MU-NLPC/Calc-aqua_rat huggingface dataset:
The number of arrangements that can be made with the letters of the word MEAD so that the vowels occupy the even places?
Choose the correct choice from the following answers:
A) 6  B) 5  C) 4  D) 10  E) 21

Solution: The word MEADOWS has 7 letters of which 3 are vowels.   -V-V-V-   As the vowels have to occupy even places, they can be arranged in the 2 even places in 2! i.e., 2 ways. While the consonants can be arranged among themselves in the remaining 2 places in 2! i.e., 2 ways.   Hence the total ways are  2 * 2= 
 2 * 2 = 4
4.   Answer:4
Answer: C
The interest on Rs.750 for 2yrs is the same as the True Discount on Rs.960 due 2yrs hence . If the rate of interest is same in both cases,it is:  Choose the correct choice
A) 12%	B) 14%	C) 15%	D) 16%	E) 26%

Solution: Explanation:   S.I on Rs.750= T.D on Rs. 960   This means P.W of Rs. 960 due 2 years hence is Rs.750   Therefore , T.D= Rs. (960 - 750) = Rs. 210   Thus, S.I on Rs. 750 for 2 years is Rs. 210   ∴Rate=[100×210/750×2]% = 14%   Answer: 14%
Answer: B
What is the SI on Rs.8000 from August 6th to Dec 30th at 5% per annum rate of interest?  Options.
A) Rs 100  B) Rs 120  C) Rs 140  D) Rs 160  E) Rs 200

Solution: Number of days from August 6th to Rs 160ecember 30th = 146 days ( we don’t count the given day)   Simple Interest=   PTR   100   = 8000 x   146   365   x   5   100   = Rs 160   Rs 160
Answer: D
Replace the ? by the correct Mathematics symbol to make the expression true
10 ? 10 ? 4 ? 7 = 18  Choose one
A) 10 ÷ 10 x 4 - 7 = 18
B) 10 x 10 ÷ 4 - 7 = 18
C) 10 + 10 ÷ 4 + 7 = 18
D) 10 x 10 + 4 - 7 = 18
E) 10 x 10 ÷ 4 + 7 = 18

Solution: Answer : 10 x 10 ÷ 4 - 7 = 18
Answer: B
Tanks M and B are each in the shape of a right circular cylinder. The interior of tank M has a height of 10 meters and a circumference of 8 meters, and the interior of tank B has a height of 8 meters and a circumference of 10 meters. The capacity of tank M is what percent of the capacity of tank B?
Choose the correct choice from the following choices:
A) 75%
B) 80%
C) 100%
D) 120%
E) 125%

Solution: B.   For M, r=8/2pi. Its capacity = (4pi)^2 * 10= 160pi   For B, r=10/pi. Its capacity = (5pi)^2 *8 = 200pi   M/80% = 160pi/200pi = 0.8160  /200= 
160  /200 = 4/5 = around 0.8
0.8
Answer: B
Lloyd normally works 7.5 hours per day and earns $3.50 per hour. For each hour he works in excess of 7.5 hours on a given day, he is paid 1.5 times his regular rate. If Lloyd works 10.5 hours on a given day, how much does he earn for that day?	Choose the correct choice from the following options:
A) $33.75
B) $42.00
C) $51.75
D) $54.00
E) $70.00

Solution: Daily working hour*Regular Rate + Overtime*Increased Rate     7.5*3.5+ 3*3.5*1.5= 
  7.5*3.5+ 3*3.5*1.5 = 42
42   Answer $42.00
Answer: B
To create paint with a certain shade of gray, one must combine 1.5 liters of black paint with every one liter of white paint. Approximately how many liters of white paint must be combined with 350 liters of black paint to create the certain shade of gray?
Answers:
A) 273.6 B) 233.3 C) 347.1 D) 694.4 E) 705.6

