MU-NLPC/Calc-aqua_rat huggingface dataset:
Rajesh spends 40% of his monthly salary on food, 20% of the medicines and saves 60% of the remaining amount. If his monthly salary is Rs.15,000, how much money does he save every month ?	Choose one:
A) Rs.1000
B) Rs.2596
C) Rs.4320
D) Rs.6489
E) Rs.4789

Solution: Explanation:   Ramesh's monthly income = Rs.15,000   He spends 40% on food.   The total money spent on food = 40/100 * 15000 = Rs. 6000   Now, his monthly remaining income = Rs.15000 – Rs.6000 = Rs. 9000   Out of Rs. 9000, he spends 20% on medicines.   The total money spent on medicines = 20/100 * 9000 = Rs.1800   Now, his monthly remaining income = Rs.9000 – Rs.1800 = Rs. 7200   Out of Rs. 7200, he saves 600%.   Amount saved = 60/100 * 7200 = RS.4320   ANSWER:Rs.4320
Answer: C
There are 4 books on fairy tales, 5 novels and 3 plays. In how many ways can you arrange these so that books on fairy tales are together, novels are together and plays are together and in the order, books on fairy tales, novels and plays.  Choose one.
A) 17280
B) 1900
C) 21548
D) 36554
E) None of these

Solution: There are 4 books on fairy tales and they have to be put together. They can be arranged in 4! ways. Similarly, there are 5 novels. They can be arranged in 5! ways. And there are 3 plays. They can be arranged in 3! ways. So, by the counting principle all of them together can be arranged in 4!*5!*3!= 17280 ways   17280nswer 17280
Answer: A
A lady bought five books namely A,B,C,D,E to distribute her 2 children. How many ways she can distribute books?  Answers:  A) 3^3  B) 3^4  C) 2^5  D) 3^6  E) 3^2

Solution: 2*2*2*2*2   2^5   ANSWER:2^5
Answer: C
A man's speed with the current is 18 km/hr and the speed of the current is 3.4 km/hr. The man's speed against the current is	Choose the correct choice from the following answers: A) 9 B) 10.4 C) 11.2 D) 12.5 E) 13

Solution: Man's rate in still water = (18 - 3.4) km/hr = 14.6 km/hr.   Man's rate against the current = (14.6 - 3.4) km/hr = 11.2 km/hr.   Answer:11.2
Answer: C
A trade analyst announced 15% reduction in the unit price of bike. As a result, the sales volume went up by 15%. What was the net effect on the sales revenue?	Choose the most appropriate option:
A) no change
B) decreases by 6.5%
C) increases by 6.5%
D) increases by 5.6%
E) None of these

Solution: Explanation :   Reduction of price = (100 -15)= 
(100 -15) = 85
85%= 0.85   Increase of sale = (100+15)= 
(100+15) = 115
115%= 1.15   Total effect = 0.85 X 1.15 = 93.5%, Decreases by 6.5%   Answer :decreases by 6.5%
Answer: B
A train 350 m long is running at a speed of 68 kmph. How long does it take to pass a man who is running at 8 kmph in the same direction as the train?  Choose the correct choice from the following answers
A) 5 sec	B) 9 sec	C) 12 sec	D) 21 sec	E) 18 sec

Solution: Speed of the train relative to man = (68 - 8) kmph   = (60* 5/18) m/sec = (50/3)m/sec   Time taken by the train to cross the man   = Time taken by It to cover 350 m at 50/3 m / sec   = 350 *3/ 50= 
350 *3/ 50 = 21
21sec   Answer : 21 sec
Answer: D
An alloy of copper and zinc contains copper and zinc in the ratio 5 : 3. Another alloy of copper and zinc contains copper and zinc in the ratio 1 : 7. In what ratio should the two alloys be mixed so that the resultant alloy contains equal proportions of copper and zinc? Choose the correct choice:
A) 1 : 5  B) 7 : 3  C) 5 : 3  D) 3 : 1  E) 4 : 3

