RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: 2^(20) + 2^(21) + 2^(22) + ... + 2^(49) + 2^(50) =
A.2^20(2^(21)-1)
B.2^20(2^(31)-1)
C.2^20(2^(28)-1)
D.2^21(2^(21)-1)
Answer: B.2^20(2^(31)-1)
Explanation: 2^(20) + 2^(21) + 2^(22) + ... + 2^(49) + 2^(50) =
2^(20)*(1+2+4+...+2^(30)) =
2^(20)*(2^(31) - 1)
The answer is B.
Question: A company bought for its 5 offices 2 computers of brand N and 3 computers of brand M. In how many ways could computers be distributed among the offices if each office can have only 1 computer.
A.1
B.10
C.25
D.29
Answer: B.10
Explanation: This problem has to do withcombinations. Here's the general idea: if you have a set of n elements, and you are going to choose r of them (r < n), then the number of combinations of size r one could choose from this total set of n is:
# of combinations = nCr = (n!)/[(r!)((n-r)!)]
where n! is the factorial symbol, which means the product of every integer from n down to 1. BTW, nCr is readn choose r.
In this problem, let's consider first the three computers of brand M. How many ways can three computer be distributed to seven offices?
# of combinations = 5C3 = 10
There are 10 different ways to distribute three computers to 7 offices. (The massive amount of cancelling that occurred there is very much typical of what happens in the nCr formula.)
One we have distributed those three M computers, we have to distribute 2 N computers to the remaining four offices. How many ways can two computer be distributed to four offices?
# of combinations = 2C2 = 1
For each of the 10 configurations of distributing the M computers, we have 1 ways of distributing the N computers to the remaining offices. Thus, the total number of configurations is 10*1 = 10. Answer choice =B
Question: A sum of Rs. 12,500 amounts to Rs. 15,500 in 4 years at the rate of simple interest .What is the rate of interest ?
A.3%
B.4%
C.5%
D.6%
Answer: D.6%
Explanation: Solution
S.I. = Rs. (15500 - 12500) = Rs. 3000.
Rate =(100x3000/12500x4) = 6 %.
Answer D
Question: Carl drove from his home to the beach at an average speed of 80 kilometers per hour and returned home by the same route at an average speed of 70 kilometers per hour. If the trip home took 1/2 hour longer than the trip to the beach, how many kilometers o did Carl drive each way?
A. 350
B. 345
C. 320
D. 280
Answer: D. 280
Explanation: Let us backsolve here.
The answer option has to be divisible by 7 to give us 1/2.
Let us try o=280 km. Time taken will be 3.5 hours and 4 hours.
Hence D is the answer.
Question: Convert 0.35 in to a vulgar fraction ?
A.18/50
B.16/50
C.7/20
D.19/50
Answer: C.7/20
Explanation: Answer
0.35 = 35/100 = 7/20
Correct Option: C
Question: A shopkeeper labeled the price of his articles so as to earn a profit of 20% on the cost price. He then sold the articles by offering a discount of 10% on the labeled price. What is the actual percent profit earned in the deal?
A.18%
B.20%
C.17%
D.19%
Answer: D.19%
Explanation: Explanation:
Let the CP of the article = Rs.100.
Then labeled price = Rs.120.
SP = Rs.120- 10% of 120 = Rs.120-13 = Rs.118.
Gain = Rs.118 â€“ Rs.100 = Rs.18
Therefore, gain/profit percent = 18%.
Answer: Option D
Question: One night 16 percent of the female officers on a police force were on duty. If 160 police officers were on duty that night and half of these were female officers, how many female officers were on the police force?
A.500
B.650
C.800
D.950
Answer: A.500
Explanation: Let x be the number of female police officers on the police force.
The number of female police officers on duty was 80.
0.16x = 80
x = 500
The answer is A.
