in pocket.   Answer: 15.
Answer: E
The chance of rain on any given day in Tel-Aviv is 50%. What is the probability Q that it rained in Tel-Aviv on exactly 4 out of 6 randomly chosen days?  Pick
A) 15/64  B) 30/64  C) 1/2  D) 1/4  E) 52/64

Solution: chances of rain on exactly 4 days and not rain on 2 days = (1/2)^4* (1/2)^2 = 1/64   Chosing 4 days out of 6 = 6!/(4!*2!) = 15   chances of rain on exactly 4 days out of 6 days Q= 15/64   15/64ns 15/64 it is.
Answer: A
Of the 15 employees of a certain company, twice as many are in the sales department as are in all of the other departments combined. What is the number of employees in the sales department? Answers
A) 10	B) 20	C) 30	D) 40	E) 45

Solution: This is ratio problem solving question.   I will prefer to use RMV box.   R M V   Sales 2 5 10   Other 1 5 5   Total 3 5 15   Answer is 10. i.e 10
Answer: A
In how many ways can five boys, three girls and a teacher sit in a row such that all boys sit together?	Options:
A) A)10000
B) B)12100
C) C)14400
D) D)1097
E) E)2781

Solution: Treat all boys as one unit. Now there are four students and a teacher and they can be arranged in 5! ways. Again five boys can be arranged among themselves in 5! ways.   Required number of arrangements   = 5! * 5! = 120 * 120= 
120 * 120 = 14_400
14400.   Answer:14400
Answer: C
A motorcyclist goes from Nagpur to Delhi, a distance of 600 kms at an average of 60 kmph speed. Another man starts from Nagpur by car 5 Â½ hours after the first, and reaches Delhi Â½ hour earlier. What is the ratio of the speed of the motorcycle and the car?	Choose the correct choice from the following answers
A) 1:2
B) 1:7
C) 1:9
D) 1:5
E) 2:5

Solution: T = 600/60= 
600/60 = 10
10 h   T= 10 - 6= 
10 - 6 = 4
4   Time Ratio= 10:4= 5:2   Speed Ratio = 2:5   Answer: 2:5
Answer: E
A boatman can row 3 km against the stream in 20 minutes and return in 9 minutes. Find the rate of current ?	Select.
A) 7/2 kmph  B) 8/2 kmph  C) 5.5 kmph  D) 1/2 kmph  E) 2/2 kmph

Solution: Explanation:   Speed in upstream = Distance / Time = 3 x 60/20 = 9 km/hr.   Speed in downstream = 3 x 60/9 = 20 km/hr   Rate of current = (20-9)/2= 
(20-9)/2 = 11/2 = around 5.5
5.5 km/hr.   Answer: 5.5 kmph
Answer: C
Find the value of * in the following
(1 5/3) ÷ 3/11 × */11 = (2 2/3 × 7/5 × 6/7)	Choose the most appropriate option:
A) 3.2
B) 3.4
C) 3.6
D) 3.8
E) 4

Solution: 3.6   Option '3.6'
Answer: C
A dishonest milkman professes to sell his milk at cost price but he mixes it with water and thereby gains 25%. The percentage of water in the mixture is:	Choose the correct option:	A) 4%	B) 61/4%	C) 20%	D) 25%	E) 30%

Solution: Let C.P. of 1 litre milk be Re. 1   Then, S.P. of 1 litre of mixture = Re. 1, Gain = 25%.   20%P of 1 lr = 100/125*1 = 4/5   Ratio of milk to water = 4/5:1/5 = 4:1   =20%   ANSWER 20%
Answer: C
What is the least integer that is a sum of four different primes each greater than 20?  Options: A) 79 B) 83 C) 120 D) 133 E) 169

Solution: Given integer must be a sum of 4 primes each greater than 20. Thus each prime must be odd.   Therefore sum of Odd + Odd + Odd + Odd = Even   Only Even option is 120   Therefore Ans: 120   To verify   120 = 23 + 29 +31 +37
Answer: C
A man buys two articles for Rs.1980 each and he gains 10% on the first and loses 10% on the next. Find his total gain or loss percent?	Choose the correct option:
A) 9%loss B) 8%loss C) 3%loss D) 2%loss E) 1%loss