Solution: Alloy-1: Copper: Zinc = 5:3, Let Quantity = x   i.e. Copper in Alloy-1 = [5/(5+3)]*x = (5/8)x   and Zinc in Alloy-1 = [3/(5+3)]*x = (3/8)x   Alloy-2: Copper: Zinc = 1:7, Let Quantity = y   i.e. Copper in Alloy-2 = [1/(1+7)]*y = (1/8)y   and Zinc in Alloy-1 = [7/(1+7)]*y = (7/8)y   After Combining the two alloys   Copper = (5/8)x + (1/8)y   Zinc = (3/8)x + (7/8)y   Now, (5x + y)/8 = (3x + 7y)/8   i.e. 2x = 6y   i.e. x = 3y   i.e. x/y = 3/1   Answer: option 3 : 1
Answer: D
In a consumer survey, 85% of those surveyed liked at least one of three products: 1, 2, and 3. 50% of those asked liked product 1, 30% liked product 2, and 16% liked product 3. If 5% of the people in the survey liked all three of the products, what percentage of the survey participants liked more than one of the three products?	Choose the most appropriate option:  A) 6  B) 10  C) 15  D) 20  E) 25

Solution: Use the forumla ;   Total = Group1 + Group2 + Group3 - (sum of 2-group overlaps) - 2*(all three) + Neither   100 = 50 + 30 + 16 - ( sum of 2) -2(5) +15   100 = 101-( sum of 2)   1 = sum of 2   so more than 1 = 6   6
Answer: A
A sum of Rs. 125000 amounts to Rs. 17500 in 4 years at the rate of simple interest. What is the rate of interest? Pick
A) 10%	B) 4%	C) 5%	D) 6%	E) 7%

Solution: S.I. = (17500 - 12500) = Rs. 5000\   Rate = (100 * 5000) / (12500 * 4)= 
(100 * 5000) / (12500 * 4) = 10
10%   10%NSWER:10%
Answer: A
Find the compound interest on $1200 for 1year at 20% p.a. if CI is component yearly?	Options
A) $120 B) $150 C) $240 D) $250 E) $300

Solution: A = P(1 + R/100)^T   = 1200(1 + 20/100)^1   = 1200*6/5= 
1200*6/5 = 1_440
$1440   $240I= A-P = 1440-1200= 
1440-1200 = 240
$240   Answer is $240
Answer: C
If GAVE is coded as 5137 and BAT is coded as 924. How is GATE coded? Choose the correct choice from the following: A) 5147 B) 5247 C) 6584 D) 7489 E) 9487

Solution: g-5 a-1 e-7 from the code gate   t - 4 from bat   5147NSWER:5147
Answer: A
6!/(6-3)!=?  Answers:	A) 120	B) 346	C) 356	D) 366	E) 396

Solution: 6!/6-3)!=6!/3!=6*5*4= 
6*5*4 = 120
120. Hence, the correct answer is 120.
Answer: A
The monthly rent of a shop of dimension 20feet × 15feet is Rs.3600. What is the annual rent per square foot of the shop?	Choose one.
A) 43  B) 144  C) 68  D) 87  E) 92

Solution: Sol. Monthly rent per square feet = 3600/(20*15)= 
3600/(20*15) = 12
12   & Annual rent per square feet=12*12= 
12*12 = 144
144   Answer : 144
Answer: B
Diane find 3 and a half cans of paint are just enough to paint one third of her room. How many more cans of paint will she need to finish her room and paint a second room of the same size? Pick one: A) 5 B) 17 and a half C) 10 D) 12 and a half E) 15

Solution: She will need 7 cans to paint the rest of this room and 10 1/2 for the next room for a total of 17 1/2 cans.   17 and a half
Answer: B
What is the product of the prime factors of 27 and the prime factors of 121?
Choose the most appropriate option:
A) 3676	B) 3762	C) 3627	D) 3267	E) 3257

Solution: The prime factors of 27 are 3*3*3   The prime factors of 121 are 11*11   3*3*3*11*11 =27*121= 
27*121 = 3_267
3267. 3267 is the correct answer
Answer: D
A dice has one of the first 8 prime number on each its six sides ,with no two sides having the same number .the dice is rolled 10 times and the results added.the addition is most likely to be closet to  Choose the correct answer
A) 41
B) 48
C) 96
D) 90
E) 70

