RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Akash leaves Chennai at 6am & reaches Bangalore at 10am. Prakash leaves Hyderabad at 8 am and reaches Chennai at 11:30 am. At what time do they cross each other?
A.5 : 54am
B.6 : 56am
C.8 : 56am
D.9 : 56am
Answer: C.8 : 56am
Explanation: Time taken by Akash = 4 h
Time taken by Prakash = 3.5 h
For your convenience take the product of times taken by both as a distance.
Then the distance = 14km
Since, Akash covers half of the distance in 2 hours(i.e at 8 am)
Now, the rest half (i.e 7 km) will be coverd by both prakash and akash
Time taken by them = 7/7.5 = 56 min
Thus , they will cross each other at 8 : 56am.
C
Question: A sock drawer contains seven socks, each one a different solid color. The colors of the socks are red, orange, yellow, green, blue, indigo, and violet. If a person reaches into the drawer and pulls out two socks, how many different color combinations are possible in the selected pair of socks?
A.12
B.15
C.21
D.36
Answer: C.21
Explanation: Since here order of socks is not important then we'll have 7C2 i.e. 21 combinations.
If order is important then we would have got 42 socks...
ANS option C is correct answer..
Question: if the average of 6 consecutive number is 27, then the largest of the number is?
A.27.5
B.28.5
C.29
D.29.5
Answer: D.29.5
Explanation: x+x+1+x+2+x+3+x+4+x+5/6=27
6x+15=162
x=24.5
x+5=29.5
ANSWER:D
Question: Rs.1200 divided among P, Q and R. P gets half of the total amount received by Q and R. Q gets one-third of the total amount received by P and R. Find the amount received by R ?
A.Rs. 1100
B.Rs. 500
C.Rs. 1200
D.Rs. 700
Answer: B.Rs. 500
Explanation: Explanation:
Let the amounts to be received by P, Q and R be p, q and r.
p + q + r = 1200
p = 1/2 (q + r) => 2p = q + r
Adding 'p' both sides, 3p = p + q + r = 1200
=> p = Rs.400
q = 1/3 (p + r) => 3q = p + r
Adding 'q' both sides, 4q = p + q + r = 1200
=> q = Rs.300
r = 1200 - (p + q) => r = Rs.500.
ANSWER IS B
Question: For any a and b that satisfy |a – b| = b – a and a > 0, then |a + 5| + |-b| + |b – a| + |ab| =
A.a-b
B.2a-2b
C.2a-2b-5
D.ab + 2b + 5
Answer: D.ab + 2b + 5
Explanation: Observation-1: |a – b| = b – a
which is possible only when signs of a and b are Same
Since Given a > 0
so we figure out that a and b are both positive
Observation-2: |a – b| must be Non-Negative and so should be the value of b-a which is possible only when absolute value of b is greater than or equal to absolute value of a
Now you may choose the values of a and b based on above observations
e.g. b = 5 and a=1 and check the value of given functions and options
|a + 5| + |-b| + |b – a| + |ab| = |1 + 5| + |-5| + |5 – 1| + |1*5| = 20
ab + 2b + 5= 1*5+10+5=20
all other options are not equal to 20
Answer : D
Question: In a can, there is a mixture of milk and water in the ratio 1 : 5. If it is filled with an additional 2 litres of milk the can would be full and ratio of milk and water would become 2 : 5. Find the capacity of the can?
A.14
B.44
C.48
D.50
Answer: A.14
Explanation: Let the capacity of the can be T litres.
Quantity of milk in the mixture before adding milk = 1/6 (T - 2)
After adding milk, quantity of milk in the mixture = 2/7 T.
2T/7 - 2 = 1/6(T - 2)
5T = 84 - 14 => T = 14.
Answer:A
Question: A, B and C started a business with capitals of Rs. 8000, Rs. 10000 and Rs. 12000 respectively. At the end of the year, the profit share of B is Rs. 1500. The difference between the profit shares of A and C is?
A.621
B.276
C.236
D.600
Answer: D.600
Explanation: Explanation:
Ratio of investments of A, B and C is 8000 : 10000 : 12000 = 4 : 5 : 6
And also given that, profit share of B is Rs. 1500
=> 5 parts out of 15 parts is Rs. 1500
Now, required difference is 6 - 4 = 2 parts
Required difference = 2/5 (1500) = Rs. 600
Answer: D
Question: Gold is 19 times as heavy as water and copper 9 times as heavy as water. The ratio in which these two metals be mixed so that the mixture is 15 times as heavy as water is:
A.1 : 2
B.2 : 3
C.3 : 2
D.19: 135
Answer: C.3 : 2
Explanation: Explanation:
This question can be solved using weighted average formula. If two quantities of weights m, n have concentrations x, y are mixed then, final concentration = mx+ny/m+n
Take 1 unit of gold and x units of copper.
