MU-NLPC/Calc-aqua_rat huggingface dataset:
Rohan spends 40% of his salary on food, 20% on house rent, 10% on entertainment and 10% on conveyance. If his savings at the end of a month are Rs. 3000. then his monthly salary is
Options:
A) Rs. 15000	B) Rs. 12000	C) Rs. 9000	D) Rs. 6000	E) Rs. 3000

Solution: Sol.   Saving = [100 - (40 + 20 + 10 + 10]% = 20%.   Let the monthly salary be Rs. x.   Then, 20% of x = 3000   â‡” 20 / 100x = 3000   â‡” x = 3000 Ã— 5 = 15000.   Rs. 15000nswer Rs. 15000
Answer: A
In a two digit number, if it is known that its units digit exceeds its ten's digit by 2 and that the product of the given number and the sum of its digits is equal to 144, then the number is	Pick:
A) 42
B) 46
C) 22
D) 24
E) None

Solution: Sol.   Let the ten's digit be x.   Then, units digit = x + 2.   Number = 10x + (x+2) = 11x + 2;   Sum of digits = x + (x+2) = 2x +2.   ∴ (11x +2)(2x+2) + ( +2)= 
+ ( +2) = 2
2x +2.   ∴ (11x +2)(2x+2)= 144   ⇔ 22x2 + 26x - 140 = 0   ⇔ 11x2 + 13x - 70 = 0   ⇔ (x - 2)(11x+35) = 0 ⇔ x =2.   Hence, required number = 11x + 2 = 24.   Answer 24
Answer: D
Suresh can complete a job in 15 hours. Ashutosh alone can complete the same job in 35 hours. Suresh works for 9 hours and then the remaining job is completed by Ashutosh. How many hours will it take Ashutosh to complete the remaining job alone?
Choose one:
A) 4 B) 5 C) 14 D) 12 E) None of these

Solution: The part of job that Suresh completes in 9 hours   = 9â„15 = 3â„5   Remaining job = 1 - 3â„5 = 2â„5   Remaining job can be done by Ashutosh in 2â„5 Ã— 35 = 14 hours   Answer 14
Answer: C
In how many ways can 7 boys be seated in a circular order?
Choose the correct choice from the following answers
A) 110	B) 230	C) 720	D) 420	E) 680

Solution: Number of arrangements possible   =(7−1)!=6!=6x5x4x3x2x1=720   Answer: 720
Answer: C
If y is 70 percent greater than x, then x is what percent less than y?  Choose the correct choice from the following answers
A) 41%
B) 47%
C) 55%
D) 63%
E) 70%

Solution: y = 1.7x   x = y/1.7 = 10y/17 = y - (7/17)*y   7/17 is about 41%.   The answer is 41%.
Answer: A
Find k if 56 / k = 4. Choose the most appropriate option.
A) 16
B) 17
C) 18
D) 14
E) 13

Solution: Since 56 /k = 4 and   56/ 14= 
  56/ 14 = 4
4, then   k= 14 correct answer 14
Answer: D
The circumferences of two circles are 264 meters and 352 meters. Find the difference between the areas of the larger and the smaller circles?	Choose the most appropriate option.
A) 4329
B) 2799
C) 4312
D) 2799
E) 2712

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
Answer: C
A certain sum of money at simple interest amounted Rs.840 in 10 years at 3% per annum, find the sum?  Pick: A) 277 B) 262 C) 298 D) 646 E) 267

Solution: 840 = P [1 + (10*3)/100]   P = 646   Answer: 646
Answer: D
Find the least number must be subtracted from 62575 so that remaining number is divisible by 99. Choose the correct choice from the following options
A) 93	B) 7	C) 54	D) 9	E) 6

Solution: On dividing 62571 by 99 we get the remainder 7, so 7 should be subtracted. Answer is   7
Answer: B
A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 18 km/hr. What is the length of the platform?  Answers
A) 80	B) 240	C) 288	D) 277	E) 221