Solution: if die is rolled then avg score = (2+3+5+7+11+13+17+19 )/8 = 77/8   so, most likely sum for 10 times = 77/8 * 10 = 96   ANSWER:96
Answer: C
By approximately what percent is x greater than 4/5 if (4/5)(x) = 1?  Choose the most appropriate option:
A) 73%
B) 56%
C) 41%
D) 37%
E) 29%

Solution: 4/5= 80%, 5/4=125% increase by 45 percentage points 45/80=56% , hence 56%
Answer: B
The cash realised on selling a 14% stock is Rs.108.25, brokerage being 1/4% is Pick.
A) 123
B) 106
C) 108
D) 156
E) 240

Solution: Explanation:   Cash realised= Rs. (108.25 - 0.25)   = Rs. 108.   Answer: 108
Answer: C
If the number obtained on interchanging the digits of a two digit number is 18 more than the original number and the sum of the digits is 8, then what is the original number?	Choose the most appropriate option:
A) 25  B) 30  C) 35  D) 40  E) 45

Solution: Sol.   Let ten's digit = x.   Then, unit's digit = (8-x).   ∴ [10 (8-x)+x] - [10x + (8-x)] = 18   ⇔ 18x = 54   ⇔x = 3   So, ten's digit = 3 and units digit = 5.   Hence, original number = 35.   Answer 35
Answer: C
If y = q/6 + r/6^2 + s/2^5, where q, r, and r are each equal to 1 or 0, then y could be any of the values below EXCEPT:	Choose the correct answer:
A) 9/8 B) 7/32 C) 1/4 D) 5/16 E) 21/16

Solution: y = q/6 + r/6^2 + s/2^5   = q/6 + r/36 + s/32   = (36q + 6r + s ) /32   Depending on whether q, r and r take 0 or 1 :   substitute 0 or 1 for the different values of q, r and r.   Answer 5/16
Answer: D
2 men and 7 boys can do a piece of work in 14 days; 3 men and 8 boys can do the same in 11 days. Then, 8 men and 6 boys can do three times the amount of this work in	Choose the correct answer:
A) 05  B) 21  C) 51  D) 11  E) 41

Solution: (2x14)men+(7x14)boys=(3x11)men+(8x11)boys   5 men= 10 boys 1man= 2 boys   Therefore (2 men+ 7 boys) = (2 x 2 +7) boys = 11 boys   ( 8 men + 6 boys) = (8 x 2 +6) boys = 22 boys.   Let the required number of days be x.   More boys , Less days (Indirect proportion)   More work , More days (Direct proportion)   21oys 22:11 and Work 1:3=:14:x   Therefore, (22x1x)=(11x3x14)   x=462/22= 
462/22 = 21
21   Hence, the required number of days= 21   Answer is 21.
Answer: B
The circumferences of two circles are 264 meters and 352 meters. Find the difference between the areas of the larger and the smaller circles?
Choose the correct option
A) 2887 sq m	B) 6866 sq m	C) 4312 sq m	D) 9277 sq m	E) 2678 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
A train passes a man standing on the platform. If the train is 170 meters long and its speed is 72 kmph, how much time it took in doing so?	Choose the correct answer:
A) 3 1/2 sec
B) 3 5/2 sec
C) 3 7/2 sec
D) 8 1/2 sec
E) 3 1/8 sec

Solution: 8 1/2 sec = 170   S = 72 * 5/18= 
72 * 5/18 = 20
20 mps   T= 170/20 = 8 1/2 sec   Answer: 8 1/2 sec
Answer: D
How much water should be added to 13 liters of a 20%-solution of alcohol to reduce the concentration of alcohol in the solution by 75% ?	Choose the correct choice:
A) 25 liters  B) 27 liters  C) 30 liters  D) 32 liters  E) 35 liters