Question: If 5% more is gained by selling an book for $ 350 than by selling it for $ 340, the cost of the book is:
A.160
B.210
C.200
D.227
Answer: C.200
Explanation: C
200
Let C.P. be $ x.
Then, 5% of x = 350 - 340 = 10
x/20 = 10 => x = 200
Question: A librarian has a set of twelve books, including four different books about Abraham Lincoln. The librarian wants to put the twelve books on a shelf with the four Lincoln books next to each other, somewhere on the shelf among the other eight books. How many different arrangements of the twelve books are possible?
A.(12!)/(4!)
B.(4!)(8!)
C.(4!)(9!)
D.(4!)(12!)
Answer: C.(4!)(9!)
Explanation: You can club the four Lincoln books as one, which leaves us with eight other books plus this one to think about. So, these nine items can be arranged in 9! ways, and since the four books can be moved around among themselves with each combination giving us a new overall combination, we have an additional 4! ways. Therefore, the answer would be 9!*4!, which is C.
Question: A trader bought a car at 20% discount on its original price. He sold it at a 40% increase on the price he bought it. What percent of profit did he make on the original price?
A.17%
B.17%
C.12%
D.82%
Answer: C.12%
Explanation: Original price = 100
CP = 80
S = 80*(140/100) = 112
100 - 112 = 12%
Answer: C
Question: Tickets to a certain concert sell for $20 each. The first 10 people to show up at the ticket booth received a 40% discount, and the next 20 received a 15% discount. If 52 people bought tickets to the concert, what was the total revenue from ticket sales?
A.$600
B.$740
C.$850
D.$900
Answer: D.$900
Explanation: Price of 1 ticket = 20$
Revenue generated from sales of first 10 tickets = 10 * (60/100 * 20 )
= 10 * 12 = 120
Revenue generated from sales of next 20 tickets = 20 *(85/100 * 20 )
=20*17 = 340
Revenue generated from sales of last 22 tickets = 20 * 22
= 440
Revenue generated from sales of 52 tickets = 120 + 340 + 440
= 900 $
Answer D
Question: In one year, the population, of a village increased by 10% and in the next year, it decreased by 10%. If at the end of 2nd year, the population was 7920, what was it in the beginning?
A.8019
B.8000
C.8279
D.2797
Answer: B.8000
Explanation: x*110/100 * 90/100 = 7920
X*0.99=7920
X=7920/0.99
=> 8000
Answer: B
Question: There are 350 zebras at a large zoo near city. The number of zebras is 5 times the number of all the other animals combined. How many more zebras are there than non zebra animals at the zoo?
A.500
B.420
C.340
D.280
Answer: D.280
Explanation: Answer is D.
Total zebras= 350 = 5 * Other Animals (X)
or X = 70.
So, Difference in zebras and X = 350-70 = 280.
Question: A pair of articles was bought for Rs. 37.40 at a discount of 15%. What must be the marked price of each of the articles ?
A.Rs15
B.Rs 20
C.Rs 22
D.Rs 25
Answer: C.Rs 22
Explanation: Explanation:
As question states that rate was of pair of articles,
So rate of One article = 37.40/2 = Rs. 18.70
Let Marked price = Rs X
then 85% of X = 18.70
=> X = 1870/85 = 22
Option C
Question: A monkey climbs 30 feet at the beginning of each hour and rests for a while when he slips back 20 feet before he again starts climbing in the beginning of the next hour. If he begins his ascent at 7.00 a.m., at what time will he first touch a flag at 120 feet from the ground?
A.4 p.m.
B.5 p.m.
C.6 p.m.
D.7 p.m.
Answer: B.5 p.m.
Explanation: Explanation:
Net ascent of the monkey in 1 hour = (30 - 20) feet = 10 feet.
So, the monkey ascends 90 feet in 9 hours i.e. till 4 p.m.
Clearly, in the next 1 hour i.e. till 5 p.m. the monkey ascends remaining 30 feet to touch the flag.
