RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Machine–A produces 40% of the total output and Machine-B produces 60% of the total output. An average of nine units out of a thousand goods manufactured by Machine-A and one unit of 250 units produced by Machine-B prove to be defective. What is the probability that a unit chosen at random from the total daily output of the factory is defective?
A.0.6
B.0.06
C.0.006
D.0.0006
Answer: C.0.006
Explanation: Suppose machine A produce 1000 units
total defective = 9
Machine B then produces=1500 units
total defective=6
probability=15/2500
=0.006
C . correct
Question: The diagonals of a rhombus are 11 cm and 16 cm. Find its area?
A.277
B.266
C.150
D.88
Answer: D.88
Explanation: 1/2 * 11 * 16 = 88
Answer: D
Question: A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn. If the area of the lawn is 2109 sq. m, then what is the width of the road?
A.2
B.3
C.5
D.6
Answer: B.3
Explanation: Area of the park = (60 x 40) m2 = 2400 m2.
Area of the lawn = 2109 m2.
Area of the crossroads = (2400 - 2109) m2 = 291 m2.
Let the width of the road be x metres. Then,
60x + 40x - x2 = 291
x2 - 100x + 291 = 0
(x - 97)(x - 3) = 0
x = 3.
B)
Question: 20-3*5^2+15 = ?
A.287
B.-40
C.-73
D.13
Answer: B.-40
Explanation: 20-3*5^2+15=-40
B
Question: A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
A.40 sec
B.50 sec
C.44 sec
D.49 sec
Answer: A.40 sec
Explanation: Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 360 + 140 = 500 m
Required time = 500 * 2/25 = 40 sec
Answer:A
Question: I have an amount of Rs 10 lakh, which I went to invest in stocks of some companies. I always invest only amounts that are multiples of Rs 1 lakh in the stock of any company. If I can choose from among the stocks of five different companies, In how many ways can I invest the entire amount that I have?
A.252
B.250
C.1001
D.1089
Answer: C.1001
Explanation: Solution:
The situation is similar to placing 10 identical balls among 5 distinguishable boxes, where a box may have zero or more balls in it.
This case can be represented as arranging ten balls and (5-1) four walls in the single row, which can be done in 14C4 ways.(The balls placed between every successive pair of walls belong to one group) 14C4 = 1001 ways.
Answer: Option C
Question: Which of the following is closer to √0.5+√0.1?
A.0.5
B.0.7
C.0.9
D.1.0
Answer: D.1.0
Explanation: √0.5+√0.1=approximately √0.49+√0.09=0.7+0.3=1.0. Hence, the correct answer is D.
Question: How long will it take for a sum of money to grow from Rs.2000 to Rs.10,000, if it is invested at 10% p.a simple interest?
A.8 years
B.64 years
C.72 years
D.40 years
Answer: D.40 years
Explanation: In this case, Rs. 2000 has become Rs.10,000.
Therefore, the interest earned = 10,000 – 2000 = 8000
Interest for Rs 2000 @ 10% for 1 year = 200
200 - 1
8000 - ? => 40 years
Answer : D
Question: Mike and Emily need to build 2 identical houses. Mike, working alone, can build a house in 6 weeks. Emily, working alone, can build a house in 8 weeks. To determine who will do the building they will roll a fair six-sided die. If they roll a 1 or 2, Mike will work alone. If they roll a 3 or 4, Emily will work alone. If they roll a 5 or 6, they will work together and independently. What is the probability both houses will be completed after 7 weeks?
A.0
B.1/3
C.1/2
D.2/3
Answer: B.1/3
Explanation: The only way for the 2 houses to get done in under 7 weeks is if they work together. If Mike works alone - it would take him 12 weeks to build 2 houses. If Emily works alone, it would take 16 weeks. The check for this is below.