Solution: Speed = 18 * 5/18= 
18 * 5/18 = 5
5 m/sec.   Length of the train=5 * 20= 
5 * 20 = 100
100 m.   Let the length of the platform be x m . Then,   (x + 100)/36= 5 => x = 80 m.   80nswer: 80
Answer: A
How many ways are there to split a group of 6 girls into two groups of 3 girls each? (The order of the groups does not matter)
Choose the correct option: A) 35 B) 10 C) 40 D) 20 E) 25

Solution: the combination is 6C3 /2   = 6!/3!*3!*2 = 20/2= 
20/2 = 10
10   10
Answer: B
A certain sum amounts to Rs.1725 in 3 years and Rs.1875 in 5 years. Find the rate % per annum? Choose the correct choice from the following choices:
A) 9%	B) 5%	C) 3%	D) 1%	E) 8%

Solution: 3 --- 1725   5 --- 1875   --------------   2 --- 150   N = 1 I = 75 R = ?   P = 1725 - 225= 
1725 - 225 = 1_500
1500   75= (1500*1*R)/100   R = 5%   Answer: 5%
Answer: B
In how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together?  Pick one:
A) 120028 ways B) 120860 ways C) 120960 ways D) 120920 ways E) 120930 ways

Solution: In the word 'MATHEMATICS', we treat the vowels AEAI as one letter.   Thus, we have MTHMTCS (AEAI).   Now, we have to arrange 8 letters, out of which M occurs twice, T occurs twice and the rest are different.   Number of ways of arranging these letters =	8!/(2!)(2!)	= 10080.   Now, AEAI has 4 letters in which A occurs 2 times and the rest are different.   Number of ways of arranging these letters =	4!/2!	= 12.   Required number of words = (10080 x 12) = 120960.   Answer:120960 ways
Answer: C
The probability that A speaks truth is 3/5 and that of B speaking truth is 4/7. What is the probability that they agree in stating the same fact?  Choose the correct option.
A) 18/35  B) 18/37  C) 18/39  D) 18/33  E) 18/31

Solution: If both agree stating the same fact, either both of them speak truth of both speak false.   Probability = 3/5 * 4/7 + 2/5 * 3/7   = 12/35 + 6/35   = 18/35   18/35nswer:18/35
Answer: A
The L.C.M of two numbers is 2310 and their H.C.F is 30. If one number is 330 the Other is  Pick:
A) 330 B) 300 C) 210 D) 250 E) 350

Solution: The other number   = L.210.M * H.210.F/given number   = 2310*30/330= 
2310*30/330 = 210
210   Answer is 210.
Answer: C
A certain car uses one gallon of gasoline every 36 miles when it travels on highway, and one gallon of gasoline every 20 miles when it travels in the city. When a car travels 4 miles on highway and 4 additional miles in the city, it uses what percent more gasoline than if it travels 8 miles on the highway? Choose one:
A) 15%  B) 20%  C) 22.5%  D) 25%  E) 40%

Solution: 4 miles on the highway = 4/36 gallons;   4 miles in the city = 4/20 gallons;   Total = 4/36 + 4/20 = 14/45 gallons.   8 miles on the highway = 8/30 gallons .   The % change = (14/45 - 8/36)/(8/36) = 0.40.   Answer: 40%.
Answer: E
If the selling price of 50 articles is equal to the cost price of 40 articles, then the loss or gain percent is:
Choose one.
A) 20% loss
B) 20% gain
C) 25% loss
D) 25% gain
E) 35% gain

Solution: Let C.P. of each article be Re. 1.   Then, C.P. of 50 articles = Rs. 50;   S.P. of 50 articles = Rs. 40.   Loss % = 10/50 * 100= 
10/50 * 100 = 20
20%   20% lossNSWER:20% loss
Answer: A
The set X consists of the following terms: {4,44,444,4444,.....}, where the nth term has n 4's in it for example 10th term is 4444444444. What is the hundreds digit of the sum of the first 35 terms of set X?	Select the correct option:
A) 1 B) 3 C) 5 D) 7 E) 9

Solution: 35*4 + 34*40 + 33*400 = 140 + 1360 + 13200= 
140 + 1360 + 13200 = 14_700
14700   The hundreds digit is 7.   The answer is 7.
Answer: D
If log10 5 + log10 (5x + 1) = log10 (x + 5) + 1, then x is equal to:
Choose the correct option: A) 15 B) 8 C) 9 D) 3 E) 10