Answer:B
Question: An express train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the express train is 54 km/hr, what is the length of the platform?
A.m
B.m
C.m
D.m
Answer: B.m
Explanation: 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:B
Question: Given that √12 = 3.464 and √120 = 10.95, find the value of √1.2 + √1200 + √0.012.
A.32.164
B.35.844
C.36.164
D.37.304
Answer: B.35.844
Explanation: Explanation:
Given exp. = √1.2 +√1200 +√0.0120 = √120/100 +√12*100 + √120/10000
= (√120)/10 + √12 * 10 + (√120)/100 = 10.95/10 + 3.464 * 10 + 10.95/100
= 1.095 + 34.64 + 0.1095
= 35.8445
ANSWER B
Question: X, Y, and Z are consecutive numbers and X > Y > Z. Also, X + 3Y + 3Z = 5Y + 6. What is the value of Z?
A.2
B.3
C.4
D.5
Answer: B.3
Explanation: If X, Y, and Z are consecutive numbers and X > Y > Z, then Y = Z+1 and X = Z+2.
X + 3Y + 3Z = 5Y + 6
Z+2+3Z+3+3Z = 5Z+5+6
2Z = 6
Z = 3
The answer is B.
Question: Excluding the stoppages, the speed of a bus is 64 km/hr and including the stoppages the speed o the bus is 48km/hr. For how many minutes does the bus stop per hour?
A.22
B.15
C.77
D.28
Answer: B.15
Explanation: Answer: B) 15 minutes
Question: A, B, C subscribe Rs. 50,000 for a business, A Subscribes Rs. 4000 more than B and B Rs. 5000 more than C. Out of a total profit of Rs. 70,000, C receives :
A.14700
B.16800
C.37798
D.13777
Answer: B.16800
Explanation: Explanation:
Let C = x. Then, B = x + 5000 and A = x + 5000 + 4000 = x + 9000.
So, x + x + 5000 + x + 9000 = 50000 <=> 3x = 36000 <=>
x = 12000.
A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12.
C's share = Rs. (70000 * 12/50 ) = Rs. 16800.
Answer: B)
Question: Faiza has 14 purses, she gives 3 purse as gift. Now how many purse did she have ?
A.2
B.5
C.11
D.9
Answer: C.11
Explanation: 14-3=11. Answer is C
Question: At a certain stage of a soccer tournament, the score ratio of teams A, B and C was 3:4:5. Eventually, the score ratio of A to B has doubled while the score ratio of A to C has halved. If the final score of team C was 40, what was the final score W of team B?
A.1)8
B.2)10
C.3)20
D.4)40
Answer: A.1)8
Explanation: A to B = 3 : 4
So, on doubling we get 6 : 4
A to C = 3 : 5
So, on halving we get 1.5 : 5 or 3 : 10 or 6 : 20
So final ratio = 6 : 4 : 20.
If 20x = 40
4x = 8
Hence, answer is A
Question: In how many different ways can the letter of the word 'LEADING ' be arranged in such a way that the vowels always come together?
A.147
B.963
C.720
D.789
Answer: C.720
Explanation: It has 7 different letters.
when the vowels EAI are always together, they can be supposed to form one letter.
then we have to arrange the letter LDNG (EAI)
now 4 letters can be arranged in 5!=120 ways
the vowels EAI can be arranged amoung themselves in 3!= 6 ways
required number of ways =120*6=720
Answer(C)
Question: In covering a distance of 42 km, A takes 2 hours more than B. If A doubles his speed, then he would take 1 hour less than B. A's speed is:
A.5 km/h
B.7 km/h
C.10 km/h
D.15 km/h
Answer: B.7 km/h
Explanation: Let A's speed be X km/hr.
Then, 42/x - 42/2x = 3
6x = 42
x = 7 km/hr.
Answer : B.
Question: If m is an integer such that (-2)^2m=2^(18-m) then m=?