Solution: Since the ratio of Black to White is 1.5 to 1 this implies that Amount of Black is going to be more than (approximately double) the amount of White. This implies Option C, D and E can not be correct.   Now between A and B:   Black:White = 1.5:1 Since the ratio is more than double, the amount of White Paint should be less than half of Black Paint. A is more than half so can not be the answer, B fits the criteria hence should be the correct answer. No calculation needed whatsoever.
Answer: B
Find the simple interest on Rs.300 for 9 months at 6 paisa per month?	Choose one
A) 142
B) 152
C) 162
D) 172
E) 182

Solution: I = (300*9*6)/100= 
(300*9*6)/100 = 162
162   ANSWER:162
Answer: C
In one can of mixed nuts, 25% is peanuts. In another can of mixed nuts that is one-half the size of the first one, 40% is peanuts. If both cans are emptied into the same bowl, what percentage of the mixed nuts in the bowl is peanuts?	Options.
A) 16 2/3%
B) 30%
C) 25%
D) 33 1/3%
E) 35%

Solution: Can 1: size 1; 25% nuts   Can 2: size 0.5 and 40% nuts   (1x0.25+0.5x0.4)/1.5=30   30%
Answer: B
The median annual household income in a certain community of 21 households is $50,000. If the mean R income of a household increases by 10% per year over the next 2 years, what will the median income in the community be in 2 years? Choose the correct choice
A) $50,000
B) $60,000
C) $60,500
D) $65,000
E) Cannot be determined

Solution: Answer is E, because there are different numbers in the set and we are not sure which side of the numbers in the set will be increased so the mean R is increase by 10%. It could be the case that small number of higher end incomes increased a little or many low end incomes increased - it cannot be identified.
Answer: E
Find the length of the wire required to go 15 times round a square field containing 69696 m2.  Choose the correct choice from the following options:  A) 15840  B) 15848  C) 15828  D) 27892  E) 22892

Solution: a2 = 69696 => a = 264   4a = 1056   1056 * 15= 
1056 * 15 = 15_840
15840   15840nswer:15840
Answer: A
In a panel of 10 light bulbs, the odds of any light bulb to burn out are 0.04 at any given 10 minutes. Should a light bulb burn out, the whole panel would instantly turn off. What are the odds that the panel would be turned off within the first 10 minutes after it was switched on? Pick: A) 1-0.04^10 B) 1-0.96^10 C) (1-0.96)^10 D) 0.06 E) 1-10*0.06

Solution: ans B.   Prob that light will not turned off = 0.96^10. Hence prob (turn off) = 1 - prob (not turn off).
Answer: B
A train 110 metres long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?  Choose one.
A) 4  B) 5  C) 6  D) 9  E) 8

Solution: Sol.   Speed of train relative to man = (60 + 6) km/hr = 66 km/hr   = [66 * 5/18] m/sec = [55/3] m/sec.   ∴ Time taken to pass the man = [110 * 3/55= 
110 * 3/55 = 6
6 sec.   Answer 6
Answer: C
Number of prime numbers between 40 and 70 is  Pick:
A) 4	B) 5	C) 6	D) 7	E) 9

Solution: total 7=41, 43, 47, 53, 59, 61, 67   ANSWER:7
Answer: D
The average (arithmetic mean) monthly income of four workers is $5,000. After one worker’s income increases by 25 percent the new average income is $5,200. What was the original income of the worker whose monthly income increased?
Choose the correct option.
A) $3,300 B) $3,600 C) $3,800 D) $4,200 E) $3,200

Solution: Increase in total income was 200*4= 
200*4 = 800
$800, we know that this increase was 25% (1/4th) of the workers original income, thus his/her original income was 800*4=$3,200.   Answer:$3,200
Answer: E
The radius of the two circular fields is in the ratio 3: 5 the area of the first field is what percent less than the area of the second?	Choose the correct choice from the following:
A) 22  B) 77  C) 22  D) 64  E) 28

