RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A club has has $329,864 in its savings account. What is the least amount of money (in whole number of dollars) that must be added to the account the money needs to be spent evenly among nine different scouts for scouting?
A.$1
B.$2
C.$3
D.$4
Answer: D.$4
Explanation: To find the least amount that must be added to the account to split the money evenly among 9 scouts, the total divisible by 9
Simply add the individual digits of the total = 3+2+9+8+6+4 = 32
If you add 4 , the number is divisible by 9 (32+ 4)
Correct Option : D
Question: Mahesh marks an article 15% above the cost price of Rs. 540. What must be his discount percentage if he sells it at Rs. 456?
A.18%
B.26.57%
C.20%
D.19%
Answer: B.26.57%
Explanation: CP = Rs. 540, MP = 540 + 15% of 540 = Rs. 621
SP = Rs. 456, Discount = 621 - 456 =165
Discount % = 165/621 * 100 = 26.57%
ANSWER:B
Question: In how many no. between 100 and 1000 exactly one of the digits is 3?
A.648
B.512
C.252
D.225
Answer: D.225
Explanation: 3 scenarios possible
3XY = 1*9*9 = 81
X3Y (with X ≠≠3 or 0) = 8*1*9 = 72
Y3X (with Y ≠≠3 or 0)= 8*1*9 = 72
Total cases possible = 144+81=225
D is the correct answer
Question: In a kickball competition of 6 teams, how many possible matches can each team play with each other?
A. 9
B. 15
C. 24
D. 36
Answer: B. 15
Explanation: 6C2 = 15
Option B
Question: The current of a stream at 1 kmph. A motor boat goes 35 km upstream and back to the starting point in 12 hours. The speed of the motor boat in still water is?
A.6 kmph
B.9 kmph
C.7 kmph
D.5 kmph
Answer: A.6 kmph
Explanation: S = 1
M = x
DS = x + 1
US = x - 1
35/(x + 1) + 35/(x - 1) = 12
x = 6
Answer:A
Question: In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the run rate in the remaining 40 overs to reach the target of 282 runs?
A.6
B.6.25
C.6.5
D.6.75
Answer: B.6.25
Explanation: Run rate is calculated by dividing runs scored by the number of overs.
in the first 10 overs there were 32 runs (10*3.2)
282-32=250
250/40=6.25 run rate for the remaining 40 overs
ANSWER : B
Question: A batch of cookies was divided among three tins: 2/3 of all the cookies were placed in either the blue tin or the green tin, and the rest were placed in the red tin. If 1/4 of all the cookies were placed in the blue tin, what fraction T of the cookies that were placed in the other tins were placed in the green tin?
A.15/2
B.9/4
C.5/9
D.7/5
Answer: C.5/9
Explanation: Blue tin or red tin: 2/3 (N)
Red tin: (1/3)N
Blue tin: (1/4)N
What the last statment meant, is it wants this fraction: (# of cookies in green tin)/(# of cookies in red and green tin)
# of cookies in green tin = 2N/3 - N/4 = 8N- 3N/12 = 5N/12
# of cookies in red and green tin = N/3 + 5N/12 = 9N/12
Fraction T= 5N/12 * 12/9N = 5/9 (C)
Question: If 0 < a < b and k = (2a + 5b)/b , which of the following must be true?
A.k < 2
B.k < 7
C.k < 9
D.k > 9
Answer: B.k < 7
Explanation: Here's another approach:
k = (2a + 5b)/b
= 2a/b + 5b/b
= 2(a/b) + 5
Since 0 < a < b, we know that a/b is less than 1, which means that 2(a/b) is some number less than 2.
So, we get k = (some number less than 2) + 5
From here, we can see that k must be less than 7
Answer: B
Question: what rate percentage is 1 minute 48 seconds to an hour?
A.1%
B.2%
C.3%
D.4%
Answer: C.3%
Explanation: 1m48s =108s
1hr=60m=3600s
% = 108*100/3600 = 3%
ANSWER:C
Question: A dealer sold two of his cattle for Rs. 500 each. On one of them he lost 10% on the other, he gained 10%. His gain or loss percent in the entire transaction was:
A.10% loss
B.1% loss
C.1% gain
D.Neither loss nor profit
Answer: C.1% gain
Explanation: Explanation:
Loss%= (common gain or loss % / 10)2 = (10/10)² % = 1%. Answer: C
Question: A full stationary oil tank that is a right circular cylinder has a radius of 100 feet and a height of 25 feet. Oil is pumped from the stationary tank to an oil truck that has a tank that is a right circular cylinder until the truck's tank is completely filled. If the truck's tank has a radius of 8 feet and a height of 10 feet, how far (in feet) did the oil level drop in the stationary tank?