A.4
B.5
C.6
D.7
Answer: C.6
Explanation: 2m = 18-m
3m = 18
m = 6
The answer is C.
Question: A and B undertake to do a piece of work for Rs. 1200. A alone can do it in 6 days while B alone can do it in 8 days. With the help of C, they finish it in 3 days. Find the share of A.
A.500
B.600
C.750
D.800
Answer: B.600
Explanation: C's 1 day's work = 1/3-(1/6+1/8)=24
A : B : C = Ratio of their 1 day's work = 1/6:1/8:1/24= 4 : 3 : 1.
A’s share = Rs. (1200 *4/8) = Rs.600, B's share = Rs. (1200 *3/8) = Rs. 450
C's share = Rs. [1200 - (300 + 225») = Rs. 150.
Answer is B
Question: Dacid obtained 86, 85, 92, 87 and 95 marks (out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks?
A.67
B.26
C.89
D.26
Answer: C.89
Explanation: Average
= (86+ 85+ 92+ 87+95)/5
= 445/5 = 89.
Answer: C
Question: When positive integer n is divided by 5, the remainder is 1. When n is divided by 7, the remainder is 3. What is the smallest positive integer k such that k+n is a multiple of 34?
A.3
B.4
C.12
D.32
Answer: A.3
Explanation: n = 5p + 1 = 6,11,16,21,26,31
n = 7q + 3 = 3,10,17,24,31
=>n = 34m + 31
To get this, we need to take LCM of co-efficients of p and q and first common number in series.
So we need to add 3 more to make it
34m + 34
Answer - A
Question: Sixty men complete a work in 25 days. One man starts working it at and thereafter one more man joins him every day. In how many
days the work will be completed?
A.22
B.52
C.24
D.55
Answer: D.55
Explanation: 1 mens 1 day work =1/1500
1/1500(1+2+3+........n)=1(as total work=1)
We need to find n it cannot be greater than 60
Here the answer is 55(approx)
ANSWER:D
Question: If the mean of numbers 28, x, 42, 78 and 104 is 90, then what is the mean of 128, 255, 511, 1023 and x?
A.395
B.275
C.355
D.423
Answer: D.423
Explanation: The mean of numbers 28, x, 42, 78 and 104 is 62: 28+x+42+78+104=90*5 --> x=198;
So, the mean of 128, 255, 511, 1023 and x is (128+255+511+1023+198)/5=423.
Answer:D.
Question: The difference between the compound interest compounded annually and simple interest for 2 years at 20% per annum is Rs.288. Find the principal?
A.2277
B.2667
C.3600
D.7200
Answer: D.7200
Explanation: P = 288(100/5)^2 => P = 7200
Answer: D
Question: The area of one square is x^2 + 8x + 16 and the area of another square is 4x^2 − 20x + 25. If the sum of the perimeters of both squares is 44, what is the value of x?
A.2
B.4
C.6
D.8
Answer: B.4
Explanation: The areas are (x+4)^2 and (2x-5)^2.
The lengths of the sides are x+4 and 2x-5.
If we add the two perimeters:
4(x+4) + 4(2x-5) = 44
12x = 48
x = 4
The answer is B.
Question: A watch was sold at a loss of 10%. If it was sold for Rs.200 more, there would have been a gain of 4%. What is the cost price?
A.1000
B.1429
C.1977
D.2778
Answer: B.1429
Explanation: 90%
104%
--------
14% ---- 200
100% ---- ? => Rs.1429
Answer: B
Question: The average of 21 numbers is 25. The average of first ten numbers is 18 and the average of last ten numbers is 32. What is the middle number?
A.195
B.175
C.184
D.201
Answer: A.195
Explanation: The total of 21 numbers = 21X25 = 525
The total of first 10 and last 10 numbers is = 10 X 14+10 X 19 = 330
So, the middle number is (525 - 330 ) = 195
A
Question: A committee of two people is to be chosen from 5 married couples. What is the number of different committees that can be chosen if two people who are married to each other cannot both serve on the committee?