Solution: Let x ltr water to be added   2ltr alcohol to be represented as (20(1-3/4(new soln.=13+x)))   2=5%*(13+x)-------->x=27   Ans 27 liters
Answer: B
The equal amounts of money are deposited in two banks each at 15% per annum for 3.5 years and 5 years respectively. If the difference between their interests is Rs.144, find the each sum?  Options:
A) 299	B) 100	C) 270	D) 278	E) 213

Solution: (P*5*15)/100 - (P*3.5*15)/100 = 144   75P/100 – 52.5P/100 = 144   22.5P = 144 * 100   => P = Rs.640.Answer: 100
Answer: B
Two pipes P and Q can fill a cistern in 12 and 15 minutes respectively. Both are opened together, but at the end of 3 minutes the first is turned off. How much longer will the cistern take to fill? Choose the correct option:
A) 11 1/7
B) 11 1/4
C) 11 1/3
D) 11 1/2
E) 11 1/1

Solution: 3/12 + x/15 = 1   x= 11 1/4.Answer: 11 1/4
Answer: B
A water tank is two-fifth full. Pipe A can fill a tank in 10 minutes and pipe B can empty it in 6 minutes. If both the pipes are open, how long will it take to empty or fill the tank completely?  Pick one
A) 6 min
B) 4 min
C) 2 min
D) 5 min
E) 8 min

Solution: Clearly, pipe B is faster than pipe A and so, the tank will be emptied.   Part to be emptied = 2/5   Part emptied by (A + B) in 1 minute = (1/6 - 1/10) = 1/15   1/15 : 2/5 :: 1 : x   x = (2/5 * 1 * 15)= 
(2/5 * 1 * 15) = 6
6 min.   So, the tank will be emptied in 6 min.   6 minnswer:6 min
Answer: A
by what least number 675 be multiplied to obtain a number which is a perfect cube ?	Choose the most appropriate option
A) 5  B) 6  C) 7  D) 8  E) 9

Solution: Solution   675 = 5 * 5 * 3 * 3 *3 .   to make it a perfect cube, it must be multiplied by 5.   5nswer 5
Answer: A
A store owner estimates that the average price of type A products will increase by 30% next year and that the price of type B products will increase by 10% next year. This year, the total amount paid for type A products was $4500 and the total price paid for type B products was $8300. According to the store owner's estimate, and assuming the number of products purchased next year remains the same as that of this year, how much will be spent for both products next year?
Pick one:
A) $14,980 B) $15,325 C) $16,000 D) $16,225 E) $17,155

Solution: cost of type $14,980 products next year = 1.30 * 4500= 
1.30 * 4500 = 5_850
5850   cost of type B products next year= 1.1 * 8300= 
1.1 * 8300 = 9_130
9130   total 5850 + 9130= 
5850 + 9130 = 14_980
14980 option $14,980
Answer: A
A 4-letter code word consists of letters O, U, AND P. If the code includes all the three letters, how many such codes are possible?	Choose the correct choice.
A) 72 B) 48 C) 4 D) 84 E) 36

Solution: Note that the correct answer to this question is 36, not 72.   O-OUP can be arranged in 4!/2!=12 ways;   U-OUP can be arranged in 4!/2!=12 ways;   P-OUP can be arranged in 4!/2!=12 ways;   Total:  12+12+12= 
 12+12+12 = 36
36.   Answer: 36
Answer: E
Magnabulk Corp sells boxes holding d magnets each. The boxes are shipped in crates, each holding c boxes. What is the price charged per magnet, in cents, if Magnabulk charges m dollars for each crate?  Pick:
A) 100cd/m  B) cd/(100m)  C) 100m/(cd)  D) m/(cd)  E) cd/m

Solution: crate has = cd magnates   100m/(cd) crate cost = m dollars = 100 m cents   each magnate cost for each crate = 100 m / cd   Ans; 100m/(cd)
Answer: C
A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? Choose the correct answer.
A) 176 m  B) 240 m  C) 267 m  D) 602 m  E) 267 m

