MU-NLPC/Calc-aqua_rat huggingface dataset:
A farmer is planting a row consisting of 5 unique apple trees and 4 unique orange trees. How many ways are there for the farmer to plant the trees such that no apple tree is adjacent to another apple tree and no orange tree is adjacent to another orange tree?  Options:  A) 512  B) 5760  C) 1,024  D) 1,152  E) 10,080

Solution: 2 possible arrangements are possible   AOAOAOAO   OAOAOAOA   2 unique type of trees are present consisting of 4 trees each   4 apple trees can be arranged in 4! ways   4 orange trees can be arranged in 4! ways   as 2 arrangements are possible   total arrangements = 2 *5! * 4! = 5760   correct answer option 5760
Answer: B
If -3x+4y=28 and 3x-2y=8, what is the product of x and y?	Select the correct option:  A) 264.  B) 428  C) 464.  D) 622  E) 642

Solution: Given -3x+4y=28 ---Eq 1   3x -2y =8 -- Eq 2   Sum both eqns we get 2Y = 36 => Y = 18   Sub 2Y in eq 2 => 3X - 36 = 8.   => X = 44/3   Now XY = 44/3 * 18= 
44/3 * 18 = 264
264.   Option 264. is correct answer.
Answer: A
A wheel that has 6 cogs is meshed with a larger wheel of 14 cogs. If the smaller wheel has made 56 revolutions, what will be the number of revolutions made by the larger wheel?
Select the correct option:
A) 15  B) 24  C) 21  D) 9  E) 22

Solution: Explanation:   Let the number of revolutions made by the larger wheel be x   More cogs, less revolutions (Indirect proportion)   Hence we can write as   (cogs) 6 : 14 :: x : 56   â‡’6Ã—56=14 Ã— x   â‡’x = 24   Answer: Option 24
Answer: B
A man can row upstream at 7 kmph and downstream at 10kmph.find manâ€™s rate in still water and the rate of current.
Choose the correct choice from the following answers.
A) 1.5 km/hr B) 2.5 km/hr C) 3.5 km/hr D) 4.5 km/hr E) 5.5 km/hr

Solution: Rate in still water=1/2(10+7)km/hr=8.5 km/hr.   Rate of current=1/2(10-7)km/hr=1.5 km/hr.   1.5 km/hrNSWER 1.5 km/hr
Answer: A
A ball is bought for Rs.400 and sold at a gain of 45% find its selling price?
Choose the correct choice from the following answers
A) A)Rs.480/-  B) B)Rs.580/-  C) C)Rs.500/-  D) D)Rs.520/-  E) E)Rs.540/-

Solution: 100 % ------> 400 (100 * 4 = 400)   145 % ------> 580 (120 * 4 = 580)   Selling price = Rs.580/-   Rs.580/-
Answer: B
On average, activated yeast cells divide once every 120 minutes; that is, each individual cell divides into two individual cells over that time span. Given that a certain yeast colony consisted of 300,000 cells two hours ago, approximately how many cells will be populating the colony six hours from now?  Choose the most appropriate option.
A) 77,500 B) 1,860,000 C) 2,480,000 D) 3,720,000 E) 4,800,000

Solution: 300,000 × 2 × 2×2×2 = 300,000 × 16 = 4,800,000
Answer: E
The greatest ratio out of 2:3, 5:8, 3:2, 8:9 and 8:5 is?	Choose the correct choice from the following choices:
A) 2:3  B) 3:2  C) 5:8  D) 8:5  E) 8:9

Solution: 2/3=0.666   5/8= 
5/8 = 5/8 = around 0.625
0.625   3/2= 
3/2 = 3/2 = around 1.5
1.5   8/9=0.888   8/5= 
8/5 = 8/5 = around 1.6
1.6   ANSWER:8:5
Answer: D
A thief steals at a car at 2.30 p.m. and drives it at 60 km/hr. The theft is discovered at 3 p.m. and the owner sets off in another car at 75 km/hr. When will he overtake the thief?
Choose the most appropriate option.
A) 6 p.m B) 9 p.m C) 5 p.m D) 2 p.m E) 1 p.m

