RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A rectangular parking space is marked out by painting three of its sides. If the length of the unpainted side is 9 feet, and the sum of the lengths of the painted sides is 37 feet, then what is the area of the parking space in square feet?
A.46
B.81
C.126
D.252
Answer: C.126
Explanation: Clearly, we have : l = 9 and l + 2b = 37 or b = 14.
∴ Area = (l × b) = (9 × 14) sq. ft. = 126 sq. ft.
Answer C
Question: To a sugar solution of 3 litres containing 40% sugar, one litre of water is added. The percentage of sugar in the new solution is
A.22
B.30
C.99
D.88
Answer: B.30
Explanation: Explanation:
Quantity of sugar = kg = 1.2 kg.
New percentage = = 30%.
Answer: B) 30
Question: A man saves Rs. 200 at the end of each year and lends the money at 5% compound interest. How much will it become at the end of 3 years?
A.Rs. 565.25
B.Rs. 635
C.Rs. 662.02
D.Rs. 666.50
Answer: C.Rs. 662.02
Explanation: Amount = [200(1 + 5/100)3 + 200(1 + 5/100)2 + 200(1 + 5/100)]
= [200 * 21/20(21/20 * 21/20 + 21/20 + 1)] = Rs. 662.02
ANSWER:C
Question: y = x2 + bx + 256 cuts the x axis at (h, 0) and (k, 0). If h and k are integers, what is the least value of b?
A.-32
B.-256
C.-255
D.-257
Answer: D.-257
Explanation: Explanatory Answer
The curve cuts the x axis at (h, 0) and (k, 0). So, h and k are the roots of the quadratic equation.
For a quadratic equation of the form ax2 + bx + c = 0, the sum of the roots = -b/a
The sum of the roots of this equation is -b/1 = -b.
Note: Higher the sum of the roots, lower the value of b.
For a quadratic equation of the form ax2 + bx + c = 0, the product of roots = c/a.
Therefore, the product of the roots of this equation = 256/1 = 256.
i.e., h * k = 256
h and k are both integers.
So, h and k are both integral factors of 256.
256 can be expressed as product of two numbers in the following ways:
1 * 256
2 * 128
4 * 64
8 * 32
16 * 16
The sum of the roots is maximum when the roots are 1 and 256 and the maximum sum is 1 + 256 = 257.
The least value possible for b is therefore -257.
The correct choice is (D)
Question: The salary of a worker is first increased by 30% and afterwards reduced by 30%. What is net change in his salary?
A.90% increase
B.45% increase
C.9% decrease
D.Same as before
Answer: D.Same as before
Explanation: (30 * 30)/100 = 9% decrease
ANSWER:D
Question: According to the directions on a packet of smoothie mix, 1 3-ounce packet of smoothie mix is to be combined with 10 ounces of water to make a smoothie. How many 3-ounce packets of smoothie mix are required to prepare 150 12-ounce smoothies?
A. 120
B. 150
C. 180
D. 240
Answer: B. 150
Explanation: This question wasn't particularly grueling, but I think it's the first where I had the opportunity to solve it via theory andinspectionthat many on this board suggest as strategy on the GMAT. It actually came to me by accident. Basically, if we thought that the 3 packets of powder were included in the 12 ounces of water, that would mean we would need 150 packets of smoothie mix (along with 12(150) ounces of water for a total of 150 packets. However, we know, after a more careful reading of the stimulus, that the 3 ounces are NOT included in the 12 ounces. As such, the answer has to be LESS than 150 packets, since 150 would be too much powder considering you already have 150(12) ounces of water and need less packets than water to make a smoothie. As such, the only answer less than 150 is 120, A. Does this make sense? Or am I way off base?
B
Question: The average of 9 observations was 9, that of the 1st of 5 being 10 and that of the last 5 being 8. What was the 5th observation?
A.9
B.12
C.15
D.17
Answer: A.9
Explanation: Explanation:
1 to 9 = 9 * 9 = 81
1 to 5 = 5 * 10 = 50
5 to 9 = 5 * 8 = 40
5th = 50 + 40 = 90 – 81 = 9
Option A
Question: The sale price sarees listed for Rs.400 after successive discount is 10% and 5% is?