Solution: Speed = (54 * 5/18) m/sec   = 15 m/sec. Length of the train   = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/36 = 15   ==> x + 300 = 540 ==> x   = 240 m   Answer: 240 m
Answer: B
A, Band C start a business each investing Rs. 20,000. After 5 months A withdrew Rs.6000 B withdrew Rs. 4000 and C invests Rs. 6000 more. At the end of the year, a total profit of Rs. 69,900 was recorded. Find the share of each. Options.
A) 19500;22500;24500
B) 18400;21900;23100
C) 20500;21200;28200
D) 22300;19850;20600
E) None of them

Solution: Ratio of the capitals of A, Band C   = 20000 x 5 + 15000 x 7 : 20000 x 5 + 16000 x 7 : 20000 x 5 + 26000 x 7   = 205000:212000 : 282000 = 205 : 212 : 282.   A’s share = Rs. 69900 x (205/699) = Rs. 20500	I   B's share = Rs. 69900 x (212/699) = Rs. 21200;   C's share = Rs. 69900 x (282/699) = Rs. 28200.   Answer is 20500;21200;28200.
Answer: C
A car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 450 kilometers per hour. At what speed, in kilometers per hour, is the car traveling?
Choose the most appropriate option
A) 370
B) 365
C) 360
D) 380
E) 350

Solution: 360   450 * T = 1 km => T = 1/450 km/h   V*(T+2/3600) = 1   V (1/450 + 2/3600) = 1 => V = 360 km/h
Answer: C
Torry has submitted 2/5 of his homework assignments, and he received an average grade of 75 for those assignments. If he wishes to receive an average grade of 84 for all his homework assignments, the average grade for Torry's remaining homework assignments must be what percent greater than the average grade for the assignments he has already submitted? Pick
A) 15% B) 20% C) 25% D) 33 1/3% E) 40%

Solution: 0.4*75 + 0.6x = 84   30 + 0.6x=84   0.6x = 54   x= 90   90/75= 
90/75 = 6/5 = around 1.2
1.2   Ans:20%
Answer: B
Excluding stoppages, the average speed of a bus is 60 km/hr and including stoppages, the average speed of the bus is 30 km/hr. For how many minutes does the bus stop per hour?	Pick
A) 22	B) 30	C) 77	D) 20	E) 99

Solution: In 1hr, the bus covers 60 km without stoppages and 30 km with stoppages.   Stoppage time = time take to travel (60 - 30) km i.e 30 km at 60 km/hr.   stoppage time = 30/60 hrs = 30 min.   Answer: 30
Answer: B
In a stack of boards at a lumber yard, the 41th board counting from the top of the stack is immediately below the 23th board counting from the bottom of the stack. how many boards are in the stack?	Choose the correct answer:	A) 68	B) 62	C) 65	D) 64	E) 36

Solution: 1 2 3 ... 14 15 16 ...................   ..............41 40 ................. 1   So the number of boards = 41+21= 
41+21 = 62
62   Option: 62
Answer: B
A, B and C can do a work in 6, 8 and 12 days respectively doing the work together and get a payment of Rs.1800. What is B’s share?  Choose the correct choice from the following answers:  A) 600  B) 278  C) 298  D) 267  E) 127

Solution: WC = 1/6:1/8:1/12 => 4:3:2   3/9 * 1800= 
3/9 * 1800 = 600
600   600nswer:600
Answer: A
What decimal of an hour is a second ?  Choose the most appropriate option:
A) 0.0027  B) 0.00027  C) 0.027  D) 0.00072  E) None of them

Solution: Required decimal = 1/60x60 = 1/3600 = .00027   Answer is 0.00027.
Answer: B
The food in a camp lasts for 40 men for 45 days. If fifteen more men join, how many days will the food last? Choose the correct choice from the following answers
A) 80 days  B) 33 days  C) 35 days  D) 16 days  E) 15 days

Solution: one man can consume the same food in 40*45= 
40*45 = 1_800
1800 days.   15 more men join, the total number of men= 55   The number of days the food will last = 1800/55   = 33 days.   Answer:33 days
Answer: B
A sum of Rs 1162.00 is divided among A, B and C such that 4 times A’s share is equal to 5 times B’s share and 7 times C’s share. What is the share of C?	Answers.
A) 280	B) 285	C) 270	D) 295	E) 255