A.0.008
B.0.08
C.0.064
D.0.64
Answer: C.0.064
Explanation: The volume of oil pumped to the tank = The volume of oil taken away from stationary cylinder.
pi*64*10 = pi*h*100*100 (h is distance that the oil level dropped)
h = 640/10,000 = 64/1000 = 0.064 ft
The answer is C.
Question: A man with his bike travels to a place 150 km away at an average speed of 50 km per hour and returns at 30 km per hour. His average speed for the whole journey in km per hour is
A.35
B.37
C.37.5
D.40
Answer: C.37.5
Explanation: Explanation :
Average speed = 2xy/(x + y) km/hr
= 2*50*30/(50 + 30)
= 37.5 km/hr
Answer : C
Question: Rates for having a manuscript typed at a certain typing service are $5 per page for the first time a page is typed and $2 per page each time a page is revised. If a certain manuscript has 100 pages, of which 40 were revised only once, 10 were revised twice, and the rest required no revisions, what was the total cost of having the manuscript typed?
A.$430
B.$620
C.$650
D.$680
Answer: B.$620
Explanation: For 100-40-10=50 pages only cost is 5$ per page for the first time page is typed - 50*5=250$;
For 40 pages the cost is: first time 5$ + 2$ of the first revision - 40*(5+2)=280$;
For 10 pages the cost is: first time 5$ + 2$ of the first revision + 2$ of the second revision - 10(5+2+2)=90$;
Total: 250+280+90=620$.
Answer: B.
Question: The value of x + x(xx) when x = 5 is:
A.A)36
B.B)16
C.C)18
D.D)130
Answer: D.D)130
Explanation: x + x(xx)
Put the value of x = 2 in the above expression we get,
5 + 5(55)
= 5+ 5(5 × 5)
= 5 + 5(25)
=5 + 125
= 130
D
Question: A train 400 meters long completely crosses a 300 meters long bridge in 45 seconds. What is the speed of the train is?
A.32
B.56
C.29
D.27
Answer: B.56
Explanation: S = (400 + 300)/45 = 700/45 * 18/5 = 56
Answer: B
Question: I bought two stocks, for Rs. 500. I sold one at a loss of 20% and other at a gain of 25% and then I found each stick was sold at the same price. Find the cost of the stock sold at a loss?
A.A)657
B.B)280
C.C)438
D.D)306
Answer: D.D)306
Explanation: x*(80/100)
= (500 - x)125/100
x = 306.4
Answer: D
Question: The maximum number of student amoung them 1080 pens and 920 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is :
A.91
B.40
C.80
D.90
Answer: B.40
Explanation: Solution
Required number of student = H.C.F of 1080 and 920 = 40. Answer B
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. 30,000, B receives:
A.s. 10,000
B.s. 10,200
C.s. 10,400
D.s. 10,700
Answer: B.s. 10,200
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.
B's share = Rs. (30000 x 17/50) = Rs. 10,200.
B
Question: A person travels equal distances with speeds of 6km/hr, 12km/hr,18km/hr. and takes a total time of 11minutes. Find the total distance ?
A.1km
B.1500mts
C.1800mts
D.2km
Answer: C.1800mts
Explanation: Let the each distance be x km
total distance = 3x
then total time,
(x/6)+(x/12)+(x/18) = 11/60
x=0.6
total distance = 3*0.6 = 1.8km = 1800 meters
correct option is C
Question: If x and y are both odd prime numbers and x < y, how many distinct positive integer factors does 2xy have?
A.3
B.4
C.6
D.8
Answer: D.8
Explanation: The solution should be the same for all numbers that fulfill the condition above. As x and y are odd prime numbers, they must be > 2. Also, they must be distinct as x<y.
I choose x=3 and y=5:
How many factors does 2x3x5=30 have:
1, 2, 3, 5, 6, 10, 15, 30 = 8 distinct positive integer factors.
Hence, the correct answer is D.
Question: At a meeting, 6 people are to be seated around a circular table. Two seating arrangements are considered different only when the positions of the people are different relative to each other. What is the total number of different possible seating arrangements for the group?