Solution: Explanation:   log10 5 + log10 (5x + 1) = log10 (x + 5) + 1   log10 5 + log10 (5x + 1) = log10 (x + 5) + log10 10   log10 [5 (5x + 1)] = log10 [10(x + 5)]   5(5x + 1) = 10(x + 5)   5x + 1 = 2x + 10   3x = 9   x = 3.   answer 3
Answer: D
One water pump can fill half of a certain empty tank in 6 hours. Another pump can fill half of the same tank in 6.5 hours. Working together, how long will it take these two pumps to fill the entire tank?	Pick
A) 6 7/13 B) 1 5/8 C) 3 1/4 D) 6 6/25 E) 3 1/2

Solution: One pump can fill a tank in 6 hours and another in 6.5 hours   so the rate at which both can half fill the tank is (1/6+1/6.5) => 25/78   Thus half of the tank can be filled in 78/25   so for filling the complete tank => 78/25*2 = 156/25 = 6 6/25   ANSWER:6 6/25
Answer: D
Annika hikes at a constant rate of 10 minutes per kilometer. She has hiked 2.5 kilometers east from the start of a hiking trail when she realizes that she has to be back at the start of the trail in 35 minutes. If Annika continues east, then turns around and retraces her path to reach the start of the trail in exactly 35 minutes, for how many kilometers total did she hike east?	Choose the correct choice:
A) 3.625  B) 3.5  C) 3  D) 4  E) 4.5

Solution: Set up two R x T =D cases.   1. 1/10 km/ min x T = 2.5   from which T= 25 mins.   We know total journey time now is  35 +25= 
 35 +25 = 60
60   The rate is the same ie 1/10km/min.   set up second R x T=D case.   1/10 km/min x 60 = 6 km   Now the total journey would be halved as distance would be same in each direction. 6/2 =3   3
Answer: C
A and B invested in a business in the ratio 7 : 11, in the annual profit they donated 10% of the profit to a charity, and after donating, A received Rs.12600 as his share in the profit, then what amount is donated to the charity ? Choose the correct choice.
A) Rs.2500
B) Rs.1800
C) Rs.3600
D) Rs.1260
E) Rs.1860

Solution: Ratio of investments of A and B = 7 : 11 = [18 units].   A received = Rs.12600.   Total profit = 12600 / 7 × 18 = Rs.324000.   Profit after donation = Rs.32400 which is [Profit – 10% = 90% of the actual profit].   Profit before donation = 32400 / 90 × 100 = Rs.36000.   Actual profit = Rs.360000 => Donation = Rs.36000 × 10 / 100 = Rs.3600   Option Rs.3600
Answer: C
In a group of 150 readers who read science fiction or literacy works or both, 120 read science fiction and 90 read literacy works. How many read both science fiction and literacy works?
Choose the most appropriate option
A) 70  B) 60  C) 90  D) 100  E) 110

Solution: Consider total number of reader n(S U L) = 150   People who read science fiction n(S) = 120   People who read literacy works n(L) = 90   both science fiction and literacy n(S âˆ© L) = ?   n(S U L) = n(S)+ n(L) - n(S âˆ© L)   150 = 120 + 90- n(S âˆ© L)   n(S âˆ© L) = 210 -150   n(S âˆ© L) = 60   SO People read both science fiction and literacy works are 160   ANSWER:60
Answer: B
5 men are equal to as many women as are equal to 8 boys. All of them earn Rs.150 only. Menâ€™s wages are? Options
A) 6Rs B) 2Rs C) 4Rs D) 9Rs E) 10Rs

Solution: 5M = xW = 8B   5M + xW + 8B ----- 150 Rs.   5M + 5M + 5M ----- 150 Rs.   15M ------ 150 Rs. => 1M = 10Rs.   Answer: 10Rs
Answer: E
A wholesaler marks his wares 60% more than the real price and allows 25% discount. His profit is: Pick:
A) 15%
B) 20%
C) 25%
D) 30%
E) None of these

