RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Train A left Centerville Station, heading toward Dale City Station, at 3: 00 p.m. Train B left Dale City Station, heading toward Centerville Station, at 4: 20 p.m. on the same day. The trains rode on straight tracks that were parallel to each other. If Train A traveled at a constant speed of 30 miles per hour and Train B traveled at a constant speed of 10 miles per hour, and the distance between the Centerville Station and Dale City Station is 90 miles, when did the trains pass each other?
A.4: 45 p.m.
B.5: 00 p.m.
C.6: 20 p.m.
D.5: 35 p.m.
Answer: C.6: 20 p.m.
Explanation: the distance travelled by the train A in first 20 minutes will be 10.
The distance which will be remaining is 80.
Now both trains are running in opposite direction.Their speed will be added so 40.
Time at which they will meet =80/40=2
time of train B will be 4:20 +2=6:20
Hence answer is C.Hope i am correct
Question: A computer store offers employees a 30% discount off the retail price. If the store purchased a computer from the manufacturer for $900 dollars and marked up the price 30% to the final retail price, how much would an employee save if he purchased the computer at the employee discount (30% off retail price) as opposed to the final retail price.
A.352
B.356
C.358
D.362
Answer: A.352
Explanation: Cost price=900
Profit=30% =30% of 900=270
selling price=CP+ Profit
SP=1170
a Discount of 30% to employees means 30% off on 1170
so 30% of 1170= 351
Ans A
Question: A certain bridge is 2,024 feet long. Approximately how many minutes does it take to cross this bridge at a constant speed of 10 miles per hour? (1 mile = 5,280 feet)
A. 1
B. 2
C. 4
D. 6
Answer: B. 2
Explanation: Distance: 2024 feet. This is (2024/5280) miles = 0.38 miles
Speed: 10 miles per hour
Time: (Distance / Speed) (0.38/10) {This will come in Hours}. Multiply by 60 to get answer in minutes. It is 2.28 minutes.
Answer to be 2 minutes.
ANS B
Question: By walking at 3/4th of his usual speed, a man reaches office 10 minutes later than usual. What is his usual time?
A.30min
B.50min
C.65min
D.60min
Answer: A.30min
Explanation: let T be the usual time.
time spent=4T/3
therefore, 4T/3=T+10
4T=3T+30...therefor T=30min
ANSWER:A
Question: A can do a piece of work in 6 hours; B and C together can do it in 4 hours, which A and C together can do it in 3 hours. How long will B alone take to do it?
A.8hours
B.6hours
C.14hours
D.12hours
Answer: D.12hours
Explanation: A's 1 hour work = 1/6;
(B + C)'s 1 hour work = 1/4;
(A + C)'s 1 hour work = 1/3
(A + B + C)'s 1 hour work = (1/4 + 1/6) = 5/12
B's 1 hour work = (5/12 - 1/3) = 1/12
B alone will take 12 hours to do the work.
Answer:D
Question: The speed of a boat in upstream is 40 kmph and the speed of the boat downstream is 70 kmph. Find the speed of the boat in still water and the speed of the stream?
A.70,10 kmph
B.55,15 kmph
C.70,70 kmph
D.78,10 kmph
Answer: B.55,15 kmph
Explanation: Speed of the boat in still water
= (40+70)/2
= 55 kmph. Speed of the stream
= (70-40)/2
= 15 kmph.
Answer:B
Question: Which of the following equations has real roots ?
A.3x2 + 4x + 5 = 0
B.x2 + x + 4 = 0
C.(x - 1)(2x - 5) = 0
D.2x2 - 3x + 4 = 0
Answer: C.(x - 1)(2x - 5) = 0
Explanation: Sol.(c) Roots of a quadratic equation
ax2 + bx + c = 0 are real if b2 - 4ac ≥ 0
Let us work with options as follows.
Option (a) : 3x2 + 4x + 5 = 0
b2 - 4ac = 42 - 4(3)(5) = -44 < 0.