Together, they have a rate of 6∗86+86∗86+8 per house. Knowing that they'll need 2, we get 2∗(6∗86+8)=6672∗(6∗86+8)=667
Knowing this - the only way to complete in under 7 weeks is to work together - we can move on to the probability. This is very simple: 2 sides of the dice (a 5 or a 6) out of 6 possible outcomes is 2/6, which reduces to 1/3.. The Answer is B.
Question: Micky has 10 different letters and 5 different envelopes with him. If he can only put one letter in an envelope, in how many ways can the letters be put in the envelopes?
A.5!
B.5555
C.10C5 * 5!
D.10C5∗5510C5∗55
Answer: C.10C5 * 5!
Explanation: The Q basically wants us to choose 5 letters from the 10 and then place it in envelopes..
choosing 5 letters out of 10 =10C5..
these 5 letters can be placed in 5! ways in 5 envelope..
total ways = 10C5*5!
ANSWER:C
Question: A cube of edge 15cm is immersed completely in a rectangular vessel containing water. If the dimensions of the base of vessel are 20cm * 14cm , find the rise in water level?
A.6cm
B.12.05cm
C.11.25cm
D.15.12cm
Answer: B.12.05cm
Explanation: Increase in volume = volume of the cube = 15*15*15 cm^3
Rise in water level = volume / area = 15*15*15/20*14 = 12.05cm
Answer is B
Question: The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
A.255
B.267
C.245
D.277
Answer: C.245
Explanation: Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (130 + x)/30 = 25/2 => 2(130 + x) = 750 => x = 245 m. Answer:C
Question: How many arrangements of the letters of the word SPECIAL can be made, without changing the place of the vowels in the word?
A.24
B.26
C.28
D.32
Answer: A.24
Explanation: E,I,A fixed. Consonants can be arrangements in 4P4 = 4! = 24 ways
Option 'A'
Question: Juan is a gold medalist in athletics. In the month of May, if Juan takes 9 seconds to run y yards, how many seconds will it take him to run x yards at the same rate?
A.10x/y
B.11x/y
C.9x/y
D.12x/y
Answer: C.9x/y
Explanation: velocity=distance/time;
since he ran at same rate both d tyms,
y/9=x/t
so t=9x/y
ANSWER:C
Question: The Arnolds purchased 550 square feet of Kentucky Gem sod at $1.69 per square foot and 270 square feet of Zelzea Blue sod at $1.38 per square foot. What was the approximate average price per square foot paid for all the sod?
A.$1.59
B.$1.64
C.$1.68
D.$1.72
Answer: A.$1.59
Explanation: Average price = (550*1.69)+(270*1.38)/550+270=1.59 (Approx)
Answer A
Question: In how much time will a train of length 100 m, moving at 36 kmph cross an electric pole?
A.15 sec
B.22 sec
C.18 sec
D.10 sec
Answer: D.10 sec
Explanation: Explanation:
Convert kmph to mps. 36 kmph = 36 * 5/18 = 10 mps.
The distance to be covered is equal to the length of the train.
Required time t = d/s = 100/10 = 10 sec.
ANSWER IS D
Question: If a, b, r are integers, 33 = abr, and a < b < r, what is the smallest possible value of a?
A.-33
B.-3
C.1
D.3
Answer: A.-33
Explanation: Given : a * b * r = 33.
33 is a Positive Odd number.Side Note:Thus, all 3 numbers will be odd.
Prime factorization will also give you numbers. 1, 3, 11. The 3 numbers will be combination of these 3 numbers with possible variation in sign(+/-).
We could have any 2 digits as negative. --> negative * negative * positive. We have negative values in answer option, so eliminate C, D and E from answer choices.
-33 * -1 * 1 = 33.
Correct answer is A
Question: 15.06 * 0.00001 = ?
A.15060000
B.0.0001506
C.0.01506
D.0.1506
Answer: B.0.0001506
Explanation: Explanation:
Clearly after decimal 7 digits should be there.
Option B
Question: Ram professes to sell his goods at the cost price but he made use of 900 grms instead of a kg, what is the gain percent?