Solution: :   Suppose the thief is overtaken x hrs after 2.30 p.m.   Then, distance covered by the owner in (x - 1/2) hrs.   60x = 75(x - 1/2) => x = 5/2 hrs.   So, the thief is overtaken at 5 p.m.'   Answer: 5 p.m
Answer: C
What is the sum of the different positive prime factors of 1092?	Choose the correct choice
A) 5	B) 12	C) 20	D) 25	E) 27

Solution: First, we make a prime factorization by dividing 1096 by 2 then 3, etc.   1096=2^2*3*7*13   2*2+3+7+13= 
2*2+3+7+13 = 27
27   Answer (27)
Answer: E
If 0 < x < 1 and x ≠ 0, which of the following inequalities must be true?
I. x^3 < x
II. x^2 < |x|
III. x^4 – x^5 > x^3 – x^2  Choose the correct choice from the following options: A) I only B) II only C) III only D) II and III only E) I, II, and III

Solution: Answer is D. Let's look at the statements one by one   Stmt I. x^3 < x   if 0<x<1 -1<x<0="" but="" if="" then="" x="" x^3="" x^3<="">x   So this statement is not always true   Stmt II. x^2 < |x|   Because we know that x is a number less than one but not equal to zero then x^2 will always be less than |x|.   Why? think of positive fractions (and you can think in terms of positive fractions because the inequality is in regards to |x|). Lets set x </x<1>= 1/2, then x^2 = 1/4 and 1/4<1/2   So Stmt II is always true   Stmt III. x^4 – x^5 > x^3 – x^2   This one may seem tricky but lets break it down. x^4 – x^5 > x^3 – x^2 = x^4(1-x)>x^2(x-1).   Because lets concentrate on (1-x) and (x-1). We are given that -1<x<1 (1-x)="" means="" that="" which="">0 and (x-1)<0. x^4 will always be positive and x^2 will always be positive so without doing any math we are looking at positive > negative... which is always true.   So Stmt III is always true   II only</x<1>
Answer: B
In how many M ways can the letters of the word JUPITER be arranged in a row so that the vowels appear in alphabetic order?
Choose the correct choice from the following answers.
A) 736 B) 768 C) 792 D) 840 E) 876

Solution: three letters can be arranged in 3! ways.   only one combination EIU is required.   7 letters can be arranged in 7! ways.   thus M=7!/ 3! * 1 = 840.   840
Answer: D
Find the mean proportional between 49 & 81? Choose the correct option
A) 59	B) 61	C) 63	D) 65	E) 67

Solution: Formula = √a×b   A = 49 and B = 81   √49×81 = 7 × 9 = 63   63
Answer: C
X and Y started a business investing Rs. 24,000 and Rs. 40,000 respectively. Out of a total profit of Rs. 16,000, Y’s share is :	Choose the most appropriate option
A) 8500	B) 9000	C) 9500	D) 10000	E) 10500

Solution: Ratio of their shares = 24000 : 40000 = 3 : 5.   B’s share = Rs. 16000 * 5/8   = Rs. 10000   ANSWER:10000
Answer: D
Express a speed of 90 kmph in meters per second? Choose one.
A) 25mps
B) 20 mps
C) 35 mps
D) 19 mps
E) 21 mps

Solution: 90 * 5/18= 
90 * 5/18 = 25
25 mps   25mpsnswer: 25mps
Answer: A
In the given series find the number which is wrong.
4,8,11,22,18,36,24,50 Choose one.
A) 8	B) 11	C) 18	D) 50	E) 36

Solution: Format : x and 2(x)   4 and 8   11 and 22   18 and 36   So,   24 and 48   ANSWER:50
Answer: D
The speed at which a man can row a boat in still water is 20 kmph. If he rows downstream, where the speed of current is 4 kmph, what time will he take to cover 80 metres?	Choose the correct choice from the following choices
A) 10.51  B) 11.51  C) 9.51  D) 13.51  E) 15.51