Solution: Let the CP = 100 Rs.   Mark Price = 160   Discount = 25%   Selling price 75/100 Ã— 160   Hence profit = 20%   Answer: 20%.
Answer: B
The principal that amounts to Rs. 5913 in 3 years at 6 1/4 % per annum C.I. compounded annually, is?
Answers:	A) s. 3096	B) s. 4076	C) s. 4085	D) s. 4096	E) s. 5096

Solution: Principal = [4913 / (1 + 25/(4 * 100))3]   = 5913 * 16/17 * 16/17 * 16/17 = Rs. 5096.   ANSWs. 5096R:s. 5096
Answer: E
Find the value of (75983*75983- 45983*45983/30000)
Choose the correct choice from the following.
A) 129166 B) 121696 C) 126196 D) 121966 E) None of them

Solution: Given expression=(75983)2-(45983)2/(75983-45983)   =(a-b)2/(a-b)   =(a+b)(a-b)/(a-b)   =(a+b)   =75983+45983= 
75983+45983 = 121_966
121966   Answer is 121966.
Answer: D
what is the radius of a circle that has a circumference of 3.14 meters?	Pick one:  A) 0.5 mtr  B) 1.5 mtr  C) 2.3 mtr  D) 0.2 mtr  E) 1.2 mtr

Solution: circumference of a cirlce = 2nr, given circumference= 3.14 mtr.   2nr= 3.14, 2 x 3.14 x r= 3.14, = 6.28 x r=3.14, r= 3.14/6.28, = 0.5mtr. correct answer: (0.5 mtr)
Answer: A
A watch was sold at a loss of 5%. If it was sold for Rs.500 more, there would have been a gain of 5%. What is the cost price?  Select:	A) 1000	B) 2998	C) 2778	D) 2788	E) 2991

Solution: 95%   105%   --------   10% ---- 500   100% ---- ? => Rs.5000   Answer:2788
Answer: D
Marketing executives for a certain chewing gum company projected a 20 percent increase in revenue this year over that of last year, but revenue this year actually decreased by 35%. What percent of the projected revenue was the actual revenue ?	Choose one
A) 54.2% B) 58% C) 62.5% D) 64% E) 75%

Solution: Last year revenue = 100 (assume);   This year revenue = 65;   Projected revenue = 120.   Actual/Projected*100=65/120*100 = 54.2%.   54.2%nswer: 54.2%.
Answer: A
A windmill is taking advantage of strong air currents in order to produce electrical energy. On a typical day the wind speed is around 20 mph and in that speed the windmill produces 400 kw/h (kilowatts per hour). On a stormy day a windmill produces 20% more energy. How much kw/h can three windmills produce in two hours on a stormy day? Choose the correct choice from the following options.
A) 2880. B) 4860. C) 5780. D) 5760. E) 6380.

Solution: Efficiency per machine = 400 watt/hr   Efficiency due to increase in wind speed = 400*120% => 480 watt/hr   Production by each machine in 2 hours is  480*2= 
 480*2 = 960
> 960 watt   Production by 3 machines=> 960 watt * 3 = 2880 watt   2880.nswer will be (2880.)
Answer: A
There are k-2 members in a certain band, including Jim and Ellen. Two members are to be selected to attend the Grammy awards ceremony. If there are 3 possible combinations in which Jim and Ellen are not selected, what is the value of k?  Choose the correct choice:
A) 6  B) 7  C) 8  D) 9  E) 10

Solution: There are k-2 members in the band, and k-4 members without Jim and Ellen.   (k-4)C2 = 3   (k-4)(k-5)/2 = 3   (k-4)(k-5) = 6 = 3*2   k = 7   The answer is 7.
Answer: B
Two cars cover the same distance at the speed of 60 and 64 kmps respectively. Find the distance traveled by them if the slower car takes 1 hour more than the faster car.
Pick
A) 398	B) 88	C) 960	D) 781	E) 2891

Solution: 60(x + 1) = 64x   X = 15   60 * 16= 
60 * 16 = 960
960 km.Answer:960
Answer: C
A sum of money at simple interest amounts to Rs. 805 in 3 years and to Rs. 854 in 4 years. The sum is:	Choose the correct choice from the following:	A) s. 650	B) s. 690	C) s. 688	D) s. 700	E) s. 718