A.11 1/7%
B.11 7/7%
C.11 1/9%
D.71 1/9%
Answer: C.11 1/9%
Explanation: 900 --- 100
100 --- ? => 11 1/9%
Answer:C
Question: If the C.I. on a sum for 2 years at 12 1/2 % per annum is Rs. 510, the S.I. on the same sum at the same rate for the same period of time is?
A.333
B.2877
C.278
D.480
Answer: D.480
Explanation: Explanation:
Let the sum be Rs. P. Then,
[P(1 + 25/(2 * 100))2 - P] = 510
P[(9/8)2 - 1] = 510.
Sum = Rs. 1920
So, S.I. = (1920 * 25 * 2) / (2 * 100) = Rs. 480
Answer: D
Question: If a: b :: 3 : 7, then what is (5a+6b): (a-b)?
A.57:11
B.-57:4
C.11 : 10
D.-11 : 10
Answer: B.-57:4
Explanation: a/b= 3/7
Dividing numerator & denominator of ' (5a+6b)/(a-2b) 'by b,
[5(a/b)+6]/[(a/b)-1]= [5*(3/7)+6]/[(3/7)-1]= -57/4
B
Question: Tough and Tricky questions: Coordinate Geometry.
Line L contains the points (2,3) and (a,q). If q = 2, which of the following could be the equation of line m, which is perpendicular to line L?
A. 2x + y = ax + 7
B. 2x + y = –ax
C. x + 2y = ax + 7
D. y – 7 = x ÷ (a – 2)
Answer: A. 2x + y = ax + 7
Explanation: we need m=a-2, so we should gety=mx+bform in answer choices
(A) 2x+y=ax+7 => y=ax-2x+7 => y=x(a-2)+7. It is what we need
(B) 2x + y = –ax => y=-px-2x => y=x(-a-2). Wrong
(C) x + 2y = ax + 7 => y=x(a-1/2)+7/2. Wrong
(D) y – 7 = x ÷ (a – 2) => y=(1/a-2)x+7. Wrong
(E) 2x + y = 7 – ax => y=-ax-2x+7 => y=x(-a-2)+7. Wrong
A=answer
Question: Seven children — A, B, C, D, E,— are going to sit in seven chairs in a row. The children CE have to sit next to each other, and the others can sit in any order in any remaining chairs. How many possible configurations are there for the children?
A.600
B.720
C.48
D.4320
Answer: C.48
Explanation: for such questions , we can treat both as one then total person=4..
these 4 can be arranged in 4! ways.. but within these 4, one consists of two people who can be arranged in 2 ways CF or FC.. so ans =4!*2=48
ans C
Question: It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. It takes 20 minutes more, if 200 km is done by train and the rest by car. The ratio of the speed of the train to that of the car is?
A.3:9
B.3:3
C.3:4
D.3:1
Answer: C.3:4
Explanation: Let the speed of the train be x km/hr and that of the car be y km/hr.
Then, 120/x + 480/y = 8 or 1/x + 4/y = 1/15 --- (i)
And, 200/x + 400/y = 25/3 or 1/x + 2/y = 1/24 --- (ii)
Solving (i) and (ii), we get x = 60 and y = 80
Ratio of speeds = 60:80 = 3:4
Answer: C
Question: A can go round a circular path 8 times in 40 minutes. If the diameter of the circle is increased to 10 times the original diameter, then the time required by A to go round the new path once, travelling at the same speed as before is
A.20 min
B.35 min
C.50 min
D.70 min
Answer: C.50 min
Explanation: Solution
Let original diameter be d metres. Then, its circumference = (Πd)metres.
Time taken to cover (8Πd)m = 40 min.
New diameter = (10d)m. Then, its circumference = (Π x 10d)m.
Time taken to go round it once
‹=› [40 / 8Πd x 10Πd]m
‹=›50 min.
Answer C
Question: In a jar there are 20 white balls, 24 green balls and 32 blue balls. How many balls must be taken out in order to make sure we have 22 balls of the same color?
