RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A 270 m long train running at the speed of 120 km/hr crosses another train running in opposite direction at the speed of 80 km/hr in 9 sec. What is the length of the other train?
A.230
B.783
C.291
D.112
Answer: A.230
Explanation: Relative speed = 120 + 80 = 200 km/hr.
= 200 * 5/18 = 500/9 m/sec.
Let the length of the other train be x m.
Then, (x + 270)/9 = 500/9 => x = 230.
Answer:A
Question: If a box contains 10 bulbs,of which just three are defective. If a random sample of five bulbs is drawn, find the probability that the sample contains no defective bulbs.
A.1/17
B.1/99
C.1/11
D.1/12
Answer: D.1/12
Explanation: Explanation:
Total number of elementary events = \inline {\color{Black}10C_{5}}
Number of ways of selecting no defective bulbs i.e., 5 non-defective bulbs out of 7 is \inline {\color{Black}7C_{5}}.
So,required probability =\inline {\color{Black}7C_{5}/10C_{5}} = 1/12.
Answer: D) 1/12
Question: If a:b = 4:8 and b:c = 3:2 find a:b:c?
A.3:8:4
B.3:4:8
C.3 : 6 : 4
D.4:6:3
Answer: C.3 : 6 : 4
Explanation: Explanation:
a:b = 4:8, b:c = 3:2
4:8
3:2
(a = 4 × 3 = 12, b = 8 × 3 = 24 and c = 8 × 2 = 16)
(a = a × b, b = b × b and c = b × c)
a:b:c = 12 : 24 : 16
a : b : c = 3 : 6 : 4
Answer: Option C
Question: A wheel that has 12 cogs is meshed with a larger wheel of 14 cogs. When the smaller wheel has made 21 revolutions, then the number of revolutions made by the larger wheel is:
A.9
B.10
C.6
D.18
Answer: D.18
Explanation: Explanation :
Let the required number of revolutions made by larger wheel be x.
Then, More cogs, Less revolutions (Indirect Proportion)
14:12::21:x => 14 * x = 21 * 12
=> x = (21 * 12)/14
=> x = 18
Answer : D
Question: A person walking at 4 Kmph reaches his office 8 minutes late. If he walks at 6 Kmph, he reaches there 8 minutes earlier. How far is the office from his house?
A.3 1/5 Km
B.2 1/5 Km
C.4 1/5 Km
D.5 1/5 Km
Answer: A.3 1/5 Km
Explanation: Formula = S1Ã—S2/S2-S1 Ã— T1+T2/60
= 4Ã—6/2 Ã— 16/6
= 24/2 Ã— 16/60
= 8 Ã— 2/5
= 16/5 = 3 1/5 Km
ANSWER IS A
Question: In a apartment, 30% of the people speak English, 20% speak Hindi and 10% speak both. If a people is selected at random, what is the probability that he has speak English or Hindi?
A.1/5
B.1/3
C.2/5
D.2/7
Answer: C.2/5
Explanation: P (E) = 30 / 100 = 3 / 10 , P (H) = 20 / 100 = 1 / 5 and P (E ∩ H) = 10 / 100 = 1 / 10
P (E or H) = P (E U H)
= P (E) + P (H) - P (E ∩ H)
= (3 / 10) + (1 / 5) - (1 / 10) = 4 / 10 = 2/5
C
Question: When tossed, a certain coin has an equal probability of landing on either side. If the coin is tossed 4 times, what is the probability that it will land on the same side each time?
A.1/4
B.1/6
C.1/8
D.1/12
Answer: C.1/8
Explanation: On the first toss, the coin will land on one side or the other.
On the second toss, the probability of landing on the same side is 1/2.
On the third toss, the probability of landing on the same side is 1/2.
On the fourth toss, the probability of landing on the same side is 1/2.
P(same side all four times)=1/2*1/2*1/2=1/8.
The answer is C.
Question: $4,000 is deposited in a savings account that pays 8% annual interest compounded semiannually. To the nearest dollar, how much is in the account at the end of the year?