Solution: S.I. for 1 year = Rs. (854 - 815) = Rs. 39.   S.I. for 3 years = Rs.(39 x 3) = Rs. 117.   Principal = Rs. (805 - 117) = Rs. 688.   Answer: Option s. 688
Answer: C
Aaron will jog from home at 2 miles per hour and then walk back home by the same route at 4miles per hour. How many miles from home can Aaron jog so that he spends a total of 3 hours jogging and walking?  Choose the correct choice from the following answers:
A) 5
B) 7
C) 3
D) 9
E) 10

Solution: xyt/(x+y)   x= 2, y=4 t= 3   2*4*3/2+4 = 18/6= 
18/6 = 3
3   Answer : 3
Answer: C
There are 7 points marked on the circumference of a circle. How many hexagons can be formed by connecting 6 points of the 7 points?  Choices.
A) 5
B) 6
C) 7
D) 8
E) 9

Solution: 776=7   The answer is 7.
Answer: C
The numerator of a certain fraction is 8 less than the denominator. If 3 is added to the numerator and 3 is subtracted from the denominator, the fraction becomes 3/4. Find the original fraction?
Choose the most appropriate option:
A) 2/5  B) 7/9  C) 3/11  D) 8/5  E) 9/5

Solution: The denominator be P, the numerator will be (P - 8).   The fraction will be (P - 8)/P.   Adding 3 to the numerator and subtracting 3 from the denominator, (P - 8 + 3)/(P - 3) = 3/4.   (P - 5)/(P - 3) = 3/4   P = 20 - 9 => P = 11.   The fraction is: 3/11.   ANSWER:3/11
Answer: C
A number whose fifth part increased by 5 is equal to its fourth part diminished by 5 is ?	Choose the correct choice from the following answers
A) 160	B) 180	C) 200	D) 220	E) None

Solution: Answer   Let the number be N.   Then, (N/5) + 5 = (N/4) - 5   ⇒ (N/4) - (N/5) = 10   ⇒ (5N - 4N)/20 = 10   ∴ N = 200   Option: 200
Answer: C
If x is a positive number and 5 the square root of x is equal to x/25, then x = Pick
A) 10
B) 25
C) 5
D) 2
E) 1

Solution: 5 of sqrt(x) = x/25, which means that sqrt(x) = x/5   or x = x^2/25 -> divide by x   1=x/25   x=25   25.
Answer: B
If x is a number such that x^2 + 2x - 24 = 0 and x^2 - 5x + 4 = 0, then x =
Select.
A) 4 B) -4 C) -3 D) -6 E) 1

Solution: x^2 + 2x - 24 = (x+6)(x-4) = 0   Then x=-6 or x=4.   x^2 - 5x + 4 = (x-4)(x-1) = 0   Then x=4 or x=1.   Thus x=4.   The answer is 4.
Answer: A
In a camp, there is a meal for 80 men or 200 children. If 150 children have taken the meal, how many
men will be catered to with the remaining meal ?	Choose the correct choice:
A) 38 men  B) 32 men  C) 34 men  D) 20 men  E) None of these

Solution: Explanation:   There is meal for 200 children. 150 children have taken the meal.   Remaining meal is to be catered to 50 children.   Now, 200 children =80 men   So, 50 Children = 80/200 * 50= 
80/200 * 50 = 20
20 men   Answer: 20 men
Answer: D
Raju purchased an item for Rs.4,500 and sold it at the gain of 15%. From that amount he purchased another item and sold it at the loss of 10%. What is his overall gain/loss?	Choices:	A) Gain of Rs.151.50	B) Gain of Rs.157.50	C) Loss of Rs.165	D) neither gain nor loss	E) None of these

Solution: Explanation:   1st SP = Rs.4500 + 15% of 4500 = Rs.4500+Rs.675 = Rs.5175   2nd CP = Rs.5175.   SP = Rs.5175 – 10% of 5175 = Rs.4657.50   Overall gain = Rs.4657.50 – 4500 = Rs.157.50   Answer: Option Gain of Rs.157.50
Answer: B
Find the compound ratio of (3:2), (4:3) and (1:4) is
Choose the correct choice from the following choices:
A) 1:2
B) 2:3
C) 3:4
D) 4:5
E) 3:2