A.a)	23
B.b)	46
C.c)	57
D.d)	63
Answer: D.d)	63
Explanation: Here, we need to find minimum number of marbles to be taken out to get 22 marbles of same color.
For a instance, if we take 21 white marbles 1st and followed by 22 Green and then 22 Blue.
Total will be 20 + 21+ 21= 62 draws.
If we choose either Green or Blue next time. This will bring the total of either of these colored marble to 22.
So Minimum we need to take 62+1 = 63 Times to get 22 marbles of same color(either Green or Blue).
Answer : D.
Question: In a fort, there are 1200 soldiers. If each soldier consumes 3 kg per day, the provisions available in the fort will last for 30 days. If some more soldiers join, the provisions available will last for 25 days given each soldier consumes 2.5 kg per day. Find the number of soldiers joining the fort in that case?
A.568
B.528
C.567
D.872
Answer: B.528
Explanation: Assume X soldiers join the fort. 1200 soldiers have provision for 1200(days for which provisions last them)(rate of consumption of each soldier)
= 1200(30)(3) kg
Also provisions available for (1200 + x) soldiers is (1200 + x)(25)(2.5) kg
As the same provisions are available
=> 1200(30)(3) = (1200 + x)(25)(2.5)
x = [1200(30)(3)]/[(25)(2.5)] - 1200
Answer: B
x = 528
Question: If the terms of a series are either2or24and the sum of all the terms G of the series is 124, then which of the following could be the number of2sin the series?
A.26
B.29
C.35
D.40
Answer: A.26
Explanation: Ans: A
Solution: we are not certain how many 2 or 24 are there. but as given sum of all the terms G is 124 means 24*5= 120 so number of 24 can't be more than 5
so 24x +2y = 124
24*5 + 2y =124 then y=2
24*4 + 2y = 124 then y=14
24*3 +2y = 124 then y= 26
24*2 +2y =124 then y = 38
24 +2y = 124 then y= 50
26 is the ans.A
Question: A sum of money invested at compound interest to Rs. 800 in 3 years and to Rs 820 in 4 years. The
rate on interest per annum is.
A.0.4%
B.5.0%
C.2.5%
D.7%
Answer: C.2.5%
Explanation: Explanation:
S.I. on Rs 800 for 1 year = 20
Rate = (100*20)/(800*1) = 2.5%
Answer: C
Question: Consider a sequence of numbers given by the expression 7 + (q - 1) * 5, where n runs from 1 to 80.What is the sum of this series ?
A.409
B.1636
C.16360
D.16000
Answer: C.16360
Explanation: terms in this sequence are 7,12,17----402
now since this is an a.p. with a common difference of 5. therefore its sum can be given as
q(a+l)/2----------------1)
q= total no. of terms =80
a= first term=7
l= last term=402
subsituting values in the expression 1 we have
80(7+402)/2
= 40(409)
=16360=C
Question: Find all integers x NOT EQUAL TO 3 such that X-3|X^3-3
A.1,2,3,4,5
B.-21,-9,-5,-3,-1,0,1,2,4,5,6,7,9,11,15,27
C.1
D.6
Answer: B.-21,-9,-5,-3,-1,0,1,2,4,5,6,7,9,11,15,27
Explanation: Let x-3=t. Thus, t is an integer not equal to such'that t|(t+3)^2-3,
which is equivalent to the condition t|3^3-3, or t|24. Therefore, it is necessary
and sufficient for t to be an integer divisor of 24, hence t must be equal
to one of the numbers +or-1, +or-2, +or-3, +or-4, +or-6, +or-8, +or-12, +or-24. For x
= t+3 we obtain the values -21, -9, -5, -3, -1,0,1,2,4,5,6,7,
9, 11, 15, and 27.
Correct Answer B -21,-9,-5,-3,-1,0,1,2,4,5,6,7,9,11,15,27
Question: How long does a train 140 m long running at the speed of 72 km/hr takes to cross a bridge 132 m length?