1×19+x×9/1+x=15⇒19+9x=15+15x
⇒x=2/3
So they are to be mixed in the ratio 1 : x = 1:2/3 or 3 : 2
Correct Option: C
Question: A began a business with Rs. 85,000. He was joined afterwards by B with Ks. 42,500. For how much period does B join, if the profits at the end of the year are divided in the ratio of 3 : 1 ?
A.4 months
B.5 months
C.6 months
D.8 months
Answer: D.8 months
Explanation: Suppose B joined for x months . Then, ( 85000 * 12 )/(42500 * x) = 3. or x = (85000 * 12) / (42500 * 3) = 8.
So, B joined for 8 months.ANSWER D
Question: The length of the bridge, which a train 160 metres long and travelling at 45 km/hr can cross in 30 seconds, is:
A.200 m
B.215 m
C.245 m
D.250 m
Answer: B.215 m
Explanation: Let the length of the bridge:L
The equation now is L+160/12.5m/s(45km/hr or12.5m/s)=30
Solving, L =215m
ANSWER:B
Question: In 1950, John was 4 times as old as Tom. In 1955, Richard was 3 times as old as Tom. In which year was John twice as old as Tom?
A. 1960
B. 1970
C. 1972
D. 1975
Answer: B. 1970
Explanation: In 1950: Jo = 4 To-------------- eq1
In 1955: Jo +5 = 3(To+5)---------eq2
Thus in 1950, solving eq1 and eq2
Jo = 10 , Jo =40
Now for each year we can calculate:
1960: Jo = 50 , To=20
1965: Jo = 55, To=25
1970: Ri= 60, Ro = 30
Thus Ans:B
Question: In the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30. In the sport formulation, the ratio of flavoring to corn syrup is three times as great as in the standard formulation, and the ratio of flavoring to water is half that of the standard formulation. If a large bottle of thesportformulation contains 5 ounces of corn syrup, how many ounces of water does it contain?
A.15
B.30
C.45
D.75
Answer: D.75
Explanation: Standard:
Fl: Corn S: Water = 1:12:30
Sport:
Fl: Corn S: Water = 3:12:180
This simplifies to 1:4:60
If the large bottle has a capacity of x ounces, then
4x / 65 = 5.
So, x = 325 / 4 ounces.
Water = (60 / 65) * (325 / 4) = 60 * 3 / 4 = 75 ounces.
Ans D
Question: Alice has 3 times the number of stamps that Doris does and Jane has 7 stamps more than Doris does. If Alice, Doris, and Jane each increase their number of stamps by 4, which of the following must be true after each person increases her number of stamps?
Alice has more stamps than Jane.
Jane has 3 more stamps than Doris.
The sum of the numbers of stamps that Alice and Doris have is a multiple of 4.
A.None
B.III only
C.I and III only
D.II and III only
Answer: B.III only
Explanation: Let Alice, Doris and jane have A, D and J stamps initially.
We know that
A =3D
and
J=d+7
After addition of 4 stamps they'll have A+4, D+4, and J+4 stamps respectively.
Lets analyze each statements:
Alice has more stamps than Jane.
this can be written as
A+4 > J+4
=> 3D+4 > D+7+4
=>D >7/3
It may not be true for many values of D.. D could very well be equal to 1,2 etc for which D<7/3. Not correct.
Jane has 3 more stamps than Doris.
this can be written as
J+4 = (D+4)+3
=> D+7+4 = D+4+3
Clealy not correct for any value of D.
The sum of the numbers of stamps that Alice and Doris have is a multiple of 4.
(A+4)+(D+4) = 4k, where k is any integer
=> 3D+4+D+4 =4k
=> 4D+8 = 4K
=> 4(D+2) = 4K
or K = D+2 .. clearly possible for any value of D. Hence Correct.
Hence Ans B. Only iii is correct.
Question: Eesha bought two varities of rice costing 50Rs per kg and 60 Rs per kg and mixed them in some ratio.Then she sold that mixture at 70 Rs per kg making a profit of 20 % What was the ratio of the micxture?