A.16
B.24
C.26
D.40
Answer: D.40
Explanation: One of the approaches:
Each couple can send only onerepresentativeto the committee. Let's see in how many ways we can choose 2 couples (as there should be 2 members) out of 5 to send only onerepresentativesto the committee: 5C2=10.
But each of these 2 couples can send two persons (husband or wife): 2*2=2^2=4.
Total # of ways: 5C2*2^2=40.
Answer: D.
Question: A sum of money amounts to Rs.9800 after 5 years and Rs.12005 after 8 years at the same rate of simple interest. The rate of interest per annum is
A.15%
B.12%
C.8%
D.7%
Answer: B.12%
Explanation: Explanation :
Simple Interest for 3 years = (Rs.12005 - Rs.9800) = Rs.2205
Simple Interest for 5 years = 22053×5=Rs.3675
Principal(P) = (Rs.9800 - Rs.3675) = Rs.6125
R = 100×SI/PT
=100×3675/6125×5
=12%
Answer : Option B
Question: In 30 years, A will be twice as old as B was 30 years ago. If A is now 5 years older than B, the present age of B is?
A.85yrs
B.95yrs
C.93yrs
D.82yrs
Answer: B.95yrs
Explanation: Let B's present age = x years
Then A's present age = x+5 years
x+5+30 = 2(x-30)
x + 35 = 2x - 60
x = 95years
Answer is B
Question: John Purchased 1375 large bottles at $1.75 per bottle and 690 small bottles at $1.35 per bottle. What was the approximate average price paid per bottle?
A.$1.62
B.$1.64
C.$1.68
D.$1.72
Answer: A.$1.62
Explanation: (1375*1.75+690*1.35)/(1375+690) =~1.62
Option (A)
Question: Mala purchased a cooker and a stove for Rs. 6000 &Rs. 9000 respectively. He sold the cooker at a loss of 4% and the mobile stove at a profit of 8%. Overall how much he make a profit.
A.480
B.220
C.120
D.596
Answer: A.480
Explanation: Let the SP of the cooker and the stove be Rs. r and Rs. m respectively.
r = 6000(1 - 4/100) = 6000 - 240
m = 9000(1 + 8/100) = 9000 + 720
Total SP - Total CP = r + m - (6000 + 9000) = -240 + 720= Rs. 480
As this is positive, an overall profit of Rs. 480 was made.
A
Question: An urn contains 10 black and 5 white balls. Two balls are drawn from the urn one after the other
without replacement. What is the probability that both drawn balls are black?
A.1/7
B.3/7
C.4/5
D.5/7
Answer: B.3/7
Explanation: Let E and F denote respectively the events that first and second ball drawn
are black. We have to find P(E n F) or P (EF).
Now P(E) = P (black ball in first draw) = 10/15
Also given that the first ball drawn is black, i.e., event E has occurred, now there are 9 black balls and five white balls left in the urn. Therefore, the probability that the second ball drawn is black, given that the ball in the first draw is black, is nothing but the conditional probability of F given that E has occurred.
That is P(F|E) = 9/14
By multiplication rule of probability, we have
P (E n F) = P(E) P(F|E)
= 10/15 × 9/14 = 3/7
B)
Question: Alice picked a number of pears, each of which she sold, canned, or poached. She canned 20 percent more than she poached, and she poached 50 percent less than she sold. If there were a total of 42 pears, then how many pears did she sell?
A.20
B.21
C.22
D.23
Answer: A.20
Explanation: Let x be the amount of pears that she sold.
Then she poached 0.5x.
Then she canned 1.2*0.5x=0.6x.
The total amount of pears is x+0.5x+0.6x=2.1x
The fraction of pears that she sold is 1/2.1=10/21.
The number of pears she sold is (10/21)*42=20.
The answer is A.