A.13.6 sec
B.12.1 sec
C.17.9 sec
D.16.8 sec
Answer: A.13.6 sec
Explanation: Speed = 72 * 5/18 = 20 m/sec
Total distance covered = 140 + 132 = 272 m.
Required time = 272/20 = 13.6 sec.
Answer: A
Question: a is what percent of b percent of c, in terms of a, b and c?
A.10^4*a/bc
B.abc
C.bc*10^4
D.1/abc
Answer: A.10^4*a/bc
Explanation: Algebraically, b% of c is just (b/100)*c, or bc/100. So we want to answer the question: a is what percent of bc/100? Say a is equal to m% of bc/100; then we have:
a = (m/100)*(bc/100)
10,000a/bc = m
A
Question: A and B together invested Rs. 10,000 in a business. At the end of the year, out of total profit is Rs. 2,000 B's share was Rs. 800. A's investment was
A.s. 4,000
B.s. 6,000
C.s. 10,500
D.s. 11,250
Answer: B.s. 6,000
Explanation: A+B=10000
total profit=2000
2000-800=1200
1200;800=3:2
then 3*10000/5=6000
ANSWER:B
Question: Mrs. Peter got a weekly raise of $145. If she gets paid every other week, write an integer describing how the raise will affect her paycheck.
A.$145
B.$231
C.$112
D.$214
Answer: A.$145
Explanation: A
$145
Let the 1st paycheck be x (integer).
Mrs. Peter got a weekly raise of $ 145.
So after completing the 1st week she will get $ (x+145).
Similarly after completing the 2nd week she will get $ (x + 145) + $ 145.
= $ (x + 145 + 145)
= $ (x + 290)
So in this way end of every week her salary will increase by $ 145.
Question: In a box there are 5 red balls and 6 blue balls. What is the probability of drawing at least one red ball when drawing 3 consecutive balls randomly?
A.201/202
B.164/165
C.256/259
D.98/103
Answer: B.164/165
Explanation: P(at least one red) = 1 - P(no red, so 3 blue) = 1- 3/11*2/10*1/9 = 164/165.
Answer is B
Question: if 28 is divided into two parts such that one fourth of the greater part is equal to one third of the lesser part,then the greater part is
A.16
B.18
C.20
D.22
Answer: A.16
Explanation: 28 divided as (16 + 12).
one fourth of 16(greater part) = 4
one third of 12(lesser part) = 4
ANSWER:A
Question: The sum of seven numbers is 235. The average of the first three is 23 and that of the last three is 42. The fourth number is
A.40
B.126
C.69
D.195
Answer: A.40
Explanation: Explanation:
Average of the first three is 23. Therefore their sum = 23 x 3
Average of the last three is 42. Therefore their sum = 42 x 3
Sum of all number = Sum of first three + Fourth number + Sum of last three
(23×3+a+42×3)=235⇒a=40
Correct Option: A
Question: How many multiples of 5 are there between 5 to 90?
A.9
B.16
C.17
D.none of these
Answer: B.16
Explanation: Explanation :
As you know, multiples of 5 are integers having 0 or 5 in the digit to the extreme right (i.e. the units place).
So the numbers are 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85.
Answer : B
Question: At Company K, 15 percent of the employees are secretaries and 60 percent are salespeople. If there are 65 other employees of Company K, how many employees does Company K have?
A. 260
B. 180
C. 190
D. 200
Answer: A. 260
Explanation: Let the total number of employees in the company be x
% of secretaries = 15%
% of salespeople = 60%
% of of employees other than secretaries and salespeople = 100 - 75 = 25%
But this number is given as 65
so 25% of x = 65
x = 260
Therefore there a total of 260 employees in the company K
Correct answer - A
Question: What is the minimum percentage increase in the mean of set G {-4, -1, 0, 6, 9} if its two smallest elements are replaced with two different primes?