A.1 : 9
B.1 by 5
C.1 : 7
D.1 : 3
Answer: B.1 by 5
Explanation: Selling price of the mixture = 70 and profit = 20%
Cost price of the mixture = 70×100120=70×5670×100120=70×56
By applying alligation rule:
So ratio = 60−1753:1753−5060−1753:1753−50 = 1 : 5
Answer:B
Question: A train covers a distance of 12 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?
A.999
B.279
C.120 metre
D.99
Answer: C.120 metre
Explanation: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/ sec = 20 m/sec.
Length of the train = 20 * 6
= 120 m.
Answer: C
Question: A certain experimental mathematics program was tried out in 2 classes in each of 34 elementary schools and involved 40 teachers. Each of the classes had 1 teacher and each of the teachers taught at least 1, but not more than 3, of the classes. If the number of teachers who taught 3 classes is n, then the least and greatest possible values of n, respectively, are
A.0 and 13
B.0 and 14
C.1 and 10
D.1 and 9
Answer: B.0 and 14
Explanation: One may notice that greatest possible values differ in each answer choice in contrast to the least values, which repeat.
To find out the greatest value you should count the total classes (34*2=68), then subtract the total #of teachers since we know from the question that each teacher taught at least one class (68-40=28). Thus we get a number of the available extra-classes for teachers, and all that we need is just to count how many teachers could take 2 more classes, which is 28/2 = 14. So the greatest possible value of the # of teachers who had 3 classes is 14.
Only answer B has this option.
Question: In a pair of fractions, fractions A is twice the fraction B and the product of two fractions is 2/25. What is the value of fraction A?
A.1/5
B.1/25
C.2/5
D.3/5
Answer: C.2/5
Explanation: a=2b
ab=2/25
2b*b=2/25
b^2=1/25
b=1/5
a=2/5
ANSWER:C
Question: A boat running downstream covers a distance of 22 km in 4 hours while for covering the same distance upstream, it takes 5 hours. What is the speed of the boat in still water?
A.5 kmph
B.4 kmph
C.4.75 kmph
D.4.95 kmph
Answer: D.4.95 kmph
Explanation: Speed Downstream = 22/4 = 5.5 kmph
Speed Upstream = 22/5 =4.4 kmph
Speed of the boat in still water = 5.5+4.4/2=4.95 kmph
Answer : Option D
Question: What is the least number of squares tiles required to pave the floor of a room 15 m 17 cm long and 9 m 2 cm broad?
A.814 tiles
B.800
C.100
D.200
Answer: A.814 tiles
Explanation: Length of largest tile = H.C.F. of 1517 cm and 902 cm = 41 cm.
Area of each tile = (41 x 41) cm2.
Required number of tiles = (1517 x 902)/41 x 41 = 814.
Answer:A
Question: In how many different ways can the letter of the word 'BOTTLE ' be arranged in such a way that the vowels occupy the odd positions?
A.63
B.48
C.85
D.52
Answer: B.48
Explanation: In the given word there 6 letters in that there are 2 vowels and 4 consonants
no of ways of arranging the vowels=2p2=2
no of ways of arranging the consonants=4p4=24
total number of ways 24*2=48
Answer(B)
Question: Evaluate (51 + 52 + 53 + ... + 100)
A.3775
B.3665
C.3456
D.3459
Answer: A.3775
Explanation: Sn = (1 + 2 + 3 + ... + 50 + 51 + 52 + ... + 100) - (1 + 2 + 3 + ... + 50)
= (50 x 101) - (25 x 51)
= (5050 - 1275)
= 3775.
Option A
Question: The sum of two consecutive integers is 31. Find the numbers.
A.17, 18
B.7, 8
C.15, 16
D.1, 2
Answer: C.15, 16
Explanation: n + (n + 1) = 31
2n + 1 = 31
2n = 30
n = 15
Answer: C
Question: There are two examinations rooms A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates are sent from B to A, then the number of students in A is double the number of students in B. The number of students in room A is:
A.20
B.80
C.100 students
D.200
Answer: C.100 students
Explanation: Let the number of students in rooms A and B be x and y respectively.
Then, x - 10 = y + 10
x - y = 20 .... (i)
and x + 20 = 2(y - 20)
x - 2y = -60 .... (ii)
Solving (i) and (ii) we get: x = 100 , y = 80.
The required answer A = 100.
ANSWER:C
Question: A number lock on a suitcase has 3 wheels each labelled with 10 digits from 0 to 9. If opening of the lock is a particular sequence of three digits with no repeats, how many such sequences will be possible?