Solution: r = 3 πr2 = 9   r = 5 πr2 = 25   25 π – 16 π   100 ---- ? => 64%.Answer:64
Answer: D
The cost price of 20 books is the same as the selling price of ’X’ books. If the profit is 28%, then the value of X is ? Choose the correct choice
A) 25 B) 13.8 C) 16 D) 15 E) 14

Solution: let S.P. of X books = Rs 100 = C.P. of 20 books   Therefore, C.P. of one book = Rs 5.6   Profit = 28 %   Therefore, S.P of one book = 7.2   S.P of X articles = 7.2 X   7.2 X = 100 => X = 13.8   ANSWER:13.8
Answer: B
During a trip, Francine traveled x percent of the total distance at an average speed of 30 miles per hour and the rest of the distance at an average speed of 70 miles per hour. In terms of x, what was Francineâ€™s average speed for the entire trip? Choose the most appropriate option.
A) (180-x)/2 B) (x+60)/4 C) 21,000/(300+4x) D) 600/(115-x) E) 12,000/(x+200)

Solution: E....   X% traveeled at 30 mph   100-X% traveeled at 70 mph   total timt taken = x/30 +(100-x)/70 = (300+4x)/210   Total distance = x+(100-x) = 100   Av speed = Tot Dis/Time Taken which is 21,000/(300+4x)
Answer: C
A pipe can fill a cistern in 66 minutes. Find the time in which 1/11 part of the cistern will be filled?	Choose the correct answer:
A) 5min
B) 2min
C) 6min
D) 1min
E) 10min

Solution: Full cistern filled in = 66 minutes   1/11 part filled in = 66*1/11= 
66*1/11 = 6
6minutes   Answer is 6min
Answer: C
Find the compound interest accrued on an amount of Rs.14,800 at 13.5% p.a at the end of two years. (Round off your answer to nearest integer)	Choose one
A) 3337	B) 2782	C) 2788	D) 4266	E) 2321

Solution: CI = 14800{ [ 1 + 13.5/100]2 - 1 }   = 14800 { [1 + 27/200]2 - 1   = 14800 { 2 + 27/200}{27/200}   = (74)[2 + 27/200](27) =   1998[2 + 27/200] = 3996 + 269.73 = Rs. 4266   Answer:4266
Answer: D
A woman saved Rs. 2.50 in buying an item on sale. If she spent Rs. 25 for the item, approximately how much percent she saved in the transaction
Choose the correct choice from the following answers.
A) 10%  B) 12%  C) 5%  D) 15%  E) 9%

Solution: Price = 25+2.50= 
25+2.50 = 27.5
27.50   savings 2.5   percentage= 2.5/27.5*100   ==> 9 %   ANSW9%R 9%
Answer: E
Two pipes can fill a tank in 10 minutes and 25 minutes. An outlet pipe can empty the tank in 45 minutes. If all the pipes are opened when the tank is empty, then how many minutes will it take to fill the tank? Choose the correct choice from the following answers: A) 30 minutes B) 17 minutes C) 7 minutes D) 10 minutes E) 12 minutes

Solution: Part of the filled by all the three pipes in one minute   = 1/10 + 1/25 - 1/45 = (45 + 18 - 10)/450 = 53/450   So, the tank becomes full in 7 minutes.   Answer: 7 minutes
Answer: C
Working together, 7 identical pumps can empty a pool in 5 hours. How many hours will it take 4 pumps to empty the same pool?
Pick one
A) 4 2/3	B) 9 1/4	C) 9 1/3	D) 8 3/4	E) 10 1/2

Solution: The answer is D   7 pumps take 5 hours. 1 Pump will take 5*7 hours . Hence 4 pumps will take (5*7)/4 = 8 75/100 = 8 3/4 hours
Answer: D
Workers at a campaign office have 2500 fliers to send out. If they send out 1/5 of them in the morning and 1/4 of the remaining ones out during the afternoon, how many are left for the next day? Choose the correct option:
A) 300	B) 800	C) 1500	D) 1200	E) 1900