A.338
B.277
C.342
D.882
Answer: C.342
Explanation: 400*(90/100)*(95/100) = 342
Answer: C
Question: Rs. 1581 is divided among A, B and C in the ratio 10 : 15 : 6. What is the share of B?
A.306
B.765
C.700
D.510
Answer: A.306
Explanation: 10+15+6=31
1581/31=51
so B's share=15*51
=765
A's share =10*51
=510
C's share =6*51
=306
ANSWER:A
Question: If P(A) = 4/5 and P (B) = 2/5, find P (A n B) if A and B are independent events.
A.8/25
B.1/25
C.2/25
D.3/14
Answer: A.8/25
Explanation: P (A n B) = P(A) . P(B)
P (A n B) = 4/5 . 2/5
P (A n B) = 8/25.
A
Question: A father is now three times as old as his son. Four years back, he was four times as old as his son. The age of the son (in years) is
A.A)12
B.B)15
C.C)18
D.D)20
Answer: A.A)12
Explanation: Explanation:
Let son's age be x years. Then, father's age = (3x) years.
Four years ago, father's age = (3x - 4) years and son's age = (x - 4) years.
So, 3x - 4 = 4 (x - 4)=> 3x - 4 = 4x - 16=> x = 12.
Answer: A
Question: If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance travelled by him is:
A.50 km
B.56 km
C.70 km
D.80 km
Answer: A.50 km
Explanation: Let the actual distance travelled be x km.
Then,	x/10	=	(x + 20)/14
=14x = 10x + 200
4x = 200
x = 50 km.
Answer :A
Question: If two numbers are in the ratio 2:3. If 10 is added to both of the numbers then the ratio becomes 3:4 then find the smallest number?
A.10
B.20
C.22
D.24
Answer: B.20
Explanation: 2:3
2x + 10 : 3x + 10 = 3 : 4
4[2x + 10] = 3[3x + 10]
8x + 40 = 9x + 30
9x - 8x = 40 - 30
x = 10
Then smallest number is = 2
2x = 20
B
Question: Rs. 6500 is divided into three parts A, B and C. How much A is more than C if their ratio is 1/2:1/3:1/4?
A.2000
B.1500
C.900
D.600
Answer: B.1500
Explanation: 1/2:1/3:1/4
= 6:4:3
3/13*6500
= 1500
Answer: B
Question: A train running at the speed of 60 km/hr crosses a pole in 3 seconds. What is the length of the train?
A.120 metres
B.180 metres
C.324 metres
D.50 metres
Answer: D.50 metres
Explanation: Speed=(60 x 5/18)/m/sec	=	50/3	m/sec.
Length of the train = (Speed x Time).
Length of the train =	50 x 3/3 m = 50 m.
ANSWER : OPTION 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 60% of the required amount. What is the net difference in the expenditure on that product?
A.25%
B.13%
C.15%
D.17%
Answer: A.25%
Explanation: Quantity X Rate = Price
1 x 1 = 1
0.6 x 1.25 = 0.75
Decrease in price = (0.25/1) × 100 = 25%
A)
Question: A bottle contains a certain solution. In the bottled solution, the ratio of water to soap is 3:4, and the ratio of soap to salt is five times this ratio. The solution is poured into an open container, and after some time, the ratio of water to soap in the open container is quartered by water evaporation. At that time, what is the ratio of water to salt in the solution?
A.26:64
B.64:9
C.9:64
D.9:60
Answer: C.9:64
Explanation: Water:soap = 3:4
Soap:Salt=15:20
=> For 15 soap, salt = 20
=> For 4 Soap, salt = (20/15)*4 = 80/15=16/3
So, water:soap:salt = 3:4:16/3= 9:12:16
After open container, water:soap:salt =2.25:12:16
So, water:salt = 2.25:16 = 9:64
ANSWER:C
Question: In an examination a pupil's average marks were 63 per paper. If he had obtained 20 more marks for his Geography paper and 2 more marks for his History paper, his average per paper would have been 64. How many papers were there in the examination?