Thus, roots are not real.
(b) : x2 + x + 4 = 0
b2 - 4ac = 12 - 4(1)(4) = 1 - 16 = -15 < 0. Thus, roots are not real. (c) :(x –1) (2x – 5) = 0 => 22 - 7x + 5 = 0
b2 - 4ac = (-7)2 - 4(2)(5) = 49 - 40 = 9 > 0.
Thus roots are real.
or x = 1 and x = 5/2 > 0; Thus, equation has real roots.
(d) : 2x2 - 3x + 4 = 0
b2 - 4ac = (-3)2 - 4(2)(4) = 9 - 32 = -23 < 0.
Thus, roots are not real. Hence, option (c) is correct.
Answer C
Question: The length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 867 sq m, then what is the breadth of the rectangular plot?
A.12
B.17
C.10
D.12
Answer: B.17
Explanation: Let the breadth of the plot be b m.
Length of the plot = 3 b m
(3b)(b) = 867
3b2 = 867
b2 = 289 = 172 (b > 0)
b = 17 m.
Answer:B
Question: If the numerator of a fraction R is tripled, and the denominator of a fraction is doubled, the resulting fraction will reflect an increase of what percent?
A.16 1⁄6%
B.25%
C.33 1⁄3%
D.50%
Answer: D.50%
Explanation: This question can be dealt with conceptually or by TESTing VALUES.
We're told that the numerator of a fraction R is tripled and the denominator of that same fraction is doubled. We're asked for the resulting increase, in percentage terms, of that fraction.
Let's TEST 2/1
If we triple the numerator and double the denominator, we end up with....
(2x3)/(1x2) = 6/2 = 3
Since we're increasing 2 to 3, we're increasing that fraction by (3-2)/2 = 1/2 of itself = 50%
D
Question: Mangala completes a piece of work in 30 days, Raju completes the same work in 40 days. If both of them work together, then the number of days required to complete the work is
A.4 days
B.6 days
C.8 days
D.17.14 days
Answer: D.17.14 days
Explanation: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days.
That is, the required No. of days = 30 × 40/70 = 17.14 days.
Answer : D
Question: There are 2 printers installed to print some pages. If you have to find out how many pages will the printers print at 35°C when one printer’s work is directly proportional and the others printer work is inversely proportional to the temperature and the total work done at 15°C is 20 pages and that done on 20°C is 25 pages?
A.40 pages
B.41.2 pages
C.40.7 pages
D.43.2 pages
Answer: B.41.2 pages
Explanation: If 1st Printer works directly proportional to the temperature with constant K1 and
2nd printer works inversely proportional to the temperature with constant K2, then
Pages printed at particular temperature= T1*K1 + K2/T2 ----(i)
15K1+ (K2/15) = 20 ----(ii) &
20K1+ (K2/20) = 25 ----(iii)
On solving (ii) & (iii), K1=8/7 ,K2=300/7
From (i), Total pages printed at 35°C = (35*8/7) + [300/(7*35)] =40 + (60/49)= 41.22
ANSWER:B
Question: In what time a sum of money double itself at 3% per annum simple interest?
A.33 1/8%
B.33 1/3%
C.33 7/3%
D.32 1/3%
Answer: B.33 1/3%
Explanation: P = (P*3*R)/100
R = 33 1/3%
Answer: B
Question: In a contest, a bowl contains 16 keys, only one of which will open a treasure chest. If a contestant selects the key that opens the treasure chest, she wins the contents of that chest. If Anna is allowed to draw two keys, simultaneously and at random, from the bowl as the first contestant, what is the probability that she wins the prize?
A.15/256
B.3/32
C.1/16
D.1/8
Answer: D.1/8
Explanation: P(not winning) = 15/16*14/15 = 7/8
P(winning) = 1 - 7/8 = 1/8
The answer is D.