Solution: (30*30)/100= 
(30*30)/100 = 9
9%loss   9%lossnswer: 9%loss
Answer: A
If the cost of x metres of wire is d rupees, then what is the cost of y metres of wire at the same rate?	Pick
A) Rs.(xy/d)  B) Rs.(yd/x)  C) Rs.(y/d)  D) Rs.(xd)  E) Rs.(x/d)

Solution: Cost of x metres = Rs. d.   Cost of 1 metre = Rs.	d/x   Cost of y metres = Rs.(d/x)* y= Rs.(yd/x)   Answer is Rs.(yd/x).
Answer: B
1370 , 1320 , 1070 , -180 ? Choices: A) -6440 B) -6680 C) -6480 D) -5480 E) -4480

Solution: 1370-1320= 
1370-1320 = 50
50 -->50*5=250   1320-250= 
1320-250 = 1_070
1070-->250*5=1250   1070-1250=-180-->1250*5=6250   -180-6250=-6430......so ans:-6480   ANSWER:-6480
Answer: C
Golu started from his house towards North. After covering a distance of 8 km. he turned towards left and covered a distance of 6 km. What is the shortest distance now from his house?
Choose the correct option:
A) 10 km.  B) 16 km.  C) 14 km  D) 2 km.  E) 4 km.

Solution: C-------------B   !   !   !   !   !   10 km.   10 km.B=8 Km BC=6Km   10 km.C=sqrtof(8^2+6^2)   10 km.C=10KM   10 km.NSWER:10 km.
Answer: A
A goods train runs at the speed of 72 km/hr and crosses a 250 m long platform in 26 sec. What is the length of the goods train? Choose the correct choice from the following
A) 49 sec B) 50 sec C) 48 sec D) 43 sec E) 32 sec

Solution: D = 540 + 180= 
540 + 180 = 720
720   S= 54 * 5/18= 
54 * 5/18 = 15
15 mps   T= 720/15= 
720/15 = 48
48 sec   Answer:48 sec
Answer: C
If the speed of a man is 45 km per hour, then what is the distance traveled by him in 30 seconds ?
Select the correct option:
A) 275m
B) 360m
C) 375 m
D) 420 m
E) 440 m

Solution: The distance traveled in 30 sec = 45*(5/18) *30= 
45*(5/18) *30 = 375
375m   ANSWER:375 m
Answer: C
A car travelling 5/7th of its actual speed covers 42 km in 1 hr 40 min 48 sec. what is the actual speed of the car? Pick:
A) 22  B) 35  C) 27  D) 10  E) 18

Solution: Explanation:   Let the Actual Speed = x   It is travelling with 5/7 of its actual speed = 5x/7.   Converting the time into seconds = 3600 + 2400 + 48 seconds.   Covers a distance with speed = 42/(3600 + 2400 + 48)   = 424048424048 × 3600 = 25 kph   Given 5x75x7 = 25 kph   So Actual Speed = 25 × (7/5) = 35 kph   Answer:35
Answer: B
What is the sum of all digits for the number 10^28 - 44?	Answers:
A) 233 B) 245 C) 257 D) 270 E) 285

Solution: 10^28 is a 29-digit number: 1 followed by 28 zeros.   10^28 - 44 is a 28-digit number: 26 9's and 56 at the end.   The sum of the digits is  26*9+5+6= 
 26*9+5+6 = 245
245.   The answer is 245.
Answer: B
8 men and 2 boys working together can do four times as much work as a man and a boy. Working capacity of man and boy is in the ratio
Choose the correct choice from the following answers:  A) 1:2  B) 1:3  C) 2:1  D) 2:3  E) None of these

Solution: Explanation:   Let 1 man 1 day work = x   1 boy 1 day work = y   then 8x + 2y = 4(x+y)   => 4x = 2y   => x/y = 2/4   => x:y = 1:2   Option 1:2
Answer: A
4 mat-weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 14 mat-weavers in 14 days?  Choose the correct choice from the following choices:
A) 25
B) 19
C) 39
D) 61
E) 49

Solution: Let the required number of bottles be x.   More weavers, More mats (Direct Proportion)   More days, More mats (Direct Proportion)   Wavers	4	:	14 :: 4 : x   Days	4:14   4 * 4 * x = 14 * 14 * 4   x =	(14 * 14 * 4)/(4 x 4)   x = 49.   Answer is 49.
Answer: E
If y ≠ 3 and 2a/y is a prime integer greater than 2, which of the following must be true?
I. xa= y
II. y = 1
III. a and y are prime integers. Choose the correct option.
A) None  B) I only  C) II only  D) III only  E) I and II