A.$4326.40
B.$4116.20
C.$4256.21
D.$4316.54
Answer: A.$4326.40
Explanation: this is the case of semi-annual compoundingso, multiply time period by 2 and divide rate by 2
So,
new time=2periods and new rate=8/2=4%
Now,
CA=4000(1+4/100)^2=$4326.40
Hence answer is A
Question: A salesman’s terms were changed from a flat commission of 5% on all his sales to a fixed salary of Rs.1100 plus 2.5% commission on all sales exceeding Rs. 4,000. If his remuneration as per new scheme was Rs. 600 more than that by the previous schema, his sales were worth?
A.14000
B.12000
C.12019
D.12197
Answer: A.14000
Explanation: [1100 + (X-4000) * (2.5/100)] - X * (5/100)
= 600
X = 14000
Answer: A
Question: Suresh started a business with Rs.20,000. Kiran joined him after 4 months with Rs.30,000. After 2 more months, Suresh withdrew Rs.5,000 of his capital and 2 more months later, Kiran brought in Rs.20,000 more. What should be the ratio in which they should share their profits at the end of the year?
A.17:12
B.12:17
C.21:32
D.32:21
Answer: C.21:32
Explanation: Here capital is not the same.
Suresh invested 20000 for initial 6 months and 15000 for the next 6 months. Hence his term of ratio
=(20000×6+15000×6)
Kiran invested Rs.30000 for 4 months and Rs.50000 for next 4 months. Hence his term of ratio
=(30000×4+50000×4)
Suresh : Kiran
=(20000×6+15000×6) :(30000×4+50000×4)
=(20×6+15×6):(30×4+50×4)=(20×3+15×3):(30×2:50×2)
=105:160=21:32
Answer is C.
Question: The radius of a circular wheel is 1.75 m, how many revolutions will it make in traveling 1 km?
A.1000
B.2991
C.8216
D.2991
Answer: A.1000
Explanation: 2 * 22/7 * 1.75 * x
= 11000
x = 1000
Answer: A
Question: Harold and Millicent are getting married and need to combine their already-full libraries. If Harold, who has 1/2 as many books as Millicent, brings 1/3 of his books to their new home, then Millicent will have enough room to bring 1/3 of her books to their new home. What fraction of Millicent's old library capacity is the new home's library capacity?
A.1/2
B.2/3
C.3/4
D.4/5
Answer: A.1/2
Explanation: Because we see H willbring 1/3 of his booksto the new home --> try to pick a number that isdivisible by 3.
Before:
Assume H = 30 books
H = 1/2 M --> M = 60 books
After:
H' = 1/3H = 10 books
M' = 1/3M = 20 books
Total = 30 books
M' = 30 = 1/2*60
Ratio: 1/2
Ans: A
Question: 39 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work?
A.11
B.12
C.13
D.15
Answer: C.13
Explanation: First codition=total hours to complete the work=39 persons * 12 days * 5 hr
Second codition=total hours to complete the work=30 persons * x days * 6 hr
since the work is still the same so
39*12*5=30*x*6
x=13
answer :C
Question: Find the area of a cuboid of length 15cm , breadth 10 cm . and height 16cm.
A.2400 cm cube
B.2410 cm cube
C.2420 cm cube
D.2430 cm cube
Answer: A.2400 cm cube
Explanation: Area of a cuboid = lxbxh =15cm x 10cm x 16cm = 2400 cm cube
answer :A
Question: By purchasing an article at 20 % discount on the original price and then selling it at a price of 25% above the original price, a trader earns Rs. 200 as the profit. What was the original price of the article?
A.444.44
B.444.409
C.444.42
D.444.429
Answer: A.444.44
Explanation: Explanation:
Let the original price of the article be Rs. 100. Hence the purchase price for the trader would be Rs. 80 and his selling price would be Rs. 125. Thus, he would earn a profit of Rs. 45 (125 – 80). Therefore,
Profit is Rs. 45 if the original price is Rs. 100
Hence, if profit is Rs. 200, then original price will be..