Solution: Speed of the boat downstream = 20+ 4= 
20+ 4 = 24
24 kmph= 24 * 5/18 = 6.66 m/sHence time taken to cover 70 m = 70/6.66= 10.51 seconds.10.51nswer:10.51
Answer: A
Two airplanes take off from one airfield at noon. One flies due east at 202 miles per hour while the other flies directly northeast at 283 miles per hour. Approximately how many miles apart are the airplanes at 2 p.m.?
Choose one.
A) 166
B) 332
C) 400
D) 483
E) 404

Solution: E   In two hours:   the plane flying East will be 404 miles away from airport.   the other plane will be 566 miles away from airport.   566/404 = ~1.4 = ~sqrt(2)   This means that planes formed a right isocheles triangle => sides of such triangles relate as 1:1:sqrt(2) => the planes are 404 miles apart. 404
Answer: E
A mobile battery in 1 hour charges to 20 percent.How much time (in minute) will it require more to charge to 40 percent. Answers
A) 120  B) 150  C) 175  D) 160  E) 130

Solution: 1 hr =20 percent.Thus 15 min=5 percent .Now to charge 40 percent 120 min.120nswer:120
Answer: A
A pool can be filled in 4 hours and drained in 5 hours. The valve that fills the pool was opened at 1:00 pm and some time later the drain that empties the pool was also opened. If the pool was filled by 7:00 pm and not earlier, when was the drain opened?  Choose one:
A) at 2:00 pm  B) at 2:30 pm  C) at 3:00 pm  D) at 3:45 pm  E) at 4:30 pm

Solution: The filling rate is 1/4 and the draining rate is 1/5.   The combined rate of filling and draining is 1/4 - 1/5 = 1/20.   Let x be the number of hours before the drain was opened.   x/4 + (6-x)/20 = 1   5x + 6 - x = 20   4x = 14   x = 3.5   The answer is 4:30 pm.   The answer is at 4:30 pm.
Answer: E
If the letters of the word CHASM are rearranged to form 5 letter words such that none of the word repeat and the results arranged in ascending order as in a dictionary what is the rank of the word CHASM ? Choose one
A) 32 B) 12 C) 82 D) 27 E) 17

Solution: The 5 letter word can be rearranged in 5!=120 Ways without any of the letters repeating.   The first 24 of these words will start with A.   Then the 25th word will start will CA _ _ _.   The remaining 3 letters can be rearranged in 3!=6 Ways. i.e. 6 words exist that start with CA.   The next word starts with CH and then A, i.e., CHA _ _.   The first of the words will be CHAMS. The next word will be CHASM.   Therefore, the rank of CH32SM will be   24+6+2= 
  24+6+2 = 32
32   32nswer: 32
Answer: A
The percentage profit earned by selling an article for Rs. 1920 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make 25% profit?
Answers
A) Rs. 500  B) Rs.2000  C) Rs.1000  D) Rs.693  E) Rs.248

Solution: Explanation:   Let C.P. be Rs. x.   Then,1920-x/x*100=(x-1280/x)*100   1920 - x = x - 1280   2x = 3200   x = 1600   Required S.P. = 125% of Rs. 1600 = Rs(125/100*1600)=Rs.2000.   Answer:Rs.2000
Answer: B
A marketing survey of Anytown found that the ratio of trucks to sedans to motorcycles was 3:7:2, respectively. Given that there are 9,800 sedans in Anytown, how many motorcycles are there? Choose the correct choice from the following answers.
A) 2800 B) 2100 C) 3600 D) 4200 E) 5200

Solution: Let the total number of trucks = 3x   total number of sedans = 7x   total number of motorcycles = 2x   total number of sedans = 9800   => 7x = 9800   => x = 1400   total number of motorcycles =2x = 2*1400= 
2*1400 = 2_800
2800   2800nswer 2800
Answer: A
1,3,3,9,27,243,? Choose one:
A) 6565	B) 6661	C) 6861	D) 6561	E) 6531