A. 25%
B. 50%
C. 75%
D. 100%
Answer: D. 100%
Explanation: Mean of G is (-4-1+0+6+9)/5=2;
In order the increase to be minimal we should replace two smallest elements of G, which are -4 and -1, with two smallest primes, which are 2 and 3. Hence our new set will be {2, 3, 0, 6, 9} --> new mean is (2+3+0+6+9)/5=4.
Percent increase=(4-2)/2*100=100%.
Answer: D.
Question: Which of the following CANNOT be a product of two distinct positive integers a and b?
A.a
B.b
C.3b + 2a
D.b - a
Answer: D.b - a
Explanation: we can eliminate answer choices A, B, and E right away. There is no reason to distinguish between aa and bb, so if aa cannot be a product, then bb cannot be either and since we cannot have two correct answers in PS problems, then neither A nor B can be correct. As for E it's clearly cannot be correct answer.
So, we are left with options C and D.
For C, can ab=3b+2aab=3b+2a? --> ab−2a=3bab−2a=3b --> a(b−2)=3ba(b−2)=3b --> a=3bb−2a=3bb−2. Now, if b=3b=3, then a=9a=9, so in this case ab=3b+2aab=3b+2a is possible.
Only option left is D.
Answer: D.
Question: How many paying stones, each measuring 2 m * 1 m are required to pave a rectangular court yard 30 m long and 16 m board?
A.240
B.18
C.26
D.17
Answer: A.240
Explanation: 30 * 16 = 2 * 1 * x => x
= 240
Answer: A
Question: The length of a rectangular floor is more than its breadth by 200%. If Rs.150 is required to paint the floor at the rate of Rs. 2 per sq m, then what would be the length of the floor?
A.65
B.15
C.18
D.16
Answer: B.15
Explanation: Let the length and the breadth of the floor be l m and b m respectively.
l = b + 200% of b = l + 2b = 3b
Area of the floor = 150/2= 75 sq m
l b = 75 i.e., l * l/3 = 75
l2 = 225 => l = 15
Answer:B
Question: A wheel that has 6 cogs is meshed with a larger wheel of 14 cogs. When the smaller wheel has made 21 revolutions, then the number of revolutions mad by the larger wheel is:
A.7
B.9
C.8
D.65
Answer: B.9
Explanation: Explanation:
Let the required number of revolutions made by larger wheel be x.
Then, More cogs, Less revolutions (Indirect Proportion)
{\color{Black} \therefore } 14 : 6 :: 21 : x {\color{Black} \Rightarrow } 14 x x = 6 x 21
x={\color{Black} \frac{6\times 21}{14} } {\color{Black} \Rightarrow } x=9
Answer: B
Question: The successive discounts 20% and 15% are equal to a single discount of?
A.35%
B.38%
C.32%
D.29%
Answer: C.32%
Explanation: Let the CP of an article be Rs. 100
Given that successive discounts are 20% and 15%.
SP = 85% of 80% of 100 = (85/100)(80/100)(100)
=> SP = Rs. 68
Clearly, single discount is 32%.
ANSWER:C
Question: A board 7ft. 9 inches long is divided into 3 equal parts . What is the length of each part?
A.5ft. 7 inches
B.3ft. 7 inches
C.4ft. 7 inches
D.2ft. 7 inches
Answer: D.2ft. 7 inches
Explanation: Length of board=7ft. 9 inches=(7*12+9)inches=93 inches.
Therefore, Length of each part = (93/3) inches = 31 inches = 2ft. 7 inches
Answer is D.
Question: Tickets numbered 1 to 50 are mixed and one ticket is drawn at random. Find the probability that the ticket drawn has a number which is a multiple of 4 or 7?
A.9/25
B.9/29
C.9/26
D.9/24
Answer: A.9/25
Explanation: Explanation:
S = {1, 2, 3, … , 49, 50}
E = {4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 7, 14, 21, 35, 42, 49}
n(S) = 50
n(E) = 18
P(E) = n(E)/n(S) = 18/50
= 9/25
ANSWER: A
Question: The average mark of 10 students is 80%. Later it was found that for one student, instead of 60%, the recorded 90%, by mistake. Now the corrected new percentage?