= 100x 200/45
= Rs. 444.44
ANSWER: A
Question: If A lends Rs.3500 to B at 10% per annum and B lends the same sum to C at 15% per annum then the gain of B in a period of 3 years is?
A.525
B.500
C.510
D.530
Answer: A.525
Explanation: (3500*5*3)/100 => 525
Answer: A
Question: The ratio between the speeds of two trains is 7 : 8. If the second train runs 400 km in 4 hours, then the speed of the first train is:
A.87 km/hr
B.88 km/hr
C.87.5 km/hr
D.67 km/hr
Answer: C.87.5 km/hr
Explanation: Let the speed of two trains be 7x and 8x km/hr.
Then, 8x =(400/4)= 100
x =100/8= 12.5
Speed of first train = (7 x 12.5) km/hr = 87.5 km/hr.
ANSWER C
Question: If d and t are integers and d^2 – t^2 is an odd integer, which of the following must be an even integer?
I. d + t + 2
II. d^2 + 2dt + t^2
III. d^2 + t^2
A.None
B.I only
C.II only
D.III only
Answer: A.None
Explanation: d^2–t^2 is an odd integer means that either d is even and t is odd or d is odd and t is even.
Check all options:
I. d + t + 2 --> even+odd+even=odd or odd+even+even=odd. Discard;
II. d^2 + 2dt + t^2 --> even+even+odd=odd or odd+even+even=odd. Discard;
III. d^2 + t^2 --> even+odd=odd or odd+even=odd. Discard.
Answer: A.
Question: There are three different hoses used to fill a pool: hose U, hose y, and hose z. Hose U can fill the pool in a days, hose y in b days, and hose z in c days, where a > b > c. When all three hoses are used together to fill a pool, it takes d days to fill the pool. Which of the following must be true?
I. d<c
II. d>b
III. c/3<d<a/3
A.I
B.II
C.III
D.II &III
Answer: B.II
Explanation: Name T = full pool
U fills a pool in a days ==> 1 day U fills: T/a
Y fills a pool in b days ==> 1 day Y fills: T/b
Z fills a pool in c days ==> 1 day Z fills: T/c
1 day (U+Y+Z) together fill: T(1/a + 1/b + 1/c)
d days (U+Y+Z) together fill: T
==> d = T1 / T(1/a+1/b+1/c) = abc/(ab+bc+ca)
==>d = abc/(ab+bc+ca)
d cannot be greater than c ; d is greater than b ; d is greater than c/3 but not less than a/3
B
Question: Billy read 2 books. He read the first one in one week with 25 pages everyday. He read the second book in 12 days with 23 pages everyday. What is the total number of pages that Billy read?
A.251 pages
B.151 pages
C.751 pages
D.451 pages
Answer: D.451 pages
Explanation: Pages read in the first book in one week which is 7 days with 25 pages everyday.
25 ? 7 = 175 pages
Pages read in the second book in 12 days with 23 pages everyday.
23 ? 12 = 276 pages
Total number of pages read
175 + 276 = 451 pages
correct answer D
Question: If 2 men can color 50 m long cloth in 2 days, then 4 men can color 100 m long cloth in?
A.3 days
B.4 days
C.5 days
D.2 days
Answer: D.2 days
Explanation: The length of cloth painted by one man in one day = 50/ 2× 2 = 12.5 m
No. of days required to paint 100 m cloth by 4 men = 100/ 4 × 12.5 = 2 days
Answer : D
Question: Marla starts running around a circular track at the same time Nick starts walking around the same circular track. Marla completes 28 laps around the track per hour and Nick completes 13 laps around the track per hour. How many minutes after Marla and Nick begin moving will Marla have completed 4 more laps around the track than Nick?