Question: The sum of two numbers is 35. Their difference is 5. The bigger number is
A.20
B.25
C.30
D.35
Answer: A.20
Explanation: X + Y = 35
X - Y = 5
Adding 2X = 40 ==> X = 20 and Y = 35 - 20 = 15
Bigger number is X = 20
Answer A.
Question: If a: b = 7: 5, b: c = 9: 11, find a: b: c?
A.63: 14: 55
B.63: 45: 55
C.14: 14: 15
D.7: 14: 15
Answer: B.63: 45: 55
Explanation: Explanation:
a: b = 7: 5
b: c = 9: 11
a: b: c = 63: 45: 55
Answer is B
Question: x = 13.165
y = 7.586
z = 11.545
The number A is obtained by first rounding the values of x, y, and z to the hundredths place and then adding the resulting values. The number B is obtained by first adding the values of x, y, and z and then rounding the sum to the hundredths place. What is the value of A – B?
A.0.01
B.0.02
C.0.03
D.0.1
Answer: D.0.1
Explanation: Rounding off the values:
x = 13.17
y = 7.59
z = 11.55
A = 13.17 + 7.59 + 11.55 = 32.31
x + y + z = 13.165 + 7.586 + 11.545 = 32.206
B = 32.21
A - B = 0.1
Option D
Question: The length of a rectangular garden is three times its width. If the area of the rectangular garden is 675 square meters, then what is the width of the rectangular garden?
A.14
B.15
C.16
D.17
Answer: B.15
Explanation: Let x be the width of the garden.
3x^2 = 675
x^2 = 225
x = 15
The answer is B.
Question: A and B can do a piece of work in 6 days. With the help of C they finish the work in 4 days. C alone can do that piece of work in?
A.10 DAYS
B.20 DAYS
C.25 DAYS
D.15 DAYS
Answer: B.20 DAYS
Explanation: C = 1/5 – 1/6 = 1/30 => 30 days
Answer:B
Question: It is required to fix a pipe such that water flowing through it at a speed of 7 metres per minute fills a tank of capacity 880 cubic metres in 10 minutes. The inner radius of the pipe should be :
A.√2 m
B.2 m
C.1⁄2 m
D.1⁄√2 m
Answer: B.2 m
Explanation: Let inner radius of the pipe be r.
Then, 880 = 22⁄7 × r2 × 7 × 10
or r2=880/22×10=4
or r = √4=2 m
Answer B
Question: If x and y are positive integers, and x^3*y^4 = 2,000, which of the following is the value of xy?
A.2
B.4
C.8
D.10
Answer: D.10
Explanation: x^3y^4 = (xy)^3 * y = 2000
a. if xy = 2 => 2^3 = 8, can't find y
b. xy = 4 (same as above)
c. xy = 8, 8^3 = 512; 2000/512 is not integer
d. xy = 10, 10^3 = 1000, y = 2000/1000 = 2
e. xy = 20, 20^3 = 8000 > 2000
so the answer is D
Question: If the ratio of a to b is 8 to 3 and the ratio of b to c is 1 to 5, what is the ratio of a to c?
A.8/15
B.1/3
C.2/5
D.4/5
Answer: A.8/15
Explanation: a:b =8:3 -- 1
b:c = 1:5
=>b:c = 3 :15 --2
From 1 and 2 , we get
a:c = 8:15
Answer A
Question: 150 men consume 1050 kg of rice in 30 days. In how many days will 70 men consume 980 kg of rice?
A.77 days
B.60 days
C.16 days
D.97 days
Answer: B.60 days
Explanation: Rate of consumption of each man = 1050/(150 * 30) = 7/30 kg/day
Let us say 70 men take x days to consume 150 kg.
Quantity consumed by each item in x days = (7x/30) kg
Quantity consumed by 70 men in x days = (7/30 x)(70) kg
= (7/30 x) * (70) = 960
x = 60 days.
Answer: B
Question: If (10^4 * 3.456789)^12 is written as a single term, how many digits would be to the right of the decimal place?
A.16
B.20
C.24
D.28
Answer: C.24
Explanation: 3.456789^12 has 6*12 = 72 decimal places.