Question: If the average of 20,21, 23, 24, 25, 28, 28, 29, 31 and x is 26, what is the value of x?
A.26
B.28
C.30
D.31
Answer: D.31
Explanation: Sum of the deviations of the numbers in the set from the mean is always zero
20, 21, 23, 24, 25, 28, 28, 29, 31
mean is 26
so the list is -6-5-3-2-1+2+2+3+5... this shud total to zero
but this is -5 , hence we need a number that is 5 more than the mean to get a +5 and make it zero
hence the answer is 26 + 5 = 31
D
Question: A, B and C are entered into a partnership. A invested Rs.6500 for 6 months, B invested Rs.8400 for 5 months and C invested for Rs.10000 for 3 months. A is a working partner and gets 5% of the total profit for the same. Find the share of C in a total profit of Rs.7400.
A.2777
B.1900
C.1887
D.20989
Answer: B.1900
Explanation: 65 * 6 : 84 * 5 : 100 * 3
26:28:20
C share = 74000 * 95/100 = 7030 * 20/74 => 1900
Answer:B
Question: A tank is filled in TWELVE hours by three pipes A, B and C. Pipe A is twice as fast as pipe B, and B is twice as fast as C. How much time will pipe B alone take to fill the tank?
A.42 hours
B.28 hours
C.55 hours
D.66 hours
Answer: A.42 hours
Explanation: 1/A + 1/B + 1/C = 1/12 (Given)
Also given that A = 2B and B = 2C
=> 1/2B + 1/B + 2/B = 1/12
=> (1 + 2 + 4)/2B = 1/12
=> 2B/7 = 12
=> B = 42 hours.
Answer: A
Question: P is a positive integer and 225 and 216 are both divisors of P. If P=(2^x)*(3^y)*(5^z), where x, y and z are positive integers, what is the least possible value of x+ y+ z?
A.4
B.5
C.6
D.8
Answer: D.8
Explanation: Lets make factorization of 225 and 216 ..
225 = 5 X 5 X 3 X 3 X 3
216 = 2 X 2 X 2 X 3 X 3 X 3
P would have to have 3 two's , 225 has 3 threes and and so does 216 but they can be the same three threes so we count them only once ... 225 has 2 fives ... So we had them together and we get 3 + 3 + 2 = 8(D)(answer) ...
Question: Two trains, each 100 m long, moving in opposite directions, cross other in 8 sec. If one is moving twice as fast the other, then the speed of the faster train is?
A.17
B.27
C.60
D.13
Answer: C.60
Explanation: Let the speed of the slower train be x m/sec.
Then, speed of the train = 2x m/sec.
Relative speed = ( x + 2x) = 3x m/sec.
(100 + 100)/8 = 3x => x = 25/3.
So, speed of the faster train = 50/3 = 50/3 * 18/5 = 60 km/hr.
Answer: C
Question: What is the least number to be subtracted from 11, 15, 21 and 30 each so that resultant numbers become proportional?
A.5
B.6
C.3
D.8
Answer: C.3
Explanation: Let the least number to be subtracted be x, then 11 - x, 15 - x, 21 - x and 30 - x are in proportion.
<=> (11 - x) : (15 - x) = (21 - x) : (30 - x)
=> (11 - x)(30 - x) = (15 - x)(21 - x)
From the options, when x = 3
=> 8 * 27 = 12 * 18
Answer:C
Question: The difference between a two-digit number and the number obtained by interchanging the digits is 36. What is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1 : 2 ?
A.4
B.8
C.16
D.18
Answer: B.8
Explanation: Since the number is greater than the number obtained on reversing the digits, so the ten's digit is greater than the unit's digit.
Let ten's and unit's digits be 2x and x respectively.
Then, (10 x 2x + x) - (10x + 2x) = 36
9x = 36
x = 4.
Required difference = (2x + x) - (2x - x) = 2x = 8.