Solution: Each number is the product of the previous two numbers, ie  27*243= 
 27*243 = 6_561
6561.   Answer : 6561
Answer: D
Two quarts containing 4⁄5 water and 2⁄5 formula are mixed with three quarts containing 7⁄10 water and 2⁄10 formula. Approximately what percent of the combined five-quart mixture is water?  Pick one
A) 50% B) 58% C) 54% D) 53% E) 52%

Solution: 4/5 of 2 quarts = 4/5 quarts of water   7/10of 3 quarts = 21/10 quarts of water    4/5= 
 4/5 = 4/5 = around 0.8
0.8   21/10= 
21/10 = 21/10 = around 2.1
2.1   Total water= 0.8 + 2.1= 
0.8 + 2.1 = 2.9
2.9   Total quarts= 5   2.9/5 = 58%   Answer : 58%
Answer: B
A certain sum is invested at simple interest at 18% p.a. for two years instead of investing at 12% p.a. for the same time period. Therefore the interest received is more by Rs. 840. Find the sum?
Select the correct option
A) 7000
B) 2787
C) 2799
D) 2699
E) 2790

Solution: Let the sum be Rs. x.   (x * 18 * 2)/100 - (x * 12 * 2)/100 = 840 => 36x/100 - 24x/100 =840   => 12x/100 = 840 => x = 7000.7000nswer:7000
Answer: A
How many of the positive factors of 42 are not factors of 56? Select
A) 1 B) 2 C) 3 D) 4 E) 5

Solution: Factors of 42 - 1,2,3,6,7,14,42   factors of 56 - 1,2,4,7,8,14,28,56   Comparing both, we have three factors of 42 which are not factors of 56 - 3,6,42 .   The answer is 3. Pls check your options again - D $ E are same.   ANSWER:3
Answer: C
A rectangular floor measures 2 by 3 meters. There are 5 white, 5 black, and 5 red parquet blocks available. Each block measures 1 by 1 meter. In how many different t colors patterns can be floor be parqueted? Select.
A) 104  B) 213  C) 3^5  D) 705  E) 726

Solution: Total number of squares we need to fill = 6   Number of colors we have t = 3   Therefore, total number of patterns = 3*3*3*3*3*3= 
3*3*3*3*3*3 = 729
729   However, this is considering that we can have a case in which all tiles are the same color. Since we are given that the quantity of each tile is 5 and the number of tiles required is 6, we know that this case cannot be possible. Therefore we must subtract the cases in which all tiles will be of the same color (3 cases since there are 3 colors).   Thus our answer should be :729 - 3= 
729 - 3 = 726
726   Answer : 726
Answer: E
The ratio between the speeds of two trains is 7 : 8. If the second train runs 400 kms in 4 hours, then the speed of the first train is:	Select the correct option.
A) 70 km/hr B) 75 km/hr C) 84 km/hr D) 87.5 km/hr E) 88.5 km/hr

Solution: Let the speed of two trains be 7x and 8x km/hr.   Then, 8x = 400/4= 
400/4 = 100
100   Let the speed of two trains be 7x and 8x km/hr.   --> x= 100/8= 
100/8 = 25/2 = around 12.5
12.5   --> Speed of first train= (7 x 12.5) km/hr = 87.5 km/hr.   Answer : 87.5 km/hr.
Answer: D
A sum of money place at compound interest doubles itself in 4 years. In how many years will it amount to eight times itself? Choose the correct choice from the following answers
A) 15 years B) 11 years C) 12 years D) 18 years E) 19 years

Solution: 100 ---- 200 ---- 4   400 ---- 4   800 ---- 4   ------   12 years   Answer: 12 years
Answer: C
The speed of a car increases by 2 km after every hour. If the distance travelled in the first hour was 35 km, what was the total distance travelled in 12 hours?
Pick:  A) 522 km  B) 456 km  C) 556 km  D) 482 km  E) None of these