10^48 moves the decimal place to the right 48 places.
(10^4 * 3.456789)^12 has 72-48 = 24 digits after the decimal point.
The answer is C.
Question: The cost of diamond varies directly as the square of its weight. Once, this diamond broke into four pieces with weights in the ratio 1 : 2 : 3 : 4. When the pieces were sold, the merchant got Rs. 70,000 less.
Find the original price of the diamond.
A.Rs. 1.4 lakh
B.Rs. 2 lakh
C.Rs. 1.4 lakh
D.Rs. 1 lakh
Answer: D.Rs. 1 lakh
Explanation: Explanation :
If we assume weight of diamond 10x. Well I came up with 10x because the ratio
Given 1 : 2 : 3 : 4 adds upto 10.
So, individual weights of diamonds will be x, 2x, 3x and 4x
Original price = k(10x)2
Price for pieces = k(x2 + 4x2 + 9x2 + 16x2) = k30x2
Thus change in price we see is 100kx2 - 30kx2 = 70kx2 which is given as 70,000.
Thus the original price 100kx2 will be 1,00,000.
Answer : D
Question: The Shopkeeper increased the price of a product by 25% so that customer finds it difficult to purchase the required amount. But somehow the customer managed to purchase only 70% of the required amount. What is the net difference in the expenditure on that product?
A.10%
B.11%
C.12.5%
D.13%
Answer: C.12.5%
Explanation: Quantity X Rate = Price
1 x 1 = 1
0.7 x 1.25 = 0.875
Decrease in price = (0.125/1) × 100 = 12.5%
C
Question: In a railway compartment, there are 2 rows of seats facing each other with accommodation for 5 in each, 4 wish to sit facing forward and 3 facing towards the rear while 3 others are indifferent. In how many ways can the 10 passengers be seated?
.
A.172000
B.12600
C.45920
D.43200
Answer: D.43200
Explanation: Start with the 4 people who want to face forward - for the first one, there are 5 options, for next one, 4 options and so on till we get 5*4*3*2.
Next, go on to 3 people who want to face back - for the first one, there are 5 options, for the next one, 4 options and so on till we get 5*4*3.
Now, we have 3 seats leftover and 3 indifferent people who can be arranged in 3*2*1 ways.
All in all, we can arrange 10 people in 5*4*3*2*5*4*3*3*2*1 = 14400 * 3 = 43200
Answer (D)
Question: If the arithmetic mean of x,y and z is 6 times the arithmetic mean of w, x and y. What is the value of the expression (x+y)?
A.(z-5w)/6
B.(z+6w)/5
C.(-z-5w)/6
D.(z-6w)/5
Answer: D.(z-6w)/5
Explanation: Arithmetic Mean 1 = (x+y+z)/3
Arithmetic Mean 2 = (w+x+y)/3
Arithmetic Mean 1=6*Arithmetic Mean 2
(x+y+z)/3=6*(w+x+y)/3
x+y+z=6w+6x+6y
x+y=(z-6w)/5
Hence, the correct answer is D
Question: How many seconds will a 800 metre long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
A.25
B.30
C.40
D.48
Answer: D.48
Explanation: Relative speed of the train=63-3=60kmph=60*5/18=50/3 m/sec
t=800*3/50=48sec
ANSWER:D
Question: A clock is observed by someone.
The hour hand is exactly at a minute mark, and the minute hand is six minutes ahead of it in the first glance.
When the clock is looked at again, the hour hand is exactly on a different minute mark, and the minute hand is seven minutes ahead of it this time.
Can you find out the time that has elapsed between the first and the second observation?
A.2 hours and 12 minutes
B.3 hours and 12 minutes
C.4 hours and 12 minutes
D.5 hours and 12 minutes
Answer: A.2 hours and 12 minutes
Explanation: Solution:
In the first observation, the time was 1:12. In the second observation, the time was 3:24.