A.5
B.8
C.12
D.16
Answer: D.16
Explanation: Maria's rate - 28 laps per hour --> 28/60 laps/min
Nick's rate - 13 laps per hour --> 13/60 laps/min
lets set equations:
28/60*t=4 (since Maria had to run 4 laps before Nick would start)
13/60*t=0 (Hick has just started and hasn't run any lap yet)
(28/60-13/60)*t=4-0 (since Nick was chasing Maria)
t=16 min needed Maria to run 4 laps
Answer : D
Question: By selling 32 carrots in a dollar, a man loses 40%. How many carrots must he sell in a dollar to gain 20% profit?
A.16
B.18
C.20
D.25
Answer: A.16
Explanation: This is a question that is much easier than it first appears. If you work with the percents directly, you can solve it very quickly. If the man sells 32 carrots for a dollar, he loses 40%. That means he is at 60% of his cost (100% - 40% = 60%). We are trying to figure out how many carrots he has to sell in order to make a 20% profit, or be at 120% (100% + 20% = 120%). 120% is double 60%, meaning that we simply cut the number of carrots in half to double our returns (from 60% to 120%), yielding 32/2 = 16 carrots, or answer choice A.
Question: A train 260 m long passed a pole in 40 sec. How long will it take to pass a platform 940 m long?
A.180
B.184
C.178
D.167
Answer: B.184
Explanation: Speed = 260/40= 6.5 m/sec.
Required time = (260 + 940)/6.5 = 184 sec.
Answer: Option B
Question: The ratio of the two natural numbers is 6 : 5. If a certain number is subtracted to both the numbers, the ratio becomes 5 : 4. If the larger number exceeds the smaller number by 5, find the number subtracted?
A.8
B.5
C.15
D.22
Answer: B.5
Explanation: Let the two numbers be 6x and 5x.
Let the numbers subtracted to both so that their ratio becomes 5 : 4 be k.
(6x - k) / (5x - k) = 5/4
=> 24x - 4k = 25x - 5k => k = x.
6x - 5x = 5 => x = 5
k = x = 5.
Answer:B
Question: On a playground, there is a number of children, out of which 1/4 wear red t-shirts, 1/20 wear blue t-shirts, and the remaining 14 children wear white t-shirts. How many children wear blue t-shirts?
A.6
B.20
C.1
D.3
Answer: C.1
Explanation: Let x be the number of children on the playground.
x/4+x/20=6x/20=3x/10 is the number of children who wear red and blue t-shirts
The number of the children who wear white t-shirts is x-3x/10=7x/10. Thus,
7x/10=14 implies x=20.
1/20*20=1. Hence, only 1 child wears a white t-shirt.
Answer C 1
Question: The number of cars present at a particular time was measured at 3,999 different locations on Tuesday and on Wednesday. The number of locations that had more cars on Wednesday was 20% higher than the number of locations that had more cars on Tuesday. How many of the locations had more cars on Tuesday?
A.1,159
B.1,333
C.1,817
D.2,460
Answer: C.1,817
Explanation: The question states that all these 3,999 locations were measured twice, once on each day.
It also breaks the 3,999 into two groups, the higher-on-Tuesday locations and the higher-on-Wednesday locations, which we can call T and W.
Therefore, we can write two equations:
For each of the first and second day count of locations, T + W = 3999
But, for the second day count, W = 1.20 T
i.e. for Second day count, T + 1.20T = 3999
i.e. 2.20 T = 3999
i.e. T = 1817
C
Question: The average (arithmetic mean) of y numbers is x. If 30 is added to the set of numbers, then the average will be x - 6. What is the value of y in terms of x ?
A.x/6 - 6
B.x/6 - 5
C.x/7 - 5
D.x/5 - 7
Answer: A.x/6 - 6
Explanation: (A1 + A2 + .. + Ay)/y = x
(A1 + A2 + .. + Ay + 30)/(y+1) = x - 6
=> (xy + 30)/(y+1) = x - 6
=> xy + 30 = yx -6y + x - 6
=> 36 = x - 6y
=> 6y = x - 36
=> y = x/6 - 6
Answer - A
Question: 1: 3 = 1 2/3: x. The value of x is?