Solution: Note that we are asked which of the following MUST be true, not COULD be true. For such kind of questions if you can prove that a statement is NOT true for one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer.   So we should try to make the listed statements not true for some x and y (which satisfy y≠3 and 2x/y=prime>2).   I. a = y --> not necessarily true: a=3 and y=2 (2a/y=3=prime>2);   II. y=1 --> not necessarily true: a=3 and y=2 (2a/y=3=prime>2);   III. a and y are prime integers --> not necessarily true: a=10 and y=4 (2a/y=5=prime>2).   Nonenswer: None.
Answer: A
The ratio of two numbers is 3 : 4 and their H.C.F. is 3. Their L.C.M. is  Choose the correct choice from the following answers:
A) 48  B) 22  C) 56  D) 27  E) 36

Solution: Explanation:   Let the numbers be 3x and 4x. Then, their H.C.F. = x. So, x = 3.   So, the numbers 9 and 12.   L.C.M. of 9 and 12 = 36.   Answer: Option 36
Answer: E
A girl sitting in a train which is travelling at 40 kmph observes that a goods train travelling in a opposite direction, takes 12 seconds to pass him. If the goods train is 1120 m long, find its speed.	Choose the correct choice from the following options: A) 295 B) 296 C) 297 D) 298 E) 299

Solution: Relative speed = (1120/12)m/s = (1120/12)*(18/5)= 
(1120/12)*(18/5) = 336
336 kmph   speed of goods train= 336-40= 
336-40 = 296
296 kmph   Answer is 296
Answer: B
There are 32 students in a class. Nine of those students are women. What percent are men? (round to the nearest tenth)
Choose the correct choice from the following answers.
A) 70.9%
B) 71.9%
C) 72.9%
D) 73.9%
E) 74.9%

Solution: Total 100% 32   Men 23   Women 9   32-9= 
32-9 = 23
23   x/100=23/32   Multiply the opposites:   100 x 23 = 2300   Divide by the remaining number:   71.87/2300.00   32   71.9%(rounded to nearest tenth)   correct answer 71.9%
Answer: B
There are 20 states in a certain country and every pair of them is connected by a road way. How many road ways are there?	Select:
A) 22  B) 277  C) 288  D) 266  E) 2A1

Solution: 22nswer:22
Answer: A
At what time between 5 and 6 o' clock are the hands of a 3 minutes apart ? Select.
A) 24min  B) 14min  C) 74min  D) 54min  E) 44min

Solution: In this type of problems the formuae is   (5*x+ or - t)*12/11   Here x is replaced by the first interval of given time. Here x is 5.   t is spaces apart   Case 1 : (5*x + t) * 12/11   (5*5 + 3) * 12/11   28 * 12/11 = 336/11= min   therefore the hands will be 3 min apart at 31 5/11 min past 5.   Case 2 : (5*x - t) * 12/11   (5*5 -3 ) * 12/11   22 *12/11= 
22 *12/11 = 24
24 min   therefore the hands will be 3 min apart at 24 min past 5   24minnswer: 24min
Answer: A
If (x + 1)(x + 3) = x^2 + x, what is a possible value of x?
Choices:
A) 2	B) 3	C) -1/3	D) -3	E) -1

Solution: Rearranging the given expression:   (x + 1)(x + 3) = x^2 + x   i.e. x^2 + 4x + 3 = x^2 + x   i.e. 3x = -3   i.e. x = -3/3 = -1   Answer: Option -1   Had it been a difficult expression to solve further, then we could have used options to check which one satisfies the expression after solving it as further as possible.
Answer: E
In how many ways can 4 black and 4 white chess pieces be arranged in a row such that they occupy alternate places? Assume that the pieces are distinct.  Choose one:
A) 144	B) 24	C) 576	D) 48	E) 16

Solution: 4 black chess pieces can be arranged in 4! ways and 4 white pieces can be arranged in 4! ways.   W_W_W_W   Number of ways = 4!*4! = 24 * 24= 
24 * 24 = 576
576   Answer 576
Answer: C
The average of six numbers is X and the average of three of these is Y.If the average of the remaining three is z, then
Choose the correct choice from the following choices
A) x = y + z
B) 2x = y + z
C) x = 2y + z
D) x = y + 2z
E) None of these