A.720
B.760
C.680
D.780
Answer: A.720
Explanation: On first wheel there can be 10 digits. On the second wheel there will be one of the 9 digits and on the third wheel there will be 8 digits. Therefore, the number of numbers is
10 x 9 x 8 = 720
ANSWER:A
Question: The original price of a camera was displayed as a whole dollar amount. After adding sales tax of 8 percent, the final price was also a whole dollar amount. Which of the following could be the final price of the camera?
A.$115
B.$101
C.$100
D.$108
Answer: D.$108
Explanation: Final price = (1+8/100) * Original Price
= 1.08* Original Price
From options given only 108 is divisible by 1.08 as it is stated OP is whole dollar amount.
Hence D
Question: A candidate who gets 30% of the marks fails by 50 marks. But another candidate who gets 45% marks gets 25 marks more than necessary for passing. Find the number of marks for passing?
A.276 Marks
B.200 Marks
C.186 Marks
D.187 Marks
Answer: B.200 Marks
Explanation: 30% ------------ 50
45% ------------ 25
----------------------
15% ------------- 75
30% -------------- ?
150 + 50 = 200 Marks
Answer: B
Question: If four coins are tossed, the probability of getting two heads and two tails is?
A.3/8
B.3/9
C.3/7
D.3/56
Answer: A.3/8
Explanation: Since four coins are tossed, sample space = 24
Getting two heads and two tails can happen in six ways.
n(E) = six ways
p(E) = 6/24 = 3/8
Answer: A
Question: A tour group of 25 people paid a total of $630 for entrance to a museum. If this price included a 5% sales tax, and all the tickets cost the same amount, what was the face value of each ticket price without the sales tax?
Choices
A.$22
B.$23.94
C.$24
D.$25.20
Answer: C.$24
Explanation: Soln:-
630/25=x+0.05x
630/25=1.05x
x=(630*100)/(25*105)
=63*10*4/21*5=24
ANSWER:C
Question: After getting 2 successive discounts, a shirt with a list price of Rs 150 is available at Rs 105. If the second discount is 12.55,find the first discount
A.38%
B.15%
C.20%
D.12%
Answer: C.20%
Explanation: Let the first discount be x%
Then,87.5% of (100-x)% of 150= 105
87.5/100*(100-x)/100*450=150=>105=>100-x=(105*100*100)/(150*87.5)=80
x=(100-80)=20
first discount = 20%
Ans: C
Question: A father can do a certain job in x hours. His son takes twice as long to do the job. Working together, they can do the job in 6 hours. How many hours does the father take to do the job?
A.9
B.18
C.12
D.20
Answer: A.9
Explanation: Explanatory Answers
The father completes the job in x hours.
So, the son will take 2x hours to complete the same job.
In an hour, the father will complete 1/x of the total job.
In an hour, the son will complete 1/2x of the total job.
So, if the father and son work together, in an hour they will complete 1/x + 1/2x of the job.
i.e., in an hour they will complete 3/2x of the job.
The question states that they complete the entire task in 6 hours if they work together.
i.e., they complete 1/6<sup>th</sup> of the task in an hour.
Equating the two information, we get 3/2x = 1/6
Cross multiplying and solving for x we get 2x = 18 or x = 9.
The father takes 9 hours to complete the job.
Answer A
Question: A 2-year certificate of deposit is purchased for Q dollars. If the certificate earns interest at a n annual rate of 6 percent compound quarterly, which of the following represents the value, in dollars, of the certificate at the end of 2 years?
A.k(1.06)^2
B.k(1.06)^8
C.k(1.015)^2
D.Q(1.015)^8
Answer: D.Q(1.015)^8
Explanation: Annual Rate of interest= 6%
Quaterly rate of interest= 6/4% = 1.5%
Now, periods of compounding in 2 years= 8 (8 quarters)
Thus Q(1.015)^8
Answer: D
Question: Walking 6/5 of his usual rate, a boy reaches his school 4 min early. Find his usual time to reach the school?
A.22
B.99
C.27
D.24
Answer: D.24
Explanation: Speed Ratio = 1:6/5 = 5:6
Time Ratio = 6:5
1 -------- 6
4 --------- ? 24 m.Answer:D
Question: 12 persons can complete the work in 18 days. after working for 6 days, 4 more persons added to complete the work fast. in how many more days they will complete the work?
A.10 days
B.9 days
C.8 days
D.7 days
Answer: B.9 days
Explanation: total work 12*18=216 units
after 6 days work finished 6*12=72 units
remaining work 216-72=144 units
remaing days =144(12+4)=9 days
ANSWER:B
Question: An investor invests in a new fund. The fund averages 20% growth annually for the first three years, but it loses 25% of its value in the fourth year. At the end of four years, the value of the fund is approximately what percent of the original amount?