A.1
B.3
C.4 1/6
D.5
Answer: D.5
Explanation: Explanation:
x * 1 = 3 * 5/3
x = 5
ANSWER IS D
Question: Two trains are traveling in the same direction at speeds of 50 kmph and 20 kmph respectively If the faster train passes the driver in the slower train in 20 seconds, What is the length of the faster train?
A.ANSWER: 169 m
B.ANSWER: 162 m
C.ANSWER: 136 m
D.ANSWER: 166 m
Answer: D.ANSWER: 166 m
Explanation: Explanation:
Given :
Speed of fast train = 50 kmph.
Speed of slow train = 20 kmph.
The driver in the slower train is moving with the speed of the slower train which is 20 kmph.
The faster train will pass the driver when it has gained a distance. Distance gained by faster train
in 1 hour = (50 – 20) = 30 km
= 8.33 m/sec
Distance gained by faster train in 20 sec = 20 * 8.33 = 166.6 m.
Therefore, Length of faster train = 166.6 m.
ANSWER:D
Question: For a particular American football game, the probability of a team's quarterback throwing an intercepted pass on each throw is 1/10. What is the least number of times that the quarterback will throw the ball that will increase the probability of throwing an intercepted pass at least once to more than 50%.
A.10
B.3
C.9
D.7
Answer: D.7
Explanation: Rule of Subtraction: P(A) = 1 - P(A')
Rule of Multiplication: P(A ∩ B) = P(A) P(B)
Probability quarterback throws an intercepted pass at least once in 2 throws is 1- (9/10)^2 = 1 - 81/100 = 11/100 < 50%
Probability quarterback throws an intercepted pass at least once in 3 throws is 1- (9/10)^3 = 1 - 729/1,000 = 271/1,000 < 50%
Probability quarterback throws an intercepted pass at least once in 4 throws is 1- (9/10)^4 = 1 - 6,561/10,000 = 4,439/10,000 < 50%
Probability quarterback throws an intercepted pass at least once in 5 throws is 1- (9/10)^5 = 40,951/100,000 < 50%
Probability quarterback throws an intercepted pass at least once in 5 throws is 1- (9/10)^6 = 468,559/1,000,000 < 50%
Probability quarterback throws an intercepted pass at least once in 5 throws is 1- (9/10)^7 = 5,217,031/10,000,000 > 50%
Answer: D
Question: A certain sum of money is invested for one year at a certain rate of simple interest. If the rate of interest is 3% higher, then the invest earned will be 25% more than the interest earned earlier. What is the earlier rate of interest?
A.28
B.65
C.89
D.12
Answer: D.12
Explanation: If the interest earned is 25% more than the earlier interest then the rate of interest also should be 25% higher than the earlier rate.
Let the earlier rate of interest be x%.
Now it will be (x + 3)%
% increase = (x + 3) - x/x * 100 = 25
=> x = 12.Answer: D
Question: In a new housing development, trees are to be planted along the sidewalk of a certain street. Each tree takes up one square foot of sidewalk space, and there are to be 14 feet between each tree. How many trees can be planted if the road is 151 feet long?
A.8
B.9
C.10
D.11
Answer: D.11
Explanation: Let T be the number of trees. Then the length required for trees on the sidewalk will be 1*T= T
To maximize the number of trees, the number of 14 feet spaces between trees should be 1 less than total number of trees.
For example, If there are 3 trees, then there should be 2 spaces between them.
So the number of 14 feet spaces will be T-1. Then, the length of sidewalk required for 14 feet spaces will be 14*(T-1)
It is given that total lenght of sidewalk is 166 feet.
or 14(T-1)+T = 151
or 14T-14+T = 151
or 15T = 165
or T=11
Answer:- D
Question: Month	Average Price
per Dozen
April $1.0
May $1.20
June $1.5
The table above shows the average (arithmetic mean) price per dozen of the large grade A eggs sold in a certain store during three successive months. If 2/3 as many dozen were sold in April as in May, and twice as many were sold in June as in April, what was the average price per dozen of the eggs sold over the three-month period?
A.1.1
B.1.29
C.1.32
D.1.42
Answer: B.1.29
Explanation: Say x dozen eggs were sold in May.