Solution: This is the problem of arithmetic progression (AP) with the first term (a) = 35, common difference (d) = 2 and total no. of terms (n) = 12. The sum of this series will be total distance travelled.   Sum (Sn) = n⁄2{2a + (n - 1)d} = 12⁄2{70 + 11 × 2}   = 12×92/2=552km   Answer None of these
Answer: E
If f(x)= 5x^2- 2x+6 and g(y)= 3y-5, then g(f(x))  Choose the correct choice from the following options.
A) 82x^2-9x+38 B) 15x^2-6x+13 C) 58x^2-4x+58 D) 87x^2-5x+96 E) 98x^2-7x+94

Solution: g(f(x))=3(5x^2-2x+6)-5   =15x^2-6x+18-5   =15x^2-6x+13   the answer is 15x^2-6x+13
Answer: B
The average age of A, B and C is 27 years. If the average age of A and C is 29 years, what is the age of B in years ?	Choose the correct choice from the following options:
A) 19
B) 35
C) 20
D) 32
E) 23

Solution: Age of B = Age of (A + B + C) â€“ Age of (A + C) = 27 Ã— 3 â€“ 29 Ã— 2 = 81 â€“ 58 = 23 years   23
Answer: E
Set #1 = {A, B}
Set #2 = {K, L, M, N, O, P}
There are these two sets of letters, and you are going to pick exactly one letter from each set. What is the probability of picking at least one vowel? Choose the correct choice from the following answers:  A) 1/6  B) 1/3  C) 7/12  D) 2/3  E) 5/6

Solution: So Not a vowel in Set-1 : 1/2   And not a vowel in Ser-2:5/6   Now,   1/2∗5/6=5/12   This is for not a vowel.   Then for at least one vowel will be = 1−5/12=7/12   Answer will be 7/12.
Answer: C
If the sides of a triangle are 39 cm, 36 cm and 15 cm, what is its area?  Choose the correct choice from the following answers
A) 230 cm^2 B) 240 cm^2 C) 250 cm^2 D) 260 cm^2 E) 270 cm^2

Solution: The triangle with sides 39 cm, 36 cm and 15 cm is right angled, where the hypotenuse is 39 cm.   Area of the triangle   = 1/2 * 36 * 15= 
1/2 * 36 * 15 = 270
270 cm^2   Answer: 270 cm^2
Answer: E
The profit earned by selling an article for Rs. 832 is equal to the loss incurred when the same article is sold for Rs. 448. What should be the sale price for making 30% profit?	Choices:
A) 220	B) 230	C) 960	D) 832	E) 400

Solution: C.P. = Rs. x.   Then, 832 - x = x - 448   2x = 1280 => x = 640   Required S.P. = 130% of Rs. 640 = 130/100 * 640 = Rs. 832.   832
Answer: D
If A:B = 2:3, B:C = 4:5 and C:D = 5:9 then A:D is equal to:
Choose the correct choice from the following answers:
A) 11:17 B) 8:27 C) 5:9 D) 2:9 E) none

Solution: Solution:   A/D = (A/B)*(B*C)*(C/D)   = (2/3)*(4/5)*(5/9)   = (2*4*5)/(3*5*9)   = 8/27.   Answer: Option 8:27
Answer: B
Jim is able to sell a hand-carved statue for $670 which was a 35% profit over his cost. How much did the statue originally cost him? Pick one:
A) $496.30  B) $512.40  C) $555.40  D) $574.90  E) $588.20

Solution: 670 is the final price that is the selling price. now suppose, x is the cost price.   therefore 670 = 1.35 * x   now while doing x = 670/1.35 calculation. I saw that the answer choices begin with 5.   So i did 135 * 5= 
135 * 5 = 675
675. As 670 is less than 675. Therefore the quotient will be less than 5.   Which is only in the answer $496.30.
Answer: A
A box contains nine light out of which 4 are defective. If four light are chosen at random, find the probability that all the four light are defective?  Pick:
A) 2/113 B) 3/121 C) 1/126 D) 3/101 E) None of these

Solution: Out of nine light , five are good and four are defective.   Required probability = ⁴1/126₄/⁹1/126₄ = 1/126   1/126
Answer: C
A person jogged 10 times along the perimeter of a rectangular field at the rate of 12 kilometers per hour for 30 minutes. If field has a length that is twice its width, find the area of the field in square meters.  Choose the correct answer
A) 60.0 B) 50.0 C) 40.0 D) 30.0 E) 20.0