A.8
B.9
C.10
D.22
Answer: D.22
Explanation: Let the number of papers be x. Then,
63x + 20 + 2 = 64x
= x = 22
ANSWER:D
Question: v, w, x, y, and z are five positive integers for which v≤w≤x≤y≤z. If the average (arithmetic mean) of the five numbers is 30 and their median is 25, which is the smallest possible value of z?
A.30
B.35
C.37
D.38
Answer: D.38
Explanation: sum=150
mid value = 25
minimize 'z'. So, 25 25 25 37 38
answer: D
Question: Sachin is younger than Rahul by 7 years. If the ratio of their ages is 7:9, find the age of Sachin
A.23.5
B.24.5
C.12.5
D.14.5
Answer: B.24.5
Explanation: Explanation:
If Rahul age is x, then Sachin age is x-7,
so (x-7)/x = 7/9
=> 9x-63 = 7x
=> 2x = 63
=> x = 31.5
So Sachin age is 31.5 - 7 = 24.5
Option B
Question: In an examination, a student's average marks were 63. If he had obtained 20 more marks for his Geography and 2 more marks for his history, his average would have been 65. How many subjects were there in the examination?
A.12
B.11
C.13
D.14
Answer: B.11
Explanation: Explanation:
Let the number of subjects = x
Then, total marks he scored for all subjects = 63x
If he had obtained 20 more marks for his Geography and 2 more marks for his history, his average would have been 65
=> Total marks he would have scored for all subjects = 65x
Now we can form the equation as 65x - 63x = additional marks of the student = 20 + 2 = 22
=> 2x = 22
=> x = 22/2 = 11
Answer: Option B
Question: If y and g are distinct prime numbers less than 10, which of the following cannot be the product of y and g?
A.6
B.9
C.10
D.14
Answer: B.9
Explanation: If y and g are distinct prime numbers less than 10 prime numbers less than 10 are 2, 3, 5, 7
all except 9 is product of any two numbers picked from above set.
Ans: B
Question: In a partnership, A invests 1/6 of the capital for 1/6 of the time, B invests 1/3 of the capital for 1/3 of the time and C, the rest of the capital for the whole time. Out of a profit of Rs.4600, B’s share is:
A.Rs.650
B.Rs.800
C.Rs.960
D.Rs.1000
Answer: B.Rs.800
Explanation: Suppose A invests x/6 for y/6 months.
B invests x/3 for y/3 months.
C invests x – x/6 + x/3 i.e x/2 for y months.
Therefore, A : B : C = x/6 * y/6 : x/3 * y/3 : x/2 * y = 1/36 : 1/9 : 1/2 = 1 : 4 : 18.
Therefore, B’s share = Rs. 4600 * 4/23
= Rs.800.
ANSWER:B
Question: if
2345 =62
6571 =73
then
8355 =?
A.93
B.94
C.95
D.96
Answer: B.94
Explanation: 2345
=(2*3)+(4*5)
=6+20
=26 reverse 62
6571
=(6*5)+(7*1)
=30+7
=37 reverse 73
so
8355
=(8*3)+(5*5)
=24+25
=49 reverse 94
ANSWER:B
Question: If n is an integer, f(n) = f(n-1) - n and f(4)=12. What is the value of f(6)?
A.1
B.0
C.-1
D.2
Answer: A.1
Explanation: Since f(n)=f(n-1)-n then: f(6)=f(5)-6 and f(5)=f(4)-5.
As given that f(4)=12 then f(5)=12-5=7 --> substitute the value of f(5) back into the first equation: f(6)=f(5)-6=7-6=1.
Answer: A.
Questions on funtions to practice:
Question: What should come in place of the question mark (X) in the following equation ?
60% of X + 2/3 of 39 = 44
A.50
B.60
C.30
D.20
Answer: C.30
Explanation: Explanation:
60% of X + 2/3 of 39 = 44
i.e. 3/5 of X + 2/3 of 39 = 44 (60% = 3/5)
3/5 * X + 2/3 * 39 = 44
3/5 * X + 26 = 44
3/5 * X = 18
X = 18 * 5/3
X = 30
ANSWER:C
Question: Of the teams competing in the world archery championships, Thirty percent are from Europe. Half as many are from the United States and one twentieth are from Africa. What fraction of teams are from neither Europe, the US or Africa.