A.12
B.72
C.120
D.144
Answer: C.120
Explanation: The number of arrangements of n distinct objects in a row is given by n!n!.
The number of arrangements of n distinct objects in a circle is given by (n−1)!(n−1)!.
From Gmat Club Math Book (combinatorics chapter):
"The difference between placement in a row and that in a circle is following: if we shift all object by one position, we will get different arrangement in a row but the same relative arrangement in a circle. So, for the number of circular arrangements of n objects we have:
R=n!n=(n−1)!R=n!n=(n−1)!"
(n−1)!=(6−1)!=120(n−1)!=(6−1)!=120
Answer: C
Question: The average weight of a group of boys is 20 kg. After a boy of weight 34 kg joins the group, the average weight of the group goes up by 1 kg. Find the number of boys in the group originally ?
A.12
B.14
C.18
D.13
Answer: D.13
Explanation: Let the number off boys in the group originally be x.
Total weight of the boys = 20x
After the boy weighing 34 kg joins the group, total weight of boys = 20x + 34
So 20x + 34 = 21(x + 1) = > x = 13.
ANSWER:D
Question: Find the compound interest and the amount on Rs.8000 at 5% per annum for 3 years when C.I is reckoned yearly?
A.1261
B.1262
C.2686
D.2687
Answer: A.1261
Explanation: A = 8000(21/20)3
= 9261
= 8000
---------
1261
Answer:A
Question: Two pipes A and B can fill a tank in 12 and 24 minutes respectively. If both the pipes are used together, then how long will it take to fill the tank?
A.9
B.8
C.6
D.4
Answer: B.8
Explanation: Part filled by pipe A in 1 minute =1/12
=1/12
Part filled by pipe B in 1 minute =1/24
=1/24
Part filled by pipe A and pipe B in 1 minute=
1/12 + 1/24 =1/8
=1/12+1/24=1/8
i.e., both the pipe together can fill the tank in 8 minutes.
Question: A thief steals a car at 4.05 P.M. and drives it at 55 km/hr. The theft is discovered at 4.20 P.M. and the owner sets off in another car at 70 km/hr. when will he overtake the thief ?
A.4.50 P.M.
B.5 P.M.
C.5.10 P.M.
D.5.15 P.M.
Answer: D.5.15 P.M.
Explanation: Explanation :
Solution: Suppose the thief is overtaken x hrs after 4.05 P.M.
Then, distance covered by the thief in x hrs. = distance covered by owner in (x - 1/4) hrs.
.'. 55x = 70(x - 1/4)
=> 15x = 70/4
=> x = 70/(15*4) hr = 14/12 hr
=> x = (14/12 * 60) min = 70 min.
So, the thief is overtaken at 5.15 pm.
Answer : D
Question: A trained covered x km at 70 kmph and another 2x km at 20 kmph. Find the average speed of the train in covering the entire 3x km.
A.22.25
B.99
C.26.25
D.66
Answer: C.26.25
Explanation: Total time taken = x/70 + 2x/20 hours
= 4x/35 hours
Average speed = 3x/(4x/35) = 26.25 kmph
Answer: C
Question: If r and s are positive integers and r-s=6, which of the following has the greatest value R?
A.2r
B.2s
C.r +s
D.2r-s
Answer: A.2r
Explanation: The simplest way to do this is to assume values.
We are told that r and s are positive integers R.
Also, r-s = 6 => r = 6+s
Hence r is 6 more than s.
Let s be 10. Hence r = 16.
Option A: 2r = 2*16 = 32
Option B: 2s = 2 * 10 = 20
Option C: r + s = 16 + 10 = 26
Option D: 2r - s = 2(16) - 10 = 32 - 10 = 22
Option E: 2s - r = 2(10) - 16 = 20 - 16 = 4
Hence option A is the greatest.
Question: The sum of money will be triple itself in 20years and simple interest find rate of interest?
A.A)5%
B.B)10%
C.C)15%
D.D)20%
Answer: B.B)10%
Explanation: T = 20 years
P= principle amount = x
A = total amount = 3x
SI = simple interest = A-P = 3x-x = 2x
R = 100SI/PT = 100.2x/20x =10%
Answer is B
Question: 66 out of 100 the how much out of 75
A.49.5
B.48.5
C.47.5
D.46.5
Answer: A.49.5
Explanation: out of 100 -- its 66
out of 75 -- x
x= 75/100 * 66
x = 49.5
ANSWER:A
Question: Rs.800 amounts to Rs.920 in 3 years at simple interest. If the interest is increased by 3%, it would amount to how much?