Solution: Required ratio = 3/2 * 4/3 * 1/4 = 1/2 = 1:2   1:2nswer is 1:2
Answer: A
A(5, w^3) is the (x, y) coordinate of point located on the parabola Y = X^2 + 2. What is the value of w?  Pick:
A) 3. B) 4. C) 5. D) 6. E) 9

Solution: Y = X^2 + 2   X= 5   Y = 5^2+2= 27   Y is in the form w^3   w^3=27   w=3   3.NSWER:3.
Answer: A
A 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 18 sec. What is the length of the platform?
Choose the correct choice from the following answers.
A) 22  B) 350  C) 268  D) 277  E) 198

Solution: Speed = 300/18 = 50/3 m/sec.   Let the length of the platform be x meters.   Then, (x + 300)/39 = 50/3   3x + 900 = 1950 => x = 350 m.   Answer:350
Answer: B
Cindy has her eye on a sundress but thinks it is too expensive. It goes on sale for 15% less than the original price. Before Cindy can buy the dress, however, the store raises the new price by 25%. If the dress cost $85 after it went on sale for 15% off, what is the difference between the original price and the final price?  Choose the correct choice from the following choices.
A) $0.00	B) $1.00	C) $3.40	D) $5.00	E) $6.25

Solution: 0.85*{Original Price} = $85 --> {Original Price} = $100.   {Final Price} = $85*1.25 = $106.25.   The difference = $106.25 - $100 = $6.25.   Answer: $6.25.
Answer: E
A table is bought for Rs.600/- and sold at a loss of 15% find its selling price	Choose the correct choice from the following options:	A) s.500/-	B) s.530/-	C) s.540/-	D) s.510/-	E) s.700/-

Solution: 100 % ------> 600 (100 * 6 = 600)   85 % ------> 510 (85 * 6 = 510)   Selling price = Rs.510/-   s.510/-
Answer: D
A card is drawn from pack of 52 cards, two cards are drawn together at random. What is the probability of getting a queen of club or king of heart?	Select.
A) 2/15
B) 7/12
C) 6/13
D) 1/6
E) 1/26

Solution: n(S) = 52   n(1/26) = 2   P(1/26) = 2/52 = 1/26   Answer is 1/26
Answer: E
A two digit number when 18 added becomes another two digit number with reversed digits. How many such two digit numbers are possible?
Select:
A) 8	B) 7	C) 1	D) 9	E) 0

Solution: Let the two digit number be 'ab' and the number formed after adding 18 to it is 'ba'   So ab + 18 = ba   ⇒⇒ (10a + b) + 18 = 10b + a   ⇒⇒ 18 = 9b – 9a   ⇒⇒ 2 = b – a   So we know that ab, ba both are two digit numbers so a, b ≠≠ 0.   Also when b = 9, a = 7; b = 8, a = 6; b = 7, a = 5; b = 6, a = 4; b = 5, a = 3; b = 4, a = 2; b = 3, a = 1   Answer:1
Answer: C
Nr Books bought Nr of People
5 3
6 3
7 7
8 2
9 8
What is the median of books bought per person? Choose the correct choice from the following answers: A) a) 2 B) b) 4 C) c) 7 D) d) 8 E) e) 18

Solution: 5, 5, 5, 6, 6, 6, 7, 7, 7, 7,7 ,7, 7, 8, 8, 9, 9, 9,... (8 times)   so you will observer that the median of the list is 7.   Ans c) 7
Answer: C
What will be the fraction of 20% Select.
A) 1/4	B) 1/5	C) 1/10	D) 1/8	E) None of above

Solution: Explanation:   It will 20*1/100 = 1/5   Answer: Option 1/5
Answer: B
The difference between a number and its two-fifth is 45. What is the number?
Choose the correct choice from the following options:
A) 64 B) 75 C) 80 D) 89 E) 78