A.10/20
B.15/20
C.13/15
D.17/20
Answer: A.10/20
Explanation: Assume 100 total people.
30% of 100 = 30 --->Europeans
1/2 of 30 ---> 15 Americans
1/20 of 100 ---> 5 Africans
Now you would add them all up, and minus it by the total (100). 100 - 50= 50. So, 50 people out of 100 are not EU, US or Africans. 50/100 is also equal to 10/20.
So therefore, the answer is A.
Question: 3 boys and 7 girls can complete John work in 10 days. 4 boys and 6 girls need 8 days to complete the same work . In how many days will 10 girls complete the same work?
A.10 days
B.20 days
C.40 days
D.60 days
Answer: C.40 days
Explanation: Work done by 4 boys and 6 girls in 1 day = 1/8
Work done by 3 boys and 7 girls in 1 day = 1/10
Let 1 man does m work in 1 day and 1 woman does w work in 1 day. The above equations can be written as
4m + 6w = 1/8 ---(1)
3m + 7w = 1/10 ---(2)
Solving equation (1) and (2) , we get m=11/400 and w=1/400
Amount of work 10 girls can do in John day = 10 × (1/400) = 1/40
Ie, 10 girls can complete the work in 40 days
C
Question: Reena took a loan of Rs. 1400 with simple interest for as many years as the rate of interest. If she paid Rs. 432 as interest at the end of the loan period, what was the rate of interest?
A.8.55%
B.5.55%
C.4.55%
D.6.55%
Answer: B.5.55%
Explanation: Let rate = R% and time = R years.
Then, (1400 * R * R) / 100 = 432
14R2 = 432
R2 = 30.8 => R = 5.55
ANSWER:B
Question: A metal company's old machine makes bolts at a constant rate of 100 bolts per hour. The company's new machine makes bolts at a constant rate of 150 bolts per hour. If both machines start at the same time and continue making bolts simultaneously, how many minutes will it take the two machines to make a total of 550 bolts?
A. 36
B. 72
C. 120
D. 132
Answer: D. 132
Explanation: Old Machine
100 bolts in 60 mins
so,
5/3 bolts in 1 min
New Machine
150 bolts in 60 mins
so,
5/2 bolts in 1 min
together,
5/3 + 5/2 =
25/6 bolts in 1 min
so, for 550 bolts
550 * 6 / 25 = 132 mins
Ans D
Question: Find the cost of fencing around a circular field of diameter 20 m at the rate of Rs.1.50 a meter?
A.287
B.94.2
C.156
D.158
Answer: B.94.2
Explanation: 2 * 22/7 * 10 = 62.8
62.8 * 1 1/2 = Rs.94.2
Answer: B
Question: A man buys an article for Rs. 27.50 and sells it for Rs 28.60. Find his gain percent
A.4%
B.2%
C.1%
D.3%
Answer: A.4%
Explanation: CP = 27.50
SP = 28.60
Gain = 28.60 - 27.50 = 1.10
gain % = gain/cost*100
(1.10/27.50*100)% = 4%
ANSWER A
Question: Meena wrote all the numbers from 1 to 59,999 inclusive. How many digits did she write in total?
A.248,889
B.268,889
C.288,889
D.308,889
Answer: C.288,889
Explanation: 1-9=>1*9 digits
10-99=>2*90=180 (numbers between 10-99 is 90 where each has 2 digits)
100-999=>3*900=2700
1000-9999=>4*9000 = 36,000
10000-59999=>5*50,000 = 250,000
The answer is 288,889
The answer is C.
Question: A company declared a semi-annual dividend of 12%. Find the annual dividend of Sam owing 2000 shares of the company having a par value of Rs. 10 each.