A.226
B.Rs.992
C.665
D.771
Answer: B.Rs.992
Explanation: (800*3*3)/ 100 = 72
920 + 72 = 992
Answer: B
Question: A trader bought a car at 20% discount on its original price. He sold it at a 100% increase on the price he bought it. What percent of profit did he make on the original price?
A.18%
B.13%
C.60%
D.40%
Answer: C.60%
Explanation: Original price = 100
CP = 80
S = 80*(200/100) = 160
100 - 160= 60%
Answer: C
Question: In june a baseball team that played 60 games had won 30% of its game played. After a phenomenal winning streak this team raised its average to 50% .How many games must the team have won in a row to attain this average?
A.20
B.30
C.34
D.24
Answer: D.24
Explanation: Number of matches won by the team in June: 30% of 60 = 18
After a phenomenal winning streak the average is 50%
Let the team played x matches continuously and won all of them to achieve an average winning percentage of 50%.
So total matches played by the team = (60+x)
Total matches won by the team = (18+x)
Total matches won = 50% of Total matches played
(18+x) = 50% of (60+x)
18+x = (50/100)*(60+x)
18+x = (1/2)*(60+x)
36+2x = 60+x
x = 24 ANSWER D
Question: The time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 36 kmph, find the speed of the stream?
A.12 kmph
B.13 kmph
C.14 kmph
D.15 kmph
Answer: A.12 kmph
Explanation: The ratio of the times taken is 2:1.
The ratio of the speed of the boat in still water to the speed of the stream = (2+1)/(2-1) = 3/1 = 3:1
Speed of the stream = 36/3 = 12 kmph.
Answer: A
Question: The speed of a boat in still water is 20 km/hr and the rate of current is 5 km/hr. The distance travelled downstream in 18 minutes is:
A.9.5
B.5.5
C.7.5
D.6.5
Answer: C.7.5
Explanation: Explanation:
Speed downstream = (20+5) kmph = 25 kmph
Distance travelled = (25*(18/60)) km = 7.5 km.
ANSWER:C
Question: A mixture has milk and water in the ratio 5:1. 20 liters of water is added and the ratio now becomes 5:6. How much milk was present in original mixture?
A.20 liters
B.22 liters
C.24 liters
D.26 liters
Answer: A.20 liters
Explanation: If milk and water in original mixture is 5x and x respectively, then
5x/(x+20) = 5/6, x=4
So milk in original mixture=5*4=20 liters
ANSWER:A
Question: Working alone at its constant rate, machine A produces x boxes in 10 minutes and working alone at its constant rate, machine B produces 2x boxes in 5 minutes. How many minutes does it take machines A and B, working simultaneously at their respective constant rates, to produce 4x boxes?
A.3 minutes
B.4 minutes
C.8 minutes
D.6 minutes
Answer: C.8 minutes
Explanation: Rate = Work / Time
Given Rate of Machine A = X / 10 min
Machine B Produces 2x boxes in 5 min hence , Machine B produces 4x boxes in 10 min .
Rate of Machine B = 4x / 10
we need tofind the combined time that machines A and B, working simultaneouslytakeat their respective constant rates
let's first find the combined Rate of Machine A and B
Rate of Machine A = X / 10 min + Rate of Machine B = 4x / 10 = 5X/10
Now combine Time = combine work needs to be done / Combine Rate = 4x/5x * 10 = 8 Min
Ans: C
Question: A dog is tied to a tree by a long nylon cord. If the dog runs from the due North side of the tree to the due South side of the tree with the cord extended to its full length at all items, and the dog ran approximately 30 feet, what was the approximate length of the nylon cord Q, in feet?
A.30
B.25
C.15
D.10
Answer: D.10
Explanation: Because the cord was extended to its full length at all items, the dog ran along a semi-circular path, from north to south.
The circumference of a full circle is 2*pi*r, but since we only care about the length of half the circle, the semi-circle path is pi*r.
Q=pi*r = 30. Round pi = 3, then r = 10.
Chord is about 10 feet long.D
Question: A rectangular garden is to be twice as long as it is wide. If 240 yards of fencing, including the gate, will completely enclose the garden, what will be the length of the garden, in yards?