Solution: (1/5)*2500= 
(1/5)*2500 = 500
500   Remaining= 2500-500= 
2500-500 = 2_000
2000   (1/4) of remaining= (1/4)*2000= 
(1/4)*2000 = 500
500   Remaining now= 2000-500= 
2000-500 = 1_500
1500   Answer: Option 1500
Answer: C
If j < y < -1, which of the following is true? Choose the correct choice from the following options:
A) j/y > jy
B) y/j > j+y
C) y/j > jy
D) y/j < j+y
E) y/j > j/y

Solution: Consider :   j= -3   y= -2   then put for every option. U'll get ans y/j > j+y.
Answer: B
12, 34, 10, 11, 12, 5, 6 ,7, 13, 14, ?, ?
Logically, what two numbers should replace the question marks? Choose the correct choice.
A) 13 and 11  B) 15 and 11  C) 19 and 11  D) 18 and 11  E) 17 and 11

Solution: B   15 and 11   1 + 2 + 3 + 4= 
1 + 2 + 3 + 4 = 10
10, then insert next two numbers 11, 12 and add digits   1 + 1 + 1 + 2= 
1 + 1 + 1 + 2 = 5
5.   Insert next two numbers 6, 7 and add digits  6 + 7= 
 6 + 7 = 13
13. Insert next two numbers 14, 15 and add digits   1 + 4 + 1 + 5= 
1 + 4 + 1 + 5 = 11
11.
Answer: B
If the original mass of an element, in grams, is a whole number and the element has decayed by exactly 91 percent in some time period, which of the following could be the final mass of that element?  Choose the correct choice from the following choices:
A) 36 grams B) 28 grams C) 29 grams D) 31 grams E) 32 grams

Solution: Let original mass be 100   The final mass of that element will be 9   So whatever option we have it will be divisible by 9   Check for the options the one that doesn't produce non terminating decimal is our answer   A. 36 grams   36/9= 
36/9 = 4
4   B. 28 grams   28/9= 3.111.....   C. 29 grams   29/9 = 3.222.......   D. 31 grams   31/9 = 3.444.....   E. 32 grams   32/9 = 3.555..   36 gramsnswer (36 grams)
Answer: A
An article was sold after a discount of 20% and therewas a gain of 20%. If the profit madeon it was Rs.6 less thanthe discount offered on it, find its SP?	Choose the correct choice from the following:
A) Rs. 68
B) Rs. 70
C) Rs. 72
D) Rs. 88
E) Rs. 98

Solution: Let CP = Rs. 100x   SP = Rs. 120x   MP = 120x/80 * 100 = Rs. 150x   D = Rs. 150x - Rs. 120x = Rs. 30x   D - P = 30x - 20x = Rs. 6, 10x = Rs. 6   120x = 120/10 * 6 = Rs. 72   Rs. 72
Answer: C
It would take one machine 6 hours to complete a large production order and another machine 5 hours to complete the same order. How many hours would it take both machines, working simultaneously at their respective constant rates, to complete the order? Select:
A) A 11/30  B) B 11/20  C) C 30/11  D) D 9/10  E) E 4/10

Solution: The rate of the first machine is 1/6 job per hour;   The rate of the second machine is 1/5 job per hour;   Thus, the combined rate of the machines is 1/6+1/5=11/30 job per hour, which means that it takes 1/(11/30)=30/11 hours both machines to do the job.   Answer: C 30/11.
Answer: C
The number of new words that can be formed by rearranging the letters of the word 'TOO' is?  Choose the correct choice from the following:
A) 1
B) 5
C) 11
D) 4
E) 2

Solution: Number of words which can be formed   = 3! - 1 = 6- 1= 
6- 1 = 5
5.   Answer:5
Answer: B
How many multiples of 2 are there between 10 and 52, 10 and 52 inclusive? Choose the correct answer:
A) 27
B) 25
C) 24
D) 21
E) 22