A.4000
B.4200
C.4400
D.4800
Answer: D.4800
Explanation: semi-annual dividend = 10×12/100 = Rs.1.2
Total semi-annual dividend = 2000 × 1.2 = Rs.2400
Total annual dividend = 2 × Rs.2400 = Rs.4800
Answer is D.
Question: A number when divided by the sum of 555 and 445 gives two times their difference as quotient and 30 as the remainder. The number is
A.1220
B.1250
C.22030
D.220030
Answer: D.220030
Explanation: Sol.
Required number = (555 + 445) x 2 x 110 + 30
= 220000 + 30
= 220030.
Answer D
Question: A train running at a speed of 36 km/h passes an electric pole in 14 seconds. In how many seconds will the whole train pass a 370-meter long platform?
A.45
B.47
C.49
D.51
Answer: D.51
Explanation: Let the length of the train be x meters.
When a train crosses an electric pole, the distance covered is its own length x.
speed = 36 km/h = 36000 m / 3600 s = 10 m/s
x = 14 * 10 = 140 m.
The time taken to pass the platform = (140 +370)/ 10 = 51 seconds
The answer is D.
Question: The amount of water (in ml) that should be added to reduce 6 ml. Lotion, containing 50% alcohol, to a lotion containing 30% alcohol, is?
A.8 ml
B.5 ml
C.4 ml
D.6 ml
Answer: C.4 ml
Explanation: 3 3
30% 70%
30% ----- 3
70% ------? => 7 - 3 = 4ml
Answer:C
Question: There are 4 prime numbers in ascending order. The multiplication of 1st 3 is 385 and that of last 3is 1001. what is the last number is
A.10
B.15
C.16
D.13
Answer: D.13
Explanation: Explanation:
abcbcd=3851001=>ad=513
abcbcd=3851001=>ad=513
So d = 13
D
Question: In a digital circuit which was to implement (A B) + (A)XOR(B), the designer implements (A B) (A)XOR(B) What is the probability of error in it ?
A.25%
B.35%
C.75%
D.45%
Answer: C.75%
Explanation: A	B	AB	A XOR B	(AB)+(A XOR B)	(AB) (A XOR B)
0	0	0	0	0	0
0	1	0	1	1	0
1	0	0	1	1	0
1	1	1	0	1	0
so, we are getting 3 wrong answers out of 4
probability of error is 3/4=75%
ANSWER:C
Question: In a consumer survey, 85% of those surveyed liked at least one of three products: 1, 2, and 3. 46% of those asked liked product 1, 30% liked product 2, and 20% liked product 3. If 5% of the people in the survey liked all three of the products, what percentage of the survey participants liked more than one of the three products?
A.6
B.10
C.15
D.20
Answer: A.6
Explanation: Use the forumla ;
Total = Group1 + Group2 + Group3 - (sum of 2-group overlaps) - 2*(all three) + Neither
100 = 46 + 30 + 20 - ( sum of 2) -2(5) +15
100 = 101-( sum of 2)
1 = sum of 2
so more than 1 = 6
A
Question: If the sides of a triangle are 32 cm, 27 cm and 12 cm, what is its area?
A.120 cm2
B.112 cm2
C.162 cm2
D.666 cm2
Answer: C.162 cm2
Explanation: The triangle with sides 32 cm, 27 cm and 12 cm is right angled, where the hypotenuse is 32 cm.
Area of the triangle = 1/2 * 27 * 12 = 162 cm2
Answer: C
Question: 65% of the employees of a company are men. 60% of the men in the company speak French and 40% of the employees of the company speak French. What is % of the women in the company who do not speak French?
A.4%
B.10%
C.97.14%
D.90.14%
Answer: C.97.14%
Explanation: No of employees=100(say)
Men=65
Women=35
Men speaking french=0.60*65=39
Employees speaking french=0.4*100=40
Therefore women speaking French=40-39=1
And women not speaking French=35-1=34
% of women not speaking French=34/35*100=97.14%
Answer C
Question: How many two digit numbers of distinct digits can be formed by using digits 3, 4, 5, 6 and 7 such that the numbers are divisible by 9?