Solution: Let us first find the distance d jogged   distance = rate × time = (12 km / hr) × 30 minutes   = (12 km/hr) × 0.5 hr = 6 km   The distance of 6 km corresponds to 10 perimeters and therefore 1 perimeter is equal to   6 km / 10 = 0.6 km = 0.6 × 1000 meters = 600 meters   Let L and W be the length and width of the field. The length is twice the width. Hence   L = 2 W   The perimeter is 600 meters and is given by   2 (L + W) = 600   Substitute L by 2 W   2 (2 W + W) = 600   Simplify and solve for W   4 W + 2 W = 600   6 W = 600   W = 100   Find L   L = 2 W = 200   Find the area A of the rectangle   A = L * W = 200 * 100 = 20,000 square meters   correct answer is 20.0)20.000
Answer: E
Insert the missing number.
3, 5, 6,10 , 9, 15, 12, 20, 15, (....)
Options:
A) 25
B) 20
C) 10
D) 30
E) 15

Solution: Explanation:   There are two series, beginning respectively with 3 and 5. In one 3 is added and in another 5 is added.   The next number is  20 + 5= 
 20 + 5 = 25
25.   25nswer: 25) 25
Answer: A
If a fair 6-sided die is rolled three times, what is the probability that exactly one 2 is rolled? Choices
A) 25/216 B) 50/216 C) 25/72 D) 25/36 E) 5/6

Solution: Total ways in which a 6-sided die can be rolled three times = 6*6*6= 
6*6*6 = 216
216   To get exactly one 2, there are three ways:   A 2 on the first roll and non 2 on other two rolls. This can be done in 1*5*5= 
1*5*5 = 25
25 ways.   The 2 could be on the second or third roll too. So total favorable cases= 25*3= 
25*3 = 75
75   Required Probability= 75/216 = 25/72   Answer (25/72)
Answer: C
An equal number of desks and bookcases are to be placed along a library wall that is 15 meters long. Each desk is 2 meters long, and each bookshelf is 1.5 meters long. If the maximum possible number of desks and bookcases are to be placed along the wall, then the space along the wall that is left over will be how many G meters long? Choose the correct choice from the following options:
A) 0.5  B) 1  C) 1.5  D) 2  E) 3

Solution: Let x be the number of desks and bookcases that are placed along the library wall.   2x + 1.5x < 15   3.5x < 15   Since x is a non negative integer, the largest number x can be is 4.   When x is 4, the desks and bookcases take up 3.5 * 4= 
3.5 * 4 = 14
14m, leaving 1m of empty space.   Thus, I believe the answer is 1) 1
Answer: B
Find the least which when divided y 16,18,20, and 25 leaves 4 as remainder in each case, but when divided by 7 leaves no remainder. Choose one
A) 17004
B) 18000
C) 18002
D) 18004
E) 18005

Solution: Solution   L.C.M. of 16,18,20,25 = 3600. required number is of the form 3600 k + 4.   Least value of k for which (3600 k + 4 ) is divisible by 7 is k = 5.   So, Required number = (3600 × 5 + 4) = 18004. Answer 18004
Answer: D
53, 60, 56, 8, 54, 3, 8
Which of the following numbers is lower than the median but greater than the mean of the set of the numbers in the list? Pick one:
A) 18
B) 29
C) 46
D) 53
E) 55

Solution: Yes, it can be solved with observation even without approximation in 30 sec.   Just observe given numbers: 3, 8, 8, 53, 54, 56, 60   Median is very easy to tell - its 53. Now we want a number lower than 55 and greater than mean. How many numbers are lower than 53? DE are already out.   Now, we have 18, 29 and 46 and we want a number among these which is greater than mean. logically whatever be the mean, if one value out of these 5 has to be greater than mean it has to be 46. (Notice, if 18 is more than mean then 46 is also. If 28 is more than mean, 46 is also. )   Hence 46 it is!
Answer: C
Double of Quarter of 4 percent written as a decimal is :  Select
A) 0.003  B) 0.0005  C) 0.25  D) 0.02  E) None of these