Therefore, 2 hours and 12 minutes have elapsed
Answer A
Question: Walking 3/2 of his usual rate, a boy reaches his school 4 min early. Find his usual time to reach the school?
A.12
B.99
C.27
D.28
Answer: A.12
Explanation: Speed Ratio = 1:3/2 = 2:3
Time Ratio = 3:2
1 -------- 3
4 --------- ? 12 m.Answer:A
Question: In a class there are 20 boys and 25 girls. In how many ways can a boy and a girl be selected?
A.657 ways
B.500 ways
C.576 ways
D.545 ways
Answer: B.500 ways
Explanation: We can select one boy from 20 boys in 20 ways.
We select one girl from 25 girls in 25 ways
We select a boy and girl in 20 * 25 ways i.e., = 500 ways.
Answer: B
Question: A team of 8 persons joins in a shooting competition. The best marksman scored 85 points. If he had scored 92 points, the average score for the team would have been 84. The number of points, the team scored was
A.665
B.127
C.272
D.287
Answer: A.665
Explanation: Let the total score be x.
(x + 92 - 85) / 8 = 84.
So, x + 7 = 672 => x = 665.
Answer: A
Question: There is enough provisions for 600 men in an army camp for 35 days. If there were 300 men less, how long will the provision last?
A.40days
B.50days
C.60days
D.70days
Answer: D.70days
Explanation: Exp: We have, M1D1 = M2D2
600*35= 300* D2
D2 = 600*35/300 = 70 days.
Answer: D
Question: In a 4 person race, medals are awarded to the fastest 3 runners. The first-place runner receives a gold medal, the second-place runner receives a silver medal, and the third-place runner receives a bronze medal. In the event of a tie, the tied runners receive the same color medal. (For example, if there is a two-way tie for first-place, the top two runners receive gold medals, the next-fastest runner receives a silver medal, and no bronze medal is awarded). Assuming that exactly three medals are awarded, and that the three medal winners stand together with their medals to form a victory circle, how many different victory circles are possible?
A.24
B.52
C.96
D.144
Answer: C.96
Explanation: Gold can be awarded in 4 ways, then silver can be awarded in 3 ways and Bronze in 2 ways.
therefore the total number of ways are : 4*3*2=24ways of awarding the medals and the same number of ways of forming the circle.
This is when there is no tie. And if there is tie, for example all three receive the GOLD or the Silver or the Bronze, then there are 4 more cases. which implies 24*4=96. ANS:C
Question: An amount of Rs.20,000 is to be distributed amongst P, Q, R and S such that “P” gets twice as that of “Q” and “S” gets four times as that of “R”. If “Q” and “R” are to receive equal amount, what is the difference between the amounts received by S and P?
A.2378
B.2697
C.2697
D.5000
Answer: D.5000
Explanation: Explanation:
We have, P = 2Q & S = 4R
Further Q = R & P + Q + R + S = 20,000
Thus we get, 2Q + Q + Q + 4Q = 20,000
8Q = 20,000 or Q = Rs. 2500
Thus, R = Rs. 2500, P = 5000 & S = Rs. 10000
Hence, the required difference = (S – P) = (10000 – 5000) = Rs. 5000
ANSWER:D
Question: By selling 45 lemons for Rs 40, a man loses 20 %. How many should he sell for Rs 24 to gain 20 % in the transaction ?
A.16
B.18
C.20%
D.22
Answer: B.18
Explanation: Explanation:
Let S.P. of 45 lemons be Rs. x.
Then, 80 : 40 = 120 : x or x = 40x120/80 = 60
For Rs.60, lemons sold = 45
For Rs.24, lemons sold =45/60x24= 18. Answer: B
Question: If Doug can mow the lawn in 3 hours, and Julie can mow the same lawn in 6 hours, how long will it take for both of them to mow the lawn together?
A.1 hr
B.2 hr
C.3 hr
D.4 hr
Answer: B.2 hr
Explanation: If Doug can mow the lawn in 3 hours, then in 1 hour he can mow 1/3 of the lawn.