A.40
B.50
C.60
D.80
Answer: D.80
Explanation: ALTERNATE APPROACH
Backsolving ( Using answer options to reach the correct answer ) can work wonders here if one is fast in calculations.
Given Perimeter is 240
So, 2 ( L + B ) = 240
Or, L + B = 120
Now use the answer options ( Given Length ; Breath will be half the length)
(A) 40
L = 40 ; B = 20
L + b = 60
(B) 50
L = 50 ; B = 25
L + b = 75
(C) 60
L = 60; B = 30
L + b = 90
(D) 80
L = 80; B = 40
L + b = 120
(E) 100
L = 100; B = 50
L + b = 150
Thus you see no, need of any calculations, U can reach the correct option only by checking options ; correct answer will be (D)
Question: A car is traveling 55 kilometers per hour. How many meters does the car travel in one minute?
A.1250m/min
B.1360m/min
C.2560m/min
D.916.67m/min
Answer: D.916.67m/min
Explanation: Convert hour into minutes ( 1 hour = 60 minutes) and kilometers into meters (1 km = 1000 m) and simplify
55 kilometers per hour = 55 km/hr
= (55 × 1000 meters) / (60 minutes) = 916.67 meters / minute
correct answer is D)916.67m/min
Question: The bus that travels from St. Louis to Chicago and back comes to St. Louis every 2 hours while the bus that travels from St. Louis to Springfield and back comes to St. Louis every 6 hours. If at 12:00 o'clock both bused arrived at St. Louis, at what time will they meet in St. Louis again?
A.16:00.
B.18:00
C.20:00
D.22:00.
Answer: B.18:00
Explanation: Time taken by bus to travel from St. Louis to Chicago and back comes to St. Louis = 2 hours
Time taken by bus to travel from St. Louis to Springfield and back comes to St. Louis = 6 hours
Time taken by both buses to meet again in St. Louis will be LCM of 2 and 6 = 12
If the buses start at 12:00 o'clock from St. Louis , they will meet again in St. Louis at 18:00 hours
Answer B
Question: The value of a machine depreciates at 20% per annum. If its present value is $1,50,000, at what price should it be sold after two years such that a profit of $24,000 is made?
A.$250000
B.$430000
C.$120000
D.$170000
Answer: C.$120000
Explanation: C
$1,20,000
The value of the machine after two years = 0.8 * 0.8 * 1,50,000 = $96,000
SP such that a profit of $24,000 is made = 96,000 + 24,000 = $1,20,000
Question: consider the sequence 1,-2,3,-4,5,-6........what is the average of first 200 terms of sequence?
A.-1
B.-0.5
C.0
D.0.5
Answer: B.-0.5
Explanation: 1-2+3-4+5-6....................+199-200
= (1-2)+(3-4)+(5-6)....................+(199-200)
= -1-1-1......................(100 terms)
= -100
so, average= (-100)/200= -0.5
ANSWER:B
Question: If z = 4p, where p is a prime number greater than 2, how many different positive even divisors does z have, including z ?
A. Two
B. Three
C. Four
D. Six
Answer: C. Four
Explanation: z=4p
since z = 4p thenevendivisors are:
4p/4p= 1
4p/2p= 2
4p/4= p
4p/2= 2p
so the answer is (C)
Question: A and B undertake to do a piece of work for Rs 600. A alone can do it in 6 days while B alone can do it in 8 days. With the help of C, they can finish it in 3 days, Find the share of each?
A.300, 225, 75
B.200, 225, 80
C.400, 300, 100
D.500, 300, 100
Answer: A.300, 225, 75
Explanation: C’s one day’s work = (1/3) - (1/6 + 1/8) = 1/24
Therefore, A : B : C = Ratio of their one day’s work = 1/6 : 1/8 : 1/24 = 4 : 3 : 1.
A’s share = Rs (600 x 4/8) = 300
B’s share = Rs (600 x 3/8) = 225
C’s share = Rs[600 - (300 + 225)] = Rs 75
ANSWER:A
Question: The cash realised on selling a 14% stock is Rs.109.25, brokerage being 1/4% is?
A.366
B.106
C.102
D.109
Answer: D.109
Explanation: Cash realised= Rs. (109.25 - 0.25)
= Rs. 109.
Answer: D
Question: When p is divided by 9, the remainder is 4. All of the following are possible values of p, except for which of the following?