Then 2x/3 dozen eggs were sold in April and 2*2x/3=4x/3 dozen eggs were sold in May.
Total x+2x/3+4x/3=3x dozen eggs were sold in three months.
Total sales: 2x/3*1.+x*1.2+4x/3*1.5= $3.86x. The average price per dozen 3.86x/3x=$1.29.
B
Question: a/(b/c)
In the expression above, a, b, and c are different numbers and each is one of the numbers 2, 3, or 6. What is the largest possible value of the expression?
A.2/18
B.6/3
C.30/2
D.18/2
Answer: D.18/2
Explanation: a/(b/c)
= (a*c)/b
The expression will have the largest value when numerator (a*c) is the largest.
=(6*3)/2
=18/2
Answer D
Question: A certain quantity of 45% concentration solution is replaced with 15% concentration solution such that the concentration of the combined amount is 35%.
What's the ratio of the amount of solution that was replaced to the amount of solution that was not replaced?
A.1:3
B.1:2
C.2:3
D.2:1
Answer: B.1:2
Explanation: 15% - - - - - - - - - 35% - - - - - - 45%
From 15 to 35 =20
From 35 to 45 = 10
So the ratio is 20/10 = 2 to 1
B it is
Question: The L.C.M of two numbers is 48. The numbers are in the ratio 8:3. The sum of numbers is:
A.22
B.30
C.40
D.50
Answer: A.22
Explanation: Let the numbers be 8x and 3x.
Then, their L.C.M = 24x. So, 24x = 48 or x = 2.
The numbers are 16 and 6.
Hence, required sum = (16 + 6) = 22.
ANSWER:A
Question: Triangle STV has sides ST = TV = 25, and SV = 14. What is the area?
A.144
B.168
C.176
D.190
Answer: B.168
Explanation: Let the base B of the triangle be SV = 14. Then we need to find the height H.
H^2 = 25^2 - 7^2 = 576 and then H = 24.
The area is (1/2)*B*H = 7*24 = 168
The answer is B.
Question: Christine selects an item at a 25% off ticket price sale. The item is ticket priced at $25. How much should Christine expect to pay at the register?
A.22.5
B.20.0
C.18.75
D.12.5
Answer: C.18.75
Explanation: R.P.=$25.00
Sale%=25
S.P.=R.P.*(1-(Sale%/100))=25*(1-(25/100))=18.75
ANSWER:C
Question: The side of a rhombus is 26 m and length of one of its diagonals is 20 m. The area of the rhombus is?
A.529 sq m
B.240 sq m
C.260 sq m
D.480 sq m
Answer: D.480 sq m
Explanation: 262 – 102 = 242
d1 = 20 d2 = 48
1/2 * 20 * 48 = 480
ANSWER:D
Question: A person has to cover a distance of 10km in 1hour. If he covers one half of the distance in half of the total time; to cover the remaining distance in the remaining time, his speed must be?
A.5km/hr
B.8km/hr
C.10km/hr
D.12km/hr
Answer: C.10km/hr
Explanation: Remaining distance = 5km
Remaining time = 1/2 * 60 = 30min = 1/2 hour
Required speed = 5*2 = 10km/hr
Answer is C
Question: If integer k is equal to the sum of all even multiples of 25 between 295 and 615, what is the greatest prime factor of k?
A.5
B.7
C.11
D.13
Answer: B.7
Explanation: if we break down what the stem is asking what is the sum of all mult of 50 between 300 and 600.
using arithmetic progression to find n : 600 = 300 + (n - 1) 50
300+ 50 = 50n
350 = 50n => n = 7
the sum would be: 11* mean
mean = [600 + 300] / 2 = 450
7*450 = 4950
B
Question: A sum of money amounts to Rs.6690 after 3 years and to Rs.10,035 after 6 years on compound interest.find the sum.