Solution: given 4x=5y=7z   so x:y=5:4   y:z=7:5   x:y:z=35:28:20   c share=20*1162/(35+28+20)= 
20*1162/(35+28+20) = 280
280.   280NSWER:280
Answer: A
A customer using a certain telephone calling plan pays a fee of $25 per month, and then receives a discount of 40% on the regular charge for all calls made to country A. If calls to country A are regularly charged at $1.60 per minute for the first 3 minutes, and $0.80 per minute for each minute thereafter, what is the maximum the customer could have saved over regular prices if he was charged for 1 hour of calls made to country A in a certain month?
Choose the correct choice from the following answers:
A) $8.75
B) $12
C) $13.40
D) $17.40
E) $24.40

Solution: Discount = 40% of spending   We want to maximise discount so we will need to maximise spending. We do that by assuming that 60 calls were made of 1 min each because the first minute is the most expensive.   Max discount = (40/100)* 60 * 1.6 = (40/100)*96   This would be slightly less than 40. About 38 to 39.   Saving = (Slightly less than 40) - 25 = Slightly less than 15   Answer ($13.40)
Answer: C
At what angle the hands of a clock are inclined at 15 minutes past 5 ?  Choose the correct choice.
A) 72 1⁄2°
B) 64°
C) 58 1⁄2°
D) 67 1⁄2°
E) None of these

Solution: At 15 minutes past 5, the minute hand is at 3 and hour hand slightly advanced from 5. Angle between their 3rd and 5th position.   Angle through which hour hand shifts in 15 minutes is   (15 × 1⁄2)° = 7 1⁄2°   ∴ Required angle = (60 + 71⁄2) = 67 1⁄2°   Answer 67 1⁄2°
Answer: D
The sum and the product of two numbers are 20 and 64 respectively, the difference of the number is?	Options:
A) 1  B) 6  C) 7  D) 8  E) 12

Solution: 12xplanation:   x + y = 20   xy = 64   (x- y)2 = (x + y)2 - 4xy   (x- y)2 = 400 - 256 => (x - y) = 12   Answer: 12
Answer: E
For the bake sale, 5 people brought cookies, 2 people brought pies, 6 brought brownies, and 5 people brought cakes. If each person only brought one item, how many people brought items in all? Choose the correct option.
A) 14
B) 18
C) 22
D) 23
E) 25

Solution: As each person only brought one item, you can simply add the number of items brought:  5+2+6+5= 
 5+2+6+5 = 18
18. As such, the correct answer is 18: 18.
Answer: B
In a race of length L metres, Johnson beats Lewis by U metres and Greene by V metres, By how many metres does Lewis beat Greene in the same race ? (U<V)	Choose one:
A) L(L-V) / L-U	B) L(V-U) / L-U	C) L-V	D) U-V	E) U+V

Solution: As the time is constant, the ratio of distances will be the same as the ratio of speeds.   If Sj,Sl,Sg are the speeds of Johnson, Lewis, and Greene respectively, then   Sj/Sl = L/(L-U)   and Sj/Sg = L/(L-V)   => Sg/Sl = (L-V)/(L-U)   Therefore the speeds of Lewis and Greene are in the ratio (L-U)/(L-V)   When Lewis finishes the race, the time run by him and Greene are same   => The ratio of the speeds of Lewis and Greene will be the same as the ratio of distances run by them.   => Distance run by Greene when Lewis finishes the race = (L-V)/(L-U) * L   => Lewis beats Greene by L - L*(L-V)/(L-U) = L [ 1 - (L-V)/(L-U)] = L (V-U) / (L-U)   Option (L(V-U) / L-U) is therefore correct.
Answer: B
What will be the compound interest on a sum of Rs. 28,000 after 3 years at the rate of 12% p.a.?
Choose the most appropriate option.
A) s.10123.77  B) s.10123.21  C) s.10123.20  D) s.10123.28  E) s.11337.98