Answer:B
Question: The food in a camp lasts for 25 men for 55 days. If five more men join, how many days will the food last?
A.80 days
B.30 days
C.46 days
D.16 days
Answer: C.46 days
Explanation: one man can consume the same food in 25*55 = 1375 days.
5 more men join, the total number of men = 30
The number of days the food will last = 1375/30
= 46 days.
Answer:C
Question: A construction company wants to number new houses using digit plates only. If the company puts an order for 522 plates, how many houses are to be given numbers? (The numbers of houses are consecutive and the number of the first house is 1).
A.220
B.230
C.210
D.240
Answer: C.210
Explanation: You know that the answer is going to be three digits, and it's easy to figure out how many 1 and 2 digit numbers (9 and 90), so the real question is how many 3 digit number are there?
99+(522-9-90*2)/3=210
Answer : C
Question: What is the remainder when the number W=14^2 * 15^8 is divided by 5?
A.0
B.1
C.2
D.4
Answer: A.0
Explanation: 14^2 has units digit 6
15^8 has units digit 5
Thus W=14^2*15^8 has units digit 0 and will be divisible by 5. The remainder will be zero
Answer: (A)
Question: A train running at the speed of 60 km/hr crosses a pole in 12 seconds. Find the length of the train?
A.150 meter
B.200 meter
C.666 meter
D.155 meter
Answer: B.200 meter
Explanation: Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (Distance) = Speed * Time
(50/3) * 12
= 200 meter
Answer: B
Question: At the foot of a mountain the elevation of its summit is 45 degrees. After ascending one
KM towards the mountain upon an incline of 30 degrees, the elevation changes to 60
degrees. Find the Height of the mountain?
A.1.333Km
B.1.366Km
C.1.233Km
D.1.266Km
Answer: B.1.366Km
Explanation: At the foot of a mountain the elevation of its summit is 45 degrees. After ascending one KM towards the mountain upon an incline of 30 degrees, the elevation changes to 60 degrees. The Height of the mountain is guven by
[ Height -- sin 30 ] = [ Height -- cos 30 ] tan 60
whence Height = [tan 60 cos 30 -- sin 30 ] / [ tan 60 -- 1 ] km = 1.366 km
ANSWER:B
Question: A developer has land that has x feet of lake frontage. The land is to be subdivided into lots, each of which is to have either 80 feet or 100 feet of lake frontage. If 1/9 of the lots are to have 80 feet of frontage each and the remaining 56 lots are to have 100 feet of frontage each, what is the value of x ?
A.400
B.3,200
C.6,160
D.4,400
Answer: C.6,160
Explanation: Total number of plots,be T
Plots with 80ft is (1/9)th of total plots.
Plots with 100ft frontage = (8/9) X total number of plots
i.e 8/9 X T = 56 T = 63
Total lake frontage = 56X100 + 7X80 = 6160
Answer : C
Question: Three machines, each working at the same constant rate, together can complete a certain job in 18 days. How many additional machines, each working at the same constant rate, will be needed to complete the job in 9 days?
A.3
B.5
C.7
D.9
Answer: A.3
Explanation: Rate of one machine = 1 job / (18*3) days
let X = number of machines needed to complete the job in 9 days
1/(3*18) * 9 * X = 1 job
X = 6
6-3= 3
ANSWER: A
Question: In a meeting of 3 representatives from each of 7 different companies, each person shook hands with every person not from his or her own company. If the representatives did not shake hands with people from their own company, how many handshakes took place?
A.189
B.179
C.159
D.169
Answer: A.189
Explanation: In fact, all 21 people will shake hands with 18 others.
So, it SEEMS like the TOTAL number of handshakes = (21)(18)
HOWEVER, we need to keep in mind that we have counted each handshake TWICE.
To account for this DUPLICATION, we must divide (21)(18) by 2.
So, the TOTAL # of handshakes = (21)(18)/2 = 189
Answer : A