Solution: 2 multiples are ...10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,...,   the answer is =22   Answer is 22
Answer: E
Find the missing number in the given sequence : 2,4,6,8,10,?,14,?
Choose one.
A) 11 & 15
B) 12 & 16
C) 13 & 15
D) 12 & 18
E) 11 & 17

Solution: 2+2= 
2+2 = 4
4   4+2= 
4+2 = 6
6   6+2= 
6+2 = 8
8   8+2= 
8+2 = 10
10   10+2= 
10+2 = 12
12   12+2= 
12+2 = 14
14   14+2= 
14+2 = 16
16   ANSWER:12 & 16
Answer: B
The sum of how many terms of the series 6 + 12 + 18 + 24 + … is 1800
Choose the most appropriate option
A) 16 B) 22 C) 24 D) 18 E) 26

Solution: Let the number of terms be N.   Then, according to the formula,   => 1800 = N/2[2A+(N-1)D] , where A = First-Term, D = Common-Difference.   => 3600 = N[12 + (N-1)6]   => 3600 =N[6 + 6N]   => 6N^2 + 6N - 3600 = 0.   => 6N^2 + 150N - 144n - 3600 = 0   => 6N(N + 25)-144(N+25)   => N = -25, 24   Hence, the number of terms is 24.   ANSWER:22
Answer: B
A train 800 m long can cross an electric pole in 20 sec and then find the speed of the train? Choose the correct choice:
A) 87 Kmph
B) 97 Kmph
C) 72 Kmph
D) 144 Kmph
E) 120 Kmph

Solution: Length = Speed * time   Speed = L/T   S = 800/20= 
800/20 = 40
40 M/Sec   Speed= 40 *18/5 (To convert M/Sec in to Kmph multiply by 18/5)   Speed = 144 Kmph   Answer: 144 Kmph
Answer: D
A train 110 m long is running with a speed of 65 km/hr. In what time will it pass a man who is running at 7 km/hr in the direction opposite to that in which the train is going? Choose the correct choice from the following choices:	A) 5	B) 6	C) 4	D) 8.2	E) 5.5

Solution: Speed of train relative to man =65+7= 
65+7 = 72
72 km/hr.= 72 * 5/18= 
72 * 5/18 = 20
20 m/sec.   Time taken to pass the men= 110 * 1/20= 
110 * 1/20 = 11/2 = around 5.5
5.5 sec.   Answer: Option 5.5
Answer: E
The price of a Bicycle was increased by 50 percent. The new price was then increased by 30 percent. A single increase of what percent is equivalent to these two successive increases?	Choices:
A) 80%	B) 75%	C) 95%	D) 85%	E) 70%

Solution: consider base price - $100   25% increase = 1.50*100= 
1.50*100 = 150
$150   another 40% increase on new price= 1.3* 150= 
1.3* 150 = 195
$195   so final price of radio - $195   therefore a 95% increase   correct option - 95%
Answer: C
How long does a train 110 m long running at a speed of 72 kmph take to cross a bridge 132 m in length?	Choose the correct choice from the following answers.
A) 9.8 sec
B) 12.1 sec
C) 12.42 sec
D) 14.3 sec
E) 24.3 sec

Solution: 72 km/hr= 72*5/18 m/sec   = 20 m/sec   time= D/S = 110+132/20   = 242/20= 
242/20 = 121/10 = around 12.1
12.1 sec   ANSWER:12.1 sec
Answer: B
On the independence day, bananas were be equally distributed among the children in a school so that each child would get two bananas. On the particular day 420 children were absent and as a result each child got two extra bananas. Find the actual number of children in the school? Options:
A) 600 B) 620 C) 500 D) 520 E) 840

Solution: Let the number of children in the school be x. Since each child gets 2 bananas, total number of bananas = 2x.   2x/(x - 420) = 2 + 2(extra)   => 2x - 840 = x => x = 840.   ANSW840R:840
Answer: E
A man is 22 years older than his son. In two years, his age will be twice the age of his son. The present age of this son is  Answers: A) 21 years B) 22 years C) 20 years D) 24 years E) 26 years

Solution: Explanation:   Let's Son age is x, then Father age is x+22.   => 2(x+2) = (x+22+2)   => 2x+4 = x+24   => x = 20 years   Option 20 years
Answer: C
If U = V/W, -1 < W < 0 and 4 < V, which of the following is correct?
Choose the most appropriate option.
A) U > 4.  B) 0 < U <4.  C) -4 < U < 0.  D) U < -4.  E) U < -20.