If Julie can mow the lawn in 6 hours, then in 1 hour she can mow 1/6 of the lawn.
Let x = number of hours it would take them together to mow the lawn so,
1/3 + 1/6 = 1/x
x=2 hours
Answer: B
Question: 60% of a number is added to 120, the result is the same number. Find the number?
A.150
B.200
C.300
D.150
Answer: C.300
Explanation: Explanation:
(60/100) * X + 120 = X
2X = 600
X = 300
C
Question: A train 220 meters 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?
A.12
B.6
C.7
D.8
Answer: A.12
Explanation: 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 = [220 * 3/55] sec = 12 sec
Answer: A
Question: The diameter of a cylindrical tin is 10 cm and height is 5 cm. Find the volume of the cylinder?
A.125
B.155
C.130
D.120
Answer: A.125
Explanation: r = 5 h = 5
π * 5 * 5 * 5 = 125 π cc
Answer:A
Question: A person walks from one end to the other of a 100-meter long moving walkway at a constant rate in 25 seconds, assisted by the walkway. When this person reaches the end, they reverse direction and continue walking with the same speed, but this time it takes 150 seconds because the person is traveling against the direction of the moving walkway. If the walkway were to stop moving, how many seconds would it take this person to walk from one end of the walkway to the other?
A.37
B.39
C.41
D.43
Answer: D.43
Explanation: Let v be the speed of the person and let x be the speed of the walkway.
25(v+x)=100 then 150(v+x)=600
150(v-x)=100
When we add the two equations:
300v=700
v=7/3
time = 100 / (7/3) = (300 / 7) seconds which is about 43 seconds
The answer is D.
Question: log base 10 root of 10 root of 10 root of 10..........infinity?
A.0
B.1
C.2
D.3
Answer: B.1
Explanation: root 10 of 10 of 10 ............infinity=10
so log base 10 of 10=1
ANSWER:B
Question: A 160 meter long train crosses a man standing on the platform in 6 sec. What is the speed of the train?
A.96 kmph
B.94 kmph
C.92 kmph
D.86 kmph
Answer: A.96 kmph
Explanation: S = 160/6 * 18/5 = 96 kmph
ANSWER:A
Question: If f(x)=x^3 and x is a natural number what CANNOT be a solution to f(x)?
A.1
B.8
C.27
D.36
Answer: D.36
Explanation: 36 is not a perfect cube. The answer is D.
Question: A person lent a certain sum of money at 4% per annum at simple interest and in 8 years the interest amounted to Rs.170 less than the sum lent. What was the sum lent?
A.228
B.278
C.250
D.500
Answer: C.250
Explanation: P - 170 = (P*4*8)/100
P = 250
Answer: C
Question: The number of new words that can be formed by rearranging the letters of the word 'ALIVE' is ?
A.287
B.266
C.119
D.166
Answer: C.119
Explanation: Number of words which can be formed = 5! - 1
= 120 - 1
= 119.
Answer:C
Question: A merchant marks his goods up by 50% and then offers a discount of 20% on the marked price. What % profit does the merchant make after the discount?
A.20%
B.25%
C.69%
D.31%
Answer: A.20%
Explanation: Let the price be 100.
The price becomes 150 after a 50% markup.
Now a discount of 20% on 150.
Profit=120-100
20%
answer A
Question: A rectangular field is 25 yards long and 12 yards wide. A fence is needed for the perimeter of the
field. Fencing is also needed to divide the field into three square sections. How many feet of fencing
are needed? (It is a good idea to make a drawing for this one.)
A.320 ft
B.273 ft
C.294 ft
D.330 ft
Answer: C.294 ft
Explanation: 25 + 12 + 25 +12 = 74 yds. for
outside of field.
12 + 12 = 24 yds. for dividing sections
74 + 24 = 98 yds. of fencing
98 x 3 = 294 ft. of fencing
correct answer C
Question: How many 4-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed?