A.135.7%
B.129.6%
C.123.5%
D.117.4%
Answer: B.129.6%
Explanation: 0.75*1.2^3 = 1.296
The answer is B.
Question: If 0 < a < b and k = (2a + 6b)/b , which of the following must be true?
A.k < 2
B.k < 7
C.k < 8
D.k > 9
Answer: C.k < 8
Explanation: Here's another approach:
k = (2a + 6b)/b
= 2a/b + 6b/b
= 2(a/b) + 6
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) + 6
From here, we can see that k must be less than 8
Answer: C
Question: A man buys an article and sells it at a profit of 20%. If he had bought it at 20% less and sold it for Rs.78 less, he could have gained 25%. What is the cost price?
A.s.370
B.s.375
C.s.375
D.s.390
Answer: D.s.390
Explanation: CP1 = 100 SP1 = 120
CP2 = 80 SP2 = 80 * (125/100) = 100
20 ----- 100
78 ----- ? => 390
ANSWER:D
Question: If 25% of a number exceeds 8% of it by 11.9, then find the number?
A.76
B.70
C.55
D.65
Answer: B.70
Explanation: Use the elimination method to find the correct option.
Of all the options only 70 fits
25% of 70 = 17.5
8% of 70 = 5.6
17.5 - 5.6 = 11.9
Required number is 70.
ANSWER:B
Question: A CAR MOVES AT THE SPEED OF 80KM/HR. WHAT IS THE SPEED OF THE CAR IN METRES PER SECOND?
A.8 m/sec
B.20 1/9 m/sec
C.22 2/0 m/sec
D.Cannot be determined
Answer: C.22 2/0 m/sec
Explanation: SPEED = (80*5/18)M/SEC=200/9 M/SEC = 22 2/9 M/SEC.
CORRECT OPTION: C
Question: Three 6 faced dice are thrown together. The probability that no two dice show the same number on them is ?
A.5/8
B.5/9
C.5/1
D.5/3
Answer: B.5/9
Explanation: No two dice show same number would mean all the three faces should show different numbers. The first can fall in any one of the six ways. The second die can show a different number in five ways. The third should show a number that is different from the first and second. This can happen in four ways.
Thus 6 * 5 * 4 = 120 favourable cases.
The total cases are 6 * 6 * 6 = 216.
The probability = 120/216
=5/9.
Answer:B
Question: 6 2/3 * 9 3/5 * 2 1/3 + 1 1/3 = ?
A.150 1/3
B.150 2/3
C.149 2/3
D.149 1/3
Answer: B.150 2/3
Explanation: Explanation:
6 2/3 * 9 3/5 * 2 1/3 + 1 1/3 = 20/3 * 48/5 * 7/3 + 4/3
= 448/3 + 4/3 = 452/3 = 150 2/3
ANSWER IS B
Question: Parameshwaran invested an amount of 12,000 at the simple interest rate of 10 pcpa and another amount at the simple interest rate of 20 pcpa. The total interest earned at the end of one year on the total amount invested became 14 pcpa. Find the total amount invested
A.22,000
B.25,000
C.20,000
D.24,000
Answer: C.20,000
Explanation: Let the amount invested at 20% rate be x. According to the question,
12000 × 10⁄100 + x × 20⁄100 = (12000 + x) × 14⁄100
or, 1200 + x⁄5 = 1680 + 7⁄50x
or, x⁄5 - 7⁄50x = 480
or, 3⁄50x = 480
\ x = 8000
\ Total amount invested = (12000 + 8000)= 20000
Answer C
Question: There are 10 members from that a total of 6 men & 4 ladies a committee of 3 is to be formed. If Mrs. A is not willing to join the committee in which Mr. B is a member, whereas Mr.B is willing to join the committee only if Mrs C is included, how many such committee are possible?
A.43
B.54
C.65
D.91
Answer: D.91
Explanation: We first count the number of committee in which
(i). Mr. Y is a member
(ii). the ones in which he is not
case (i): As Mr. Y agrees to be in committee only where Mrs. Z is a member.
Now we are left with (6-1) men and (4-2) ladies (Mrs. X is not willing to join).
We can choose 1 more in5+\inline {\color{Blue} 2C_{1}}=7 ways.
case (ii): If Mr. Y is not a member then we left with (6+4-1) people.
we can select 3 from 9 in \inline {\color{Blue} 9C_{3}}=84 ways.