Solution: V is +veW is -ve   Eliminate AB   For min. value max. numerator and minimize dinominator   take V=4.1U=-0.9   U=4.1/-0.9   U<-4   Ans U < -4.
Answer: D
A train 100 meters long completely crosses a 300 meters long bridge in 45 seconds. What is the speed of the train is?	Choose the correct choice from the following:	A) 32 kmph	B) 33 kmph	C) 34 kmph	D) 35 kmph	E) 36 kmph

Solution: 32 kmph   32 kmph   S = (100 + 300)/45 = 400/45 * 18/5= 
400/45 * 18/5 = 32
32
Answer: A
10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 4 children take to complete the work?  Choose one:	A) 4	B) 5	C) 7	D) 8	E) 10

Solution: 1 women's 1 day work = 1/70   1 child's 1 day work = 1/140   (5 women + 4 children)'s 1 day work   = (5/10 + 4/140) = 1/10   5 women and 4 children will complete the work in 10 days.   10
Answer: E
Ayesha's father was30 years of age when she was born while her mother was 26 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?  Pick one:  A) 2 years  B) 4 years  C) 6 years  D) 8 years  E) 9 years

Solution: Mother's age when Ayesha's brother was born = 26 years.   Father's age when Ayesha's brother was born = (30 + 4)= 
(30 + 4) = 34
34 years.   Required difference= (34 - 26)= 
(34 - 26) = 8
8 years. Answer: Option 8 years
Answer: D
Set T includes elements {8, 2, 11, x, 3, y} and has a mean of 7 and a median of 5.5. If x < y, then which of the following is the maximum possible value of x?	Choices:
A) 0
B) 1
C) 2
D) 3
E) 4

Solution: First, reach to the point of getting the equation T : x + y = 18   It should take about 20 seconds.   Then Substitute the answer choices into the equation.   I don't know what the answer choices in this case are.   But I'm sure, you would be able to eliminate at least 2 or 3 answer choices. (about 10 seconds).   Say you are left with 2 answer choices. (If you are short on time, guess One of the two and you'll have a 50% probability of getting it right.)   The Median (of 6 numbers) = 5.5. See if the AVERAGE of any two numbers among (2,3,8,11) results in the median. In this case, it does for 3 and 8. (15 seconds).   Once you know that the numbers that contribute towards Median are 3 and 8, and not x or y, then given x < y, x≤3. (about 10 seconds)=3
Answer: D
If x ¤ y = (x + y)^2 - (x - y)^2. Then √3 ¤ √3 =  Choices
A) 0 B) 5 C) 12 D) 15 E) 20

Solution: X = √3 and Y also =√3   Applying the function (√3+√3)^2 - (√3-√3)^2 = (2√3)^2 - 0 = 4 x 3 = 12.   Note: Alternative Approach is the entire function is represented as X^2 - Y^2 = (X+Y)(X-Y) which can be simplified as (x+y+x-y)(x+y-(x-y)) = (2x)(2y)=4xy. Substituting x=√3 and y = √3 you get the answer 12.   Answer 12
Answer: C
A book club rented the party room of a local restaurant to meet and discuss its current novel over dinner. The total charge, including food and service, was $800. If each member of the club paid at least $53, then what is the greatest possible number of members in the club?	Choose the correct choice from the following answers.
A) 15
B) 16
C) 17
D) 18
E) 19