A.40
B.400
C.5040
D.5400
Answer: C.5040
Explanation: 'LOGARITHMS' contains 10 different letters.
Required number of words	= Number of arrangements of 10 letters, taking 4 at a time.
= 10P4
= (10 x 9 x 8 x 7)
= 5040.
Answer: Option C
Question: In a certain store, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit?
A.60%
B.70%
C.80%
D.90%
Answer: B.70%
Explanation: Let C.P.= Rs. 100. Then, Profit = Rs. 320, S.P. = Rs. 420.
New C.P. = 125% of Rs. 100 = Rs. 125
New S.P. = Rs. 420.
Profit = Rs. (420 - 125) = Rs. 295.
Required percentage = 295/420	x 100	%	=	1475/21	% = 70% (approximately).
B)
Question: The radius of a cylindrical vessel is 8cm and height is 3cm. Find the whole surface of the cylinder?
A.308 sq cm
B.220 sq cm
C.440 sq cm
D.553.1 sq cm
Answer: D.553.1 sq cm
Explanation: r = 8 h = 3
2πr(h + r) = 2 * 22/7 * 8(11) = 553.1
ANSWER:D
Question: If the space diagonal of cube C is 5 inches long, what is the length, in inches, of the diagonal of the base of cube C?
A.5/(√6)
B.5·√(2/3)
C.5·√(3/2)
D.5·√3
Answer: B.5·√(2/3)
Explanation: n cube C, let's say that each side has side length x
So, the diagonal = √(x² + x² + x²) = √(3x²)
Here, we're told that the diagonal has length 5, so we can write:
5 = √(3x²)
Square both sides to get: 25 = 3x²
Divide both sides by 3 to get: 25/3 = x²
Square root both sides: √(25/3) = x
Or.... (√25)/(√3) = x
Simplify: 5/(√3) = x
ANSWER:B
Question: The number of stamps that Kaye and Alberto had were in the ration of 5:3 respectively. After Kaye gave Alberto 15 of her stamps, the ration of the number of Kaye had to the number of Alberto had was 4:3. As a result of the gift, Kaye had how many more stamps than Alberto?
A.20
B.30
C.70
D.60
Answer: C.70
Explanation: C
K1 = 5x
A1 = 3x
K2 = 5x - 15
A2 = 3x + 15
K2/A2 = 7/5
(5x-15)/(3x+15) = 4/3
3*(5x-15) = 4*(3x+15)
15x - 45 = 12x + 60
3x = 105
x = 35
K2 = 5*35 - 15 = 160
A2 = 3*35 + 15 = 90
K2 - A2 = 70
Answer : C
Question: The sum of four consecutive even numbers is 292. What would be the smallest number?
A.74
B.76
C.70
D.68
Answer: C.70
Explanation: Let the four consecutive even numbers be 2(x - 2), 2(x - 1), 2x, 2(x + 1)
Their sum = 8x - 4 = 292 => x = 37
Smallest number is: 2(x - 2) = 70.
ANSWER:C
Question: A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 700 m long?
A.287 Sec
B.190 Sec
C.187 Sec
D.286 Sec
Answer: B.190 Sec
Explanation: L = S*T
S= 1200/120
S= 10 m/Sec.
Total length (D)= 1900 m
T = D/S
T = 1900/10
T =190 Sec
Answer: B
Question: In a group of 28 junior high school students, 7 take French, 10 take Spanish, and 4 take both languages. The students taking both French and Spanish are not counted with the 7 taking French or the 10 taking Spanish. How many students are not taking either French or Spanish?
A.7
B.6
C.8
D.4
Answer: A.7
Explanation: A
7
Seven students are not taking a language. Add 7 + 10 + 4 to get 21. Then subtract 21 from the total students: 28 - 21 = 7.
Question: 70% of x is greater than 1/3rd of x by 110.what is x?
A.100
B.200
C.300
D.350
Answer: C.300
Explanation: 7x/10-x/3=110
11x/30=110
x=300
ANSWER:C