Solution: Explanation:   X =((3y+3z)/6)   or   2X= y + z   Option 2x = y + z
Answer: B
The ratio of a compound, by weight, consisting only of substances x, y, and z is 4:6:10,
respectively. Due to a dramatic increase in the surrounding temperature, the composition of the
compound is changed such that the ratio of x to y is halved and the ratio of x to z is tripled. In the
changed compound, if the total weight is 406 lbs, how much does substance x weigh?  Choose the correct choice from the following options
A) 68
B) 76
C) 84
D) 92
E) 110

Solution: x:y=4:6   if the ratio is halevd then x:y=2:6   The old ratio of x to z was 4:10. If this ratio is tripled, then the new ratio of x to z is 12:10.   x:y=2:6=12:36 ( multiplied the ration with 6/6 to have a common co eff x in both the rations x:y and x:z)   so x:y:z= 12:36:10   and we know x + y + z = 406 lbs   from the ratio of x ,y and z we have x=12k y=36k z=10K   put it in the equation we have 12k+36k+10k=406   k=7   Hence x=12(7)=84   Ans 84
Answer: C
Adam and Beth each drove from Smallville to Crown City by different routes. Adam drove an an average speed of 40 miles per hour and completed the trip in 30 minutes. Beth's route was 5 miles longer, and it took her 20 minutes more than Adam to complete the trip. How many miles per hour was Beth's average speed on this trip?
Select:
A) 24 B) 30 C) 48 D) 54 E) 75

Solution: Speed = Distance/Time   Distance for Adam = Speed * Time = 40 * 1/2= 
40 * 1/2 = 20
20 miles   Distance for 30eth= Distance for Adam+5 = 20+5= 
20+5 = 25
25 miles   Time taken by 30eth= Time taken by Adam + (1/3 hour) = 1/2+1/3 = 5/6   Speed of 30eth = D/T = 25/(5/6) = 25*6/5= 
25*6/5 = 30
30 miles per hour   Hence, 30 is the answer.
Answer: B
The number of new words that can be formed by rearranging the letters of the word 'garden' is?  Choose one.
A) 720	B) 721	C) 719	D) 700	E) 721

Solution: Number of words which can be formed   = 6! - 1 = 720 - 1= 
720 - 1 = 719
719.   Answer:719
Answer: C
In an election, candidate Smith won 52% of the total vote in Counties A and E. He won 61% of the vote in County A. If the ratio of people who voted in County A to County E is 3:1, what percent of the vote did candidate Smith win in County E ? Pick one:
A) A.25%  B) B.27%  C) C.34%  D) D.43%  E) E.49%

Solution: (61%)*3x + (y%)*x = (52%)*4x   y = 25% of County E   hence answer is A.25%.
Answer: A
A goods train runs at a speed of 72 kmph and crosses a 240 m long platform in 26 seconds.What is the length of the goods train?
Select the correct option
A) 230 m
B) 240 m
C) 260 m
D) 270 m
E) 280 m

Solution: s=240+x/t   72*5/18=240+x/26   x=280   ANSW280 mR:280 m
Answer: E
A train traveled 580 miles in 2 hours 20 minutes. What was the averge speed of train in miles per hour?  Choose the correct choice from the following choices
A) 270 miles / hour	B) 280 miles / hour	C) 290 miles / hour	D) 300 miles / hour	E) 310 miles / hour

Solution: We first convert the time of 2 hours 20 minutes in minutes   2 hours 20 minutes = 2* 60 + 20= 
2* 60 + 20 = 140
140 minutes   Average speed S is given by distance / time. Hence   S= 580 miles / 140 minutes = 4.83 miles / minute   = 290 miles / hour   correct answer 290 miles / hour
Answer: C
When each of the opposite sides of a square is increasedby 8cm then ratio of sides of the rectangle thus formed is 5:3. What is the area of the original square?	Choose one:  A) 123  B) 132  C) 154  D) 144  E) 175

Solution: Sol. (x+8)/x = 5/3   X = 12   Required area = 12*12= 
12*12 = 144
144   144
Answer: D