A.55
B.66
C.77
D.88
Answer: C.77
Explanation: lets assume the total marks in the exam per student is 100.
and given that avg mark of 10 student is 80%
so, total mark=80*10=800 ;
but instead of 60 mark they take wrong as 90 mark;
so,800-90 + 60=770
this is correct mark of 10 student
and then average of 10 student is =770/10=77
ANSWER:C
Question: A box contains ELEVEN bulbs out of which 5 are defective. If four bulbs are chosen at random, find the probability that atleast one bulb is good
A.65/66
B.67/66
C.69/66
D.64/66
Answer: A.65/66
Explanation: Required probability = 1-5C4/11C4 = 1 - 1/66 = 65/166.Answer:A
Question: In a renowned city, the average birth rate is 6 people every two seconds and the death rate is 2 people every two seconds. Estimate the size of the population net increase that occurs in one day.
A.32,300
B.172,800
C.468,830
D.338,200
Answer: B.172,800
Explanation: Every 2 seconds, 4 persons are added (6-2). Every second 2 persons are added.
In a day 24hrs = 24 * 60 Minutes = 24 * 60 * 60 = 86400 seconds.
86400 * 2 = 172800
Option B is the answer.
Question: The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder. What is the smaller number ?
A.198
B.243
C.270
D.290
Answer: C.270
Explanation: Let the smaller number be x. Then larger number = (x + 1365).
x + 1365 = 6x + 15
5x = 1350
x = 270
Smaller number = 270.
C
Question: The equation x = 2y^2 + 5y - 19, describes a parabola in the xy coordinate plane. If line l, with slope of 3, intersects the parabola in the upper-left quadrant at x = -5, the equation for l is
A.3x + y + 15 = 0
B.y - 3x - 11 = 0
C.-3x + y - 20 = 0
D.-2x - y - 7 = 0
Answer: C.-3x + y - 20 = 0
Explanation: The question is made to look difficult though it is pretty simple if you focus on just the line and use process of elimination. (Remember that GMAT does not focus on parabolas so basically, the question should be quite do-able even if someone doesn't know how to handle parabolas.)
We need equation of l. Its slope must be 3.
Slope in option A and D is not 3 so we are left with B, C and E
The line has a point (-5, y) on it where y is positive (since the point lies in upper left quadrant).
In options B and E, if you put x = -5, you get -ve value for y co-ordinate. So ignore them.
Answer must be (C)
Question: An article is bought for Rs.600 and sold for Rs.900, find the gain percent?
A.50%
B.63 1/3%
C.33 1/3%
D.93 1/3%
Answer: A.50%
Explanation: Explanation:
600 ---- 300
100 ---- ? => 50%
Answer:A
Question: How many integers between 50 and 100 can be evenly divided by neither 3 nor 5?
A.24
B.25
C.26
D.27
Answer: C.26
Explanation: divisible by 3 between 50 and 100 = 17 (51,54,57,60,63,66,69,72,75,78,81,84,87,90,93,96,99)
divisible by 5 between 50 and 100 = 9 (55,60,65,70,75,80,85,90,95)
Common divisible for 5 and 3 = 3 (60, 75, 90)
Total divisible by 5 and 3 between 50 and 100 = 17+9-3 => 23
There are 49 numbers between 50 to 100 i.e 51 to 99
so the integers that are not divisible by 3 and 5 => 49 - 23 => 26
ANSWER:C
Question: If e<0, which of the following must be true?
A.–100 < e < 100
B.e ≤ –1
C.e ≤ 1
D.e^2 ≥ 1/4
Answer: C.e ≤ 1
Explanation: e is a negative number.
A. –100 < e < 100e can be a negative number less than -100
B. e ≤ –1e can be a fraction, in which case it would be greater than -1
C. e ≤ 1must be true since 1 is positive and e is negative
D. e^2 ≥ 1/4not true if e is a negative fraction like -1/5
E. –100 < e < 0e can be a negative number less than -100=C