A.1
B.2
C.3
D.4
Answer: D.4
Explanation: CONCEPT: A number will be divisible by 9 if sum of all the digits of the number is divisible by 9
Here the Possible sum of the two distinct digits can be 9 only in order to satisfy the given condition
If sum of Digits = 9, No. = 36, 45, 54, 63 --- 4 Cases
Answer: option D
Question: Today is Monday. After 61 days, it will be:
A.Wednesday
B.Saturday
C.Tuesday
D.Thursday
Answer: B.Saturday
Explanation: EXPLANATION
Each day of the week is repeated after 7 days.
So, after 63 days, it will be Monday.
After 61 days, it will be Saturday.
Answer B
Question: The cost of 3 pens and 5 pencils is Rs.150. Also the cost of one pen and one pencil is in the ratio of 5:1 respectively. What is the cost of one dozen pens?
A.Rs.200
B.Rs.250
C.Rs.300
D.Rs.450
Answer: D.Rs.450
Explanation: Explanation:
Let the cost of one pen is ‘5x’ and pencil is ‘x’
3 X 5x + 5x = Rs.150
15x + 5x = Rs.150
X = 150/20 = 7.50
:. Cost of 1 pen = 5x = 5 x 7.50 = 37.50
:. Cost of 12 pens, i.e. (one dozen) = 37.50x 12 = Rs.450
Answer: Option D
Question: A certain galaxy is known to comprise approximately 6 x 10^11 stars. Of every 50 million of these stars, one is larger in mass than our sun. Approximately how many stars in this galaxy are larger than the sun?
A.800
B.1,250
C.8,000
D.12,000
Answer: D.12,000
Explanation: 6*10^11
50 mln = 5*10^7
we divide 10^11 by 10^7 and we get (10^4)*6 = 60,000 and divide by 5. the result is 12,000
D
Question: If a certain number is divided by 12, the quotient, dividend, and divisor, added together, will amount to 64. What is the number?
A.18
B.28
C.48
D.38
Answer: A.18
Explanation: Let x = the number sought.
Then x/12 + x + 12 = 64.
And x - 624/13 = 48.
Question: If A:B = 1/2: 1/3 B:C = 1/2:1/3 then A:B:C?
A.9:6:4
B.2:3:3
C.1:2:6
D.2:3:5
Answer: A.9:6:4
Explanation: A:B = 1/2:1/3 = 3:2
B:C = 1/2:1/3 = 3:2
--------------------
A:B:C = 9:6:4
ANSWER A
Question: If x-y=8, which of the following must be true?
I. Both x and y are positive
II. If x is positive, y must be positive
III. If x is negative, y must be negative
A.I only
B.II only
C.III only
D.I and II
Answer: C.III only
Explanation: The best way to approach such questions is to plug in values for x and y
Given: x-y=8
I. Both x and y are positive:
Let x=10 and y=2
x-y=8
But,
Let x=6 and y=-2
x-y=8
Therefore, NOT TRUE
II. If x is positive, y must be positive
Let x=10 and y=2
x-y=8
But,
Let x = 6 and y=-2
x-y=8
Therefore, NOT TRUE
III. If x is negative, y must be negative
If x is negative, for the expression x-y=8 to be true, y must be a -ve number. Otherwise, the sum of two negative numbers will yield another negative number!
Therefore, TRUE
Ans: 'C'
Question: A student completes a 3 part exam as follows. The student completes sections A in 4 minutes and takes an equal time to complete the two remaining sections. What is the ratio of time spent on section C to section A if the total duration is 1 hour?
A.10:3
B.9:2
C.7:1
D.8:3
Answer: C.7:1
Explanation: The time spent on section B and section C is 28 minutes each.
The ratio of C to A is 28:4 = 7:1
The answer is C.
Question: The average of 11 numbers is 10.9. If the average of first six is 10.5 and that of the last six is 11.1 the sixth number is?
A.9.7
B.10
C.10.5
D.11.5
Answer: A.9.7
Explanation: Explanation:
1 to 11 = 11 * 10.9 = 119.9
1 to 6 = 6 * 10.5 = 63
6 to 11 = 6 * 11.1 = 66.6
63 + 66.6 = 129.6 – 119.9 = 9.7
6th number = 9.7
Option A
Question: Every year an amount increases by 1/8th of itself. How much will it be after two years if its present value is Rs.70400?