Solution: Explanation:   Let the number be x.   x – (2 / 5) x = 45   (3/5) x = 45   x = 75   ANSWER:75
Answer: B
When x is multiplied by 3, the result is 4 more than the result of subtracting x from 16. What is the value of x?	Choose the correct choice from the following answers:
A) -4
B) -2
C) 5
D) 13
E) 22

Solution: The equation that can be formed is:   3x-4=16-x   or, 4x=20   or, x=5.   Answer : 5
Answer: C
On Monday morning, Chris receives tickets to a baseball game that will be played at 7pm on the next evening that it does not rain. However, Chris is only in town until Wednesday morning, at which point he must fly to another city. If there is a 10% chance of rain each of the next two evenings, what is the probability that Chris will be able to attend the game?
Choose the most appropriate option
A) 36%  B) 60%  C) 66%  D) 80%  E) 99%

Solution: Chris won't be able to attend the game if it be raining on Monday eveningandTuesday evening. The probability of that is 0.1*0.1 = 0.01. So, the probability that he will be able to attend is 1 - 0.01 = 0.99.   Answer: 99%.
Answer: E
A password of a computer used four digits where they are from 0 and 9. What is the probability that the password only consists of even numbers?
Choices
A) 1/4
B) 1/16
C) 1/32
D) 1/400
E) 1/800

Solution: There are five possibilities out of ten that the each digit is even, so the overall probability is 1/2 * 1/2 * 1/2 * 1/2 (answer 1/16)
Answer: B
In a certain alphabet, 10 letters contain a dot and a straight line. 24 letters contain a straight line but do not contain a dot. If that alphabet has 40 letters, all of which contain either a dot or a straight line or both, how many letters contain a dot but do not contain a straight line? Choose the correct option
A) 6 B) 8 C) 14 D) 20 E) 28

Solution: We are told that all of the letters contain either a dot or a straight line or both, which implies that there are no letters without a dot and a line (no line/no dot box = 0).   First we find the total # of letters with lines:  10+24= 
 10+24 = 34
34;   Next, we find the total # of letters without line:  40 - 34= 
 40 - 34 = 6
6;   Finally, we find the # of letters that contain a dot but do not contain a straight line: 6 - 0= 
6 - 0 = 6
6.   6
Answer: A
A train 800 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is? Choose the correct answer
A) 298 m  B) 279 m  C) 500 m  D) 289 m  E) 287 m

Solution: Speed = 78 * 5/18 = 65/3 m/sec.   Time = 1 min = 60 sec.   Let the length of the train be x meters.   Then, (800 + x)/60 = 65/3   x = 500 m.   Answer: 500 m
Answer: C
John had a stock of 1100 books in his bookshop. He sold 75 on Monday, 50 on Tuesday, 64 on Wednesday, 78 on Thursday and 135 on Friday. What percentage of the books were not sold? Options.
A) 50.4% B) 63.4% C) 66.5% D) 34.9% E) 43.5%

Solution: Let N be the total number of books sold. Hence   N = 75 + 50 + 64 + 78 + 135= 
75 + 50 + 64 + 78 + 135 = 402
402   Let M be the books NOT sold   M= 1100 - N = 1100 - 402= 
1100 - 402 = 698
698   Percentage   63.4%ooks not sold / total number of books= 698/1100 = 0.634 = 63.4%   correct answer 63.4%
Answer: B
If 22^n is a divisor of 97!+98! ,what is the maximum possible value of integer n?	Choices:
A) 8 B) 9 C) 10 D) 11 E) 12

Solution: 22^n means power of 11 as 2 would surely have more power than 11 in a factorial..   97!+98!=97!(1+98)=97!*99....   99 will have ONE 11 and 97! will have 97/11 or 8..   Total 1+8= 
1+8 = 9
9   ANSWER:9
Answer: B
If a number 105 divides into n with no remainder, which of the following must be a factor of n?  Pick:
A) 2 B) 4 C) 6 D) 7 E) 11

Solution: 105 / n = k (with k an integer)   (7)(5)(3) / n = k   n must have a 7 in his prime factorization to divide 105 without remainder.   answer 7
Answer: D