Solution: Amount = [28000 * (1 + 12/100)3]   = 28000 * 28/25 * 28/25 * 28/25   = Rs. 39337.984   C.I. = (39337.984 - 28000)   = Rs. 11337.98   Answer:s.11337.98
Answer: E
There are 24 girls in hostel whose average age is decreased by 2 months, when one girl 18 yrs is replaced by a new boy.Find the age of new girl. Answers:
A) 1 year  B) 1 years 2 months  C) 2 years 5 months  D) 4 years  E) None

Solution: Total decrease = 24 * 2= 
24 * 2 = 48
48 months= 4 years   4 years
Answer: D
A student was asked to find the arithmetic mean of the numbers 3, 11, 7, 9, 15, 13, 8, 19, 17, 21, 14 and x. He found the mean to be 12. What should be the number in place of x ? Options.
A) 9
B) 7
C) 6
D) 1
E) 5

Solution: Explanation:   Clearly, we have (3 + 11 + 7 + 9 + 15 + 13 + 8 + 19 + 17 + 21 + 14 + x) / 12 = 12.   or 137 + x = 144 or x = 144 - 137= 
144 - 137 = 7
7.   Answer: 7
Answer: B
If x dollars is invested at 10 percent for one year and y dollars is invested at 8 percent for one year, the annual income from the 10 percent investment will exceed the annual income from the 8 percent investment by $56. If $2,000 is the total amount invested, how much is invested at 8 percent?
Pick: A) $280 B) $800 C) $892 D) $1,108 E) $1,200

Solution: (A) $280 ($800) $800 (C) $892 (D) $1,108 (E) $1,200   y = 2000 - x   .1x - .08(2000-x) = 56   .-160+.18x = 56   x = 1200 and y = 800   ANSWER:$800
Answer: B
In a certain book club, the members are voting between two books – a comic novel and a biography – to decide which book the group will read next. There are 3 times as many votes for the comic novel as there are votes for the biography. The ratio of biography votes to the comic votes is
Choose the correct choice from the following:
A) 1 to 2
B) 1 to 3
C) 1 to 4
D) 2 to 3
E) 3 to 4

Solution: IMO : Answer 1 to 3 1 to 3
Answer: B
A man rows his boat 120 km downstream and 60 km upstream, taking 2 hours each time. Find the speed of the stream?	Choose one
A) 6 B) 15 C) 17 D) 18 E) 2

Solution: Speed downstream = d/t = 120/(2 )= 
120/(2 ) = 60
60 kmph   Speed upstream= d/t = 60/(2)= 
60/(2) = 30
30 kmph   The speed of the stream= (60 - 30)/2= 
(60 - 30)/2 = 15
15 kmph   Answer:15
Answer: B
What is the sum of all possible solutions to the equation √2x^2−x−9 = x+1 ?	Choose the correct answer.
A) -2	B) 2	C) 3	D) 5	E) 6

Solution: First of all notice that since LHS is the square root of a number, it must be non-negative (the square root function cannot give negative result), then the RHS must also be non-negative: x+1≥0 --> x≥−1   Square the equation: 2x^2−x−9=x^2+2x+1 --> x^2−3x−10=0 --> x=-2 or x=5. Discard x=-2 because it's not >=-1. We are left with only one root: 5.   Answer: 5
Answer: D
Jayes can eat 25 marshmallows is 20 minutes. Dylan can eat 25 in one hour. In how much time will the two eat 150 marshmallows? Choose the correct choice:
A) 40 minutes.
B) 1 hour and 30 minutes.
C) 1 hour.
D) 1 hour and 40 minutes.
E) 2 hours and 15 minutes.

Solution: Rate =Output/Time   Jayes Rate=25/20=5/4   Dylan Rate=25/60=5/12   1 hour.ombined rate = 5/4+5/12= 20/12   1 hour.ombinedRate*1 hour.ombinedTime= 1 hour.ombinedOutput   20/12*t=150   t=90 mins => 1 hr 30 min
Answer: C
What positive number, when squared, is equal to the cube of the positive square root of 14?  Select.
A) 64  B) 32  C) 8  D) 4  E) 2

Solution: Let the positive number be x   x^2 = ((16)^(1/2))^3   =>x^2 = 4^3 = 4   => x =4   Answer 4
Answer: D