Solution: Explanation :   Solution: (2)*(1/4)*4= 
(2)*(1/4)*4 = 2
2*(1/4 * 1/100)= 0.02.   Answer : 0.02
Answer: D
There are 10 points on a circle. A hexagon can be formed by linking 5 of the 10 points. How many such hexagons are possible?  Pick.
A) 60	B) 120	C) 200	D) 252	E) 600

Solution: 5 points can be selected out of 10 points in 10C5 ways   =10 !/5!*5!=252   Ans 252
Answer: D
20 throws of a die produces following results
SCORE -- NUMBER OF OCCURRENCES
---1-------------------4
---2-------------------3
---3-------------------5
---4-------------------2
---5-------------------2
---6-------------------4
What is the probability L that one more throw to this series will increase the mean score?
Choose the correct choice from the following options
A) 1/6 B) 1/3 C) 1/2 D) 2/3 E) 5/6

Solution: I get the mean as 67/20 --> 3.35. Thus in order to raise this mean we would need a 4,5,or 6.   Thus probability L is 1/2.1/2
Answer: C
A fort had provision of food for 150 men for 45 days. After 10 days, 25 men left the fort. The number of days for which the remaining food will last, is:
Select the correct option:
A) 29 1/5 B) 37 1/4 C) 42 D) 54 E) 48

Solution: After 10 days : 150 men had food for 35 days.   Suppose 125 men had food for x days.   Now, Less men, More days (Indirect Proportion)   Therefore 125 : 150 :: 35 : x <=> 125 x x = 150 x 35   => x =150 x 35/125   => x = 42.   42orrect answer is 42
Answer: C
If it is true that x< 8 and 2x> -4, which of the following must be true? Choose the correct choice.
A) -8 < x< 4
B) x> 2
C) x> -8
D) x< 4
E) None of the above

Solution: Two points:   1) x< 8   2) 2x> -4 or x> -2   From 1 and 2: -2 < x< 8   (A) is not true because x could be > 4.   (B) is not true because x could be < 2.   (C) is true because x value is always > -8.   (D) is not true because x could be >4.   (E) is not true because x> -8 is true.
Answer: C
If $ 5,000 is invested in an account that earns 10% interest compounded semi-annually, then the interest earned after one year would be how much greater than if the $ 5,000 had been invested at 8% simple yearly interest?  Choose the correct option:
A) $ 4	B) $ 8	C) $ 12	D) $ 16	E) $ 10

Solution: Solution   Amount (CI) = P+(1+r/n)^nt = 5000+(1+0.10/2)^2= 5410   Amount (SI) = P+PTR/100 = 5000+(5000*1*10/100)=5400   Difference = 5410-5400= 
5410-5400 = 10
10 $   $ 10
Answer: E
A train sets off at 2 p.m. at the speed of 70 kmph. Another train starts at 3:30 p.m. in the same direction at the rate of 85 kmph. At what time the trains will meet?	Choose the correct choice:
A) 10.39
B) 10.37
C) 10.3
D) 10.31
E) 10.32

Solution: D = 70 * 1 ½ = 105 km   RS = 85 – 70 = 15   T = 105/15= 
105/15 = 7
7 h     3.30 + 7= 
  3.30 + 7 = 10.3
10.30 p.m.Answer:10.3
Answer: C
John found that the average of 15 numbers is 40. If 14 is added to each number then the mean of number is?  Choose one.
A) 54  B) 45  C) 65  D) 78  E) 64

Solution: (x+x1+...x14)/15 = 40   54   Option 54
Answer: A
Given a spinner with four sections of equal size labeled R, B, C, and D, what is the probability of NOT getting an R after spinning the spinner two times? Choose the correct option:
A) 15/16	B) 9/16	C) 1/2	D) 1/4	E) 1/8

Solution: The probability of NOT getting an R after spinning the spinner two times is 3/4*3/4=9/16 (so getting any of the remaining 3 letters out of 4).   Answer: 9/16.
Answer: B