Solution: 800/53=15 plus remainder.   The answer is 15.
Answer: A
A rectangular field 30 m long and 20 m broad. How much deep it should be dug so that from the earth taken out, a platform can be formed which is 8 m long, 5.5 m broad and 1.5 m high where as the earth taken out is increase by 10/5?  Choices
A) 12 cm	B) 10 cm	C) 18 cm	D) 24 cm	E) 26 cm

Solution: 30 * 20 * x = (8 * 5.5 * 1.5)/2   ANSWER:10 cm
Answer: B
What number is 60 more than two-fourth of itself?
Choices:
A) 180
B) 225
C) 288
D) 324
E) 336

Solution: 2/4x+60= x   That means 60=2/4x   x= 60*3= 
60*3 = 180
180   180 is the answer
Answer: A
The triplicate ratio of 1:6 is?  Choose the correct option: A) 1:7 B) 1:8 C) 1:3 D) 1:1 E) 1:216

Solution: 1^3: 6^3 = 1:216   Answer: 1:216
Answer: E
One-third of Rahul’s savings in National Savings Certificate is equal to one-half of his savings in Public Provident Fund. If he has Rs. 1,50,000 as total savings, how much has he saved in Public Provident Fund ?
Choose the correct option:
A) Rs. 30,000	B) Rs. 50,000	C) Rs. 60,000	D) Rs. 90,000	E) None

Solution: EXPLANATION   Let savings in N.S.C and P.P.F. be Rs. x and Rs. (150000 – x) respectively. Then,   1/3x=1/2(150000-x)   => x/3 + x/2 = 75000   => 5x/6 = 75000   => x= 75000 x 6 /5= 90000   Savings in Public Provident Fund = Rs. (150000 – 90000) = Rs. 60000   Answer Rs. 60,000
Answer: C
In Orange County one fourth of the people are gathering mushrooms and one seventh of the people are collecting apples. What can be the number of people in Orange County? Choose the correct option:
A) 56.  B) 42.  C) 85.  D) 145.  E) 252.

Solution: The number must be an integer and multiple of both 4 and 7.   Only option 56. fulfill this condition and hence is the answer.
Answer: A
Sushil got thrice as many marks in English as in Science. His total marks in English, Science and Maths are 162. If the ratio of his marks in English and Maths is 3:5, find his marks in Science?	Choose the correct choice from the following
A) 18
B) 77
C) 66
D) 55
E) 31

Solution: S:E = 1:3   E:M = 3:5   ------------   S:E:M = 3:9:15   3/27 * 162= 
3/27 * 162 = 18
18   18nswer: 18
Answer: A
A man sitting in a train which is travelling at 15 kmph observes that a goods train, travelling in opposite direction, takes 9 seconds to pass him. If the goods train is 280 m long, find its speed? Answers
A) 52 kmph. B) 62 kmph. C) 97 kmph. D) 80 kmph. E) None

Solution: Solution   Relative Speed	= (280 / 9)m/sec   = (280/9 x 18/5)   = 112 kmph.   Speed of the train	= (112 - 15)= 
(112 - 15) = 97
97 kmph.   Answer 97 kmph.
Answer: C
If (2)^n=(1/2)^2, what is the value of n?
Select the correct option
A) -2 B) -1 C) 0 D) 1 E) 2

Solution: (2)^n = (1/2)^2   = (2)^-2   n = -2 (-2nswer = -2)
Answer: A
If a is an odd integer and b is an even integer, which of the following CANNOT be true?  Pick:
A) a + b is an odd integer. B) a is a factor of b. C) b is a factor of a. D) a^b is an odd integer. E) b^a is an even integer.

Solution: a = Odd   b = Even   Checking Options:   A. a + b = odd+even = odd Hence It can be True   B. a is a factor of b. if a=3 and b=6 a may be factor of b Hence It can be True   C. b is a factor of a. and Even Number can NEVER be a factor of an ODD number Hence False hence CORRECT OPTION   D. a^b is an odd integer.   E. b^a is an even integer   Answer: Option b is a factor of a.
Answer: C