A.89100
B.81028
C.27772
D.29889
Answer: A.89100
Explanation: 70400* 9/8 * 9/8 = 89100.Answer:A
Question: John can divide his herd into 5 equal parts and also to 6 equal parts, but not to 9 equal parts. What could be the number of cows John has in his herd?
A.180
B.336
C.456
D.120
Answer: D.120
Explanation: On first look B, C,E are not divisible either by 5 or 6 - ruled out.
A,D divisible by both 5,6, but 180 is divisible by 9.
Answer : D
Question: What is the ratio between perimeters of two squares one having 11 times the diagonal then the other?
A.3: 8
B.3: 6
C.3: 7
D.11: 1
Answer: D.11: 1
Explanation: d = 11d d = d
a√2 = 11d a√2 = d
a = 11d/√2 a = d/√2 => 11: 1
Answer:D
Question: If the sum of two numbers is 55 and the H.C.F. and L.C.M. of these numbers are 5 and 120 respectively, then the sum of the reciprocals of the numbers is equal to:
A.11/122
B.11/120
C.11/121
D.11/140
Answer: B.11/120
Explanation: Explanation:
Let the numbers be a and b.
Then, a + b = 55 and ab = 5 x 120 = 600.
The required sum
Answer: B) 11/120
Question: A and B starts a business with Rs.8000 each, and after 7 months, B withdraws half of his capital . How should they share the profits at the end of the 18 months?
A.18:11
B.22:13
C.23:12
D.36:25
Answer: D.36:25
Explanation: A invests Rs.8000 for 18 months, but B invests Rs.8000 for the first 7 months and then withdraws Rs.4000. So, the investment of B for remaining 11 months is Rs.4000 only.
A : B
8000*18 : (8000*7) + (4000*11)
144000 : 100000
A:B = 36:25
ANSWER:D
Question: The number 50 is divided into two equal parts, the ratio of the largest part to the smallest is 2/3, then the largest part is?
A.30
B.35
C.40
D.45
Answer: A.30
Explanation: assume two numbers are x and y
x/y = 2/3.. 2x = 3y ----1
The number 50 is divided into two equal parts. If you make equal parts there is no question of Largest part and Smallest Part. So assuming 50 is devided in to two parts.
x+ y = 50 ---- 2
simplyfy 1 and 2 x =30 and y = 20
ANSWER:A
Question: How many W ways can you group 3 people from 4 sets of twins if no two people from the same set of twins can be chosen?
A.3
B.16
C.28
D.32
Answer: D.32
Explanation: Ways to select 3 people from 8 people (4 twins x 2) = 8C3 = 56
Ways to select 1 twin + 1 people = 4C1*6C1 = 24
Ways to select a group 3 people from 4 sets of twins if no two people from the same set of twins can be chosen W= 56 - 24 = 32
Ans: D
Question: Two boys starting from the same place walk at a rate of 5kmph and 5.5kmph respectively. What time will they take to be 8.5km apart, if they walk in the same direction?
A.67 hours
B.47 hours
C.17 hours
D.27 hours
Answer: C.17 hours
Explanation: Explanation:
In this type of questions we need to get the relative speed between them,
The relative speed of the boys = 5.5kmph â€“ 5kmph
= 0.5 kmph
Distance between them is 8.5 km
Time = Distance/Speed
Time= 8.5km / 0.5 kmph = 17 hrs
Answer: C
Question: The speed of the boat in still water in 12 kmph. It can travel downstream through 60 kms in 3 hrs. In what time would it cover the same distance upstream?
A.8 hours
B.6 hours
C.4 hours
D.15 hours
Answer: D.15 hours
Explanation: Still Water=12km/hr
Downstream=60/3=20km/hr
Upstream=>> still water=(u+v/2) =>> 12=u+20/2 = 4km/hr
So time taken in upstream = 60/4 =15hrs
ANSWER:D