A.13
B.31
C.49
D.55
Answer: D.55
Explanation: If a number is divisible by 9, the sum of its digits must be divisible by 9. --> If a number leaves a remainder 4 when divided by 9 the sum of its digits must be 4.
55
Answer: D
Question: Zaya purchase 13 jars in a store then she returned 10 jars to store .Now how many jars she had?
A.A)5
B.B)11
C.C)19
D.D)3
Answer: D.D)3
Explanation: 13-10=3. Answer is D
Question: Indu gave Bindu Rs.4375 on compound interest for 2 years at 4% per annum. How much loss would Indu has suffered had she given it to Bindu for 2 years at 4% per annum simple interest?
A.s.10
B.s.7
C.s.5
D.s.3
Answer: B.s.7
Explanation: 4375 = D(100/4)2
D = 7
ANSWER:B
Question: The number of defects in the first five cars to come through a new production line are 8, 7, 10, 4, and 6, respectively. If the sixth car through the production line has either 3, 7, or 12 defects, for which of theses values does the mean number of defects per car for the first six cars equal the median?
I. 3
II. 7
III. 12
A.I only
B.II only
C.III only
D.I and III only
Answer: C.III only
Explanation: C
for 7 we will have mean as 7.16(approx) and median as 7 but for 3 we will have mean and median = 6.5 and for 12 we will have median and mean =8
Question: Two dogsled teams raced across a 300 mile course in Wyoming. Team A finished the course in 3 fewer hours than team Q. If team A's average speed was 5 mph greater than team Q's, what was team Q's average mph?
A.12
B.15
C.18
D.20
Answer: D.20
Explanation: This is a very specific format that has appeared in a handful of real GMAT questions, and you may wish to learn to recognize it: here we have a *fixed* distance, and we are given the difference between the times and speeds of two things that have traveled that distance. This is one of the very small number of question formats where backsolving is typically easier than solving directly, since the direct approach normally produces a quadratic equation.
Say Team Q's speed was s. Then Team Q's time is 300/s.
Team A's speed was then s+5, and Team A's time was then 300/(s+5).
We need to find an answer choice for s so that the time of Team A is 3 less than the time of Team Q. That is, we need an answer choice so that 300/(s+5) = (300/s) - 3. You can now immediately use number properties to zero in on promising answer choices: the times in these questions will always work out to be integers, and we need to divide 300 by s, and by s+5. So we want an answer choice s which is a factor of 300, and for which s+5 is also a factor of 300. So you can rule out answers A and C immediately, since s+5 won't be a divisor of 300 in those cases (sometimes using number properties you get to the correct answer without doing any other work, but unfortunately that's not the case here). Testing the other answer choices, if you try answer D, you find the time for Team Q is 15 hours, and for Team A is 12 hours, and since these differ by 3, as desired, D is correct.
Question: A triangle has two angles with ratio of 4:3, and the third angle is the sum of the first two. Find the smallest angle of the triangle in degrees.
A.130/11
B.270/7
C.270/11
D.310/7
Answer: B.270/7
Explanation: The angles are 4x, 3x, and (4x+3x) = 7x for some value x
the three angles of a triangle add up to 180, so
4x+3x+7x=180
14x=180
x=180/14
x=90/7
the smallest angle is 3x = 3*(90/7) = 270/7
B
Question: The average of seven numbers is 18. The average of first three numbers is 14 and the average of last three numbers is 19. What is the middle number?
A.19
B.22
C.27
D.29
Answer: C.27
Explanation: The total of seven numbers = 7X18 = 126
The total of first 3 and last 3 numbers is = 3 X 14+3 X 19 = 99
So, the middle number is (126 - 99 ) = 27
C)
Question: Of the 3,600 employees of Company X, 1/6 are clerical. If the clerical staff were to be reduced by 1/4, what percent of the total number of the remaining employees would then be clerical?
A. 13%
B. 22.2%
C. 20%
D. 12.5%
Answer: A. 13%
Explanation: Welcome, just post the question and the choices
Let's see, the way I did it was
1/6 are clerical out of 3600 so 600 are clerical
600 reduced by 1/4 is 1200*1/4
so it reduced 150 people , so there is 450 clerical people left
but since 150 people left, it also reduced from the total of 3600 so there are 3450 people total
since 450 clerical left / 3450 people total
you get (A) 13%
Answer : A