Thus, total number of ways is 7+84= 91 ways.
D
Question: In a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. The duration of the flight is?
A.1 hr
B.3 hr
C.2 hr
D.6 hr
Answer: A.1 hr
Explanation: A
1 hr
Let the duration of the flight be x hours. Then,
600/x - 600/(x + 1/2) = 200
x(2x + 1) = 3 2x2 + x - 3 = 0
(2x + 3)(x - 1) = 0
x = 1 hr
Question: The price of a cycle is reduced by 25 per cent. The new price is reduced by a further 40 per cent. The two reductions together are equal to a single reduction of
A.45%
B.55%
C.35%
D.32.5%
Answer: B.55%
Explanation: Price = p
initially price reduced by 25% which means new price is 3/4P
Now on this new price further 40percent is reduced which means the new price is merely 60percent of 3/4P
==> (3/4)x(3/5)P = 9/20P is the new price after both deduction which is 45percent of the original value P. This implies this entire series of deduction is worth having discounted 55% of P. So answer is B = 55%
Question: One pump drains one-half of a pond in 8 hours, and then a second pump starts draining the pond. The two pumps working together finish emptying the pond in one-half hour. How long would it take the second pump to drain the pond if it had to do the job alone?
A.1 hour
B.1.1 hour
C.3 hours
D.5 hours
Answer: B.1.1 hour
Explanation: First pump drains 1/2 of the tank in 8 hours
so 16 hours it will take to drain the full tank.
Let, 2nd pump drains the full tank in a hours
so both together can drain (1/16+1/a) part in 1 hour
son in 1/2 hour they drain 1/2*(1/16+1/a) part of the tank
given that in 1/2 hour they drain 1/2 of the tank
hence we can say
1/2*(1/16+1/a) = 1/2
solving u get a = 16/15=1.1
Hence answer is B
Question: At what rate of compound interest per annum will a sum of $1200 becomes 1348.32 in 2 years?
A.5%
B.6%
C.7%
D.8%
Answer: B.6%
Explanation: Let the rate be R% p.a.
1200*(1+R/100)^2 = 1348.32
(1+R/100)^2 = 134832/120000 = 11236/10000
(1+R/100)^2 = (106/100)^2
1+R/100 = 106/100
R = 6%
Answer is B
Question: If two numbers are in the ratio 5:2. If 20 is subtracted from both of the numbers then the ratio becomes 4:2 then find the smallest number?
A.30
B.20
C.40
D.50
Answer: C.40
Explanation: 5:2
5x - 20 : 3x - 20 = 4 : 2
2[5x - 20] = 4[3x - 20]
10x - 40 = 12x - 80
12x - 10x = 80 - 40
x = 20
Then smallest number is = 2x
2x = 40
C
Question: In his pocket, a boy has 3 red marbles, 5 blue marbles, and 5 green marbles. How many will he have to take out of his pocket to ensure that he has taken out at least one of each color?
A.9
B.10
C.11
D.12
Answer: C.11
Explanation: The worst case scenario would be that he has taken 5 blue and 5 green, a total of 10 marbles, and still doesn't have 3 distinct colors. But the next draw, marble number 11, will surely be red as only the red marbles are left in his pocket.
The answer is C.
Question: What is the ratio W of the surface area of a cube to the surface area of a rectangular solid identical to the cube in all ways except that its length has been doubled?
A.1/4
B.3/8
C.1/2
D.3/5
Answer: D.3/5
Explanation: Let X be the side of the cube. Therefore X^2*6= surface area.
the rectangle is the same other than length is 2X. The width and height are the same as the cube. 2*W*H+2*W*L+2*H*L= 2X^2+4X^2+4X^2= 10X^2.
6X^2/10X^2 = 3/5 = W.
Answer = D
Question: A fruit seller had some apples. He sells 40% apples and still he has 420. Originally he had how many apples?
A.400
B.500
C.700
D.450
Answer: C.700
Explanation: Suppose originally he had x apples
then (100-40)% of x = 420
60x/100 = 420
x= 700
Answer is C
Question: If two girls starting from same point, walking in the opposite directions with 5km/hr and 10km/hr as average speeds respectively. Then the distance between them after 5 hours is?
A.45
B.55
C.65
D.75
Answer: D.75
Explanation: Explanation:
Total distance = Distance traveled by person A+ Distance traveled by person B
= (5Ã— 5) + (10Ã— 5)
= 25+ 50
= 75 Km
Answer:D