A.4360
B.4460
C.4560
D.4660
Answer: B.4460
Explanation: Let the sum be Rs.P.then
P(1+R/100)3=6690 …(i) P(1+R/100)6=10035…(ii)
On dividing,we get (1+R/100)3=10025/6690=3/2.
Substituting this value in (i),we get:
P*(3/2)=6690 or P=(6690*2/3)=4460
Hence,the sum is Rs.4460. answer : B
Question: Two pipes A and B can fill a tank in 30 hours and 45 hours respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank?
A.18 hours
B.15 hours
C.10 hours
D.12 hours
Answer: A.18 hours
Explanation: Part filled by A in 1 hour = 1/30
Part filled by B in 1 hour = 1/45
Part filled by (A+B) in 1 hour = 1/30 + 1/45 = 5/90 = 1/18
Both the pipes together fill the tank in 18 hours
Answer is A
Question: There are r red ball, b blue ball and w white ball in a bag. What is the ratio of the number of blue ball to the total no. of ball in terms of r, b and w.?
A.r / (r + b + w)
B.(r + b + w)
C.r * (r + b + w)
D.(r + b + w)/r
Answer: A.r / (r + b + w)
Explanation: The total number of marbles is
r + b + w
The total ratio of blue marbles to the total number of marbles is
r / (r + b + w)
A
Question: The sum of two numbers is 56, and one of them is 12 more than the other. What are the two numbers?
A.36-48
B.22-34
C.60-24
D.42-42
Answer: B.22-34
Explanation: In this problem, we are asked to find two numbers. Therefore, we must let x be one of them. Let x, then, be the first number.
We are told that the other number is 12 more, x + 12.
The problem states that their sum is 56:
word problem = 56
The line over x + 12 is a grouping symbol called a vinculum. It saves us writing parentheses.
We have:
2x = 56 âˆ’ 12
= 44.
x = 44/2
= 22.
This is the first number. Therefore the other number is
x + 12 = 22 + 12 = 34.
The sum of 22 + 34 is 56.
B
Question: A man complete a journey in 10 hrs. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km?
A.876 km
B.224 km
C.657 km
D.176 km
Answer: B.224 km
Explanation: Let the total distance be x km.
Then, [(1/2 x) / 21 + (1/2 x) / 24] = 10
15x = 168 * 20 => x = 224 km.
Answer: B
Question: Find the sum of first 20 natural numbers
A.470
B.210
C.465
D.463
Answer: B.210
Explanation: Explanation:
Sum of n natural numbers
=n(n+1)/2
=20(20+1)/2=20(21)/2=210
Answer: Option B
Question: In a rectangular coordinate system, what is the area of a rectangle whose vertices have the coordinates (-3, 1), (1, 1), (1, -2) and (-3, -2)?
A.12
B.24
C.20
D.30
Answer: A.12
Explanation: Length of side 1= 3+1=4
Length of side 2= 2+1= 3
Area of rectangle= 4*3= 12
A is the answer
Question: If 6^k = 4, then 6^(2k+3) =
A.2925
B.3456
C.4581
D.3683
Answer: B.3456
Explanation: 6^k=4
6^2k=4^2
6^2k=16
6^(2k+3)
=6^2k*6^3
=16*216
=3456
Answer: B
Question: Magnabulk Corp sells boxes holding y magnets each. The boxes are shipped in crates, each holding b boxes. What is the price charged per magnet, in cents, if Magnabulk charges m dollars for each crate?
A.100by/m
B.m/(by)
C.by/(100m)
D.100m/(by)
Answer: D.100m/(by)
Explanation: We're given some facts to work with:
1) Magnabulk Corp sells boxes holding Y magnets each.
2) The boxes are shipped in crates, each holding B boxes.
3) Magnabulk charges M DOLLARS for each crate
We're asked for the price charged per magnet, in CENTS....
IF....
Y = 2
B = 3
M = 12
(2 magnets per crate)(3 crates) = 6 magnets
$12 for 6 magnets = $2 per magnet = 200 cents per magnet
So we're looking for an answer that equals 200 when Y=2, B=3 and M=12. There's only one answer that matches...
Answer is D