RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Set #1 = {A, B, C, D, E}
Set #2 = {K, L, M, N, O, P}
There are these two sets of letters, and you are going to pick exactly one letter from each set. What is the probability of picking at least one vowel?
A.1/6
B.1/3
C.1/2
D.2/3
Answer: C.1/2
Explanation: So Not a vowel in Set-1 : 3/5
And not a vowel in Ser-2:5/6
Now,
3/5∗5/6=12
This is for not a vowel.
Then for at least one vowel will be = 1−1/2=1/2
Answer will be C.
Question: find out the wrong number in the given sequence of numbers
15,16,34,105,424,2124,12756
A.105
B.424
C.2124
D.15
Answer: C.2124
Explanation: 15*1+1=16
16*2+2=34
34*3+3=105
105*4+4=424
424*5+5=2125
2125*6+6=12756
wrong number is 2124
ANSWER:C
Question: Lloyd normally works 7.5 hours per day and earns $4.00 per hour. For each hour he works in excess of 7.5 hours on a given day, he is paid 1.5 times his regular rate. If Lloyd works 10.5 hours on a given day, how much does he earn for that day?
A.$33.75
B.$48.00
C.$51.75
D.$54.00
Answer: B.$48.00
Explanation: Daily working hour*Regular Rate + Overtime*Increased Rate
7.5*4.0+ 3*4.0*1.5=48
Answer B
Question: If x is an integer, and 225 < x^2 <= 361, which of the following is the sum of all possible values of x?
A. None of the above
B. 124
C. 116
D. 105
Answer: A. None of the above
Explanation: The range of x is from 16 .. to 19 and -16 to -19 so the sum is 0 hence ans A, I guess, unless I am missing something!
Question: Which of the following is closer to √0.1+√0.05?
A.0.5
B.0.7
C.0.9
D.1.1
Answer: A.0.5
Explanation: √0.1+√0.05=approximately √0.09+√0.04=0.3+0.2=0.5. Hence, the correct answer is A.
Question: If A is 25% greater than B then how much percentage is B smaller than A?
A.10%
B.20%
C.30%
D.40%
Answer: B.20%
Explanation: A = 125
B = 100
A-B/A × 100 = 25/125 × 100 = 20 % smaller smaller than A
B)
Question: A train 120 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:
A.22
B.48.2
C.99
D.288
Answer: B.48.2
Explanation: Speed of the train relative to man = (120/10) m/sec = (12) m/sec. [(12) * (18/5)] km/hr = 43.2 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 43.2 ==> x = 48.2 km/hr.Answer: B
Question: A man can row with a speed of 15 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is?
A.5 kmph
B.10 kmph
C.15 kmph
D.20 kmph
Answer: D.20 kmph
Explanation: Explanation:
M = 15
S = 5
DS = 15 + 5 = 20kmph
Answer: D
Question: 5356 x 51 = ?
A.273156
B.273243
C.273247
D.273250
Answer: A.273156
Explanation: 5356 x 51	= 5356 x (50 + 1)
= 5356 x 50 + 5356 x 1
= 267800 + 5356
= 273156.
A
Question: (12345679 x 72) = ?
A.88888888
B.888888888
C.898989898
D.9999999998
Answer: B.888888888
Explanation: Explanation: 12345679 x 72 = 12345679 x (70 +2)
= 12345679 x 70 + 12345679 x 2
= 864197530 + 24691358
= 888888888
Answer: Option B
Question: A cistern is normally filled in 6 hrs,but takes 2 hrs longer to fill because of a leak on its bottom,if Cistern is full ,how much time citern would empty?
A.24 hours
B.20 hours
C.30 hours
D.40 hours
Answer: A.24 hours
Explanation: If leakage/hour=1/x, then 1/6 -1/x= 1/8, solving 1/x=1/24
So in 24 hours full cistern will be empty.
ANSWER:A
Question: The pages of a report are numbered consecutively from 1 to 11. If the sum of the page numbers up to and including page number x of the report is equal to six more than the sum of the page numbers following page number x, then x =
A.5
B.6
C.7
D.8
Answer: D.8
Explanation: sum of the first few numbers =1+2+3+4+5+6+7+8 =36
sum of the last few = 9 +10+11 =30 page no.8 answer .D
Question: What is the average (arithmetic mean) of the numbers 100, 150, 200, 200, 250, and 300?
A. 100
B. 150
C. 140
D. 200
Answer: D. 200
Explanation: {100, 150, 200, 200, 250, 300}={200-100,200-50, 200, 200,200+50,200+100} --> the average = 200.
Answer: D.
Question: Ajay can walk 3km in 1 hour. In how many hours he can walk 50km?
A.5hrs
B.16.6 hrs
C.15.6 hrs
D.20.4 hrs
Answer: B.16.6 hrs
Explanation: 1 hour he walk 3km
he walk 50km in = 50/3 * 1 = 16.6hours
Answer is B
Question: an unbaised coin is tossed until it shows up the same face in 2 consicative throws wat is the probability that the no of tosses is not more than 4.
A.3/4
B.1/4
C.7/8
D.1/8
Answer: C.7/8
Explanation: using 0 and 1 for head and tail respectively and considering binary system , we find that
Out of 16 possibilities, 14 are desired options.
Then probability = 14/16=7/8
ANSWER:C
Question: A tap can fill a tank in 16 minutes and another can empty it in 8 minutes. If the tank is already 1/2 full and both the taps are opened together, will the tank be filled or emptied? How long will it take before the tank is either filled or emptied completely as the case may be ?
A.Emptied; 16 min
B.Filled; 8 min
C.Emptied; 8 min
D.Filled; 12 min
Answer: C.Emptied; 8 min
Explanation: If both the pumps are opened together, then the tank will be emptied because the working efficiency of pump empting is more than that of the pump filling it. Thus in 1 min net proportion of the volume of tank filled
= (1⁄8 - 1⁄16) = 1⁄16
or the tank will be emptied in 16 min
⇒ 1⁄2 tank will be emptied in 8 min.
Answer C
Question: A, B and C enter into a partnership. They invest Rs. 60,000, Rs. 80,000 and Rs. 1,20,000 respectively. At the end of the first year, B withdraws Rs. 40,000, while at the end of the second year, C withdraws Rs. 80,000. In what ratio will the profit be shared at the end of 3 years?
A.9 : 3 : 4
B.9 : 2 : 4
C.9: 2 : 1
D.9: 8: 14
Answer: D.9: 8: 14
Explanation: Sol.
A : B : C = (60000 * 36) : (80000 * 12 + 40000 * 24)
: (120000 * 24 + 40000 * 12) =216 : 192 : 336 = 9: 8: 14
Answer D
Question: A wheel of a car of radius 21 cms is rotating at 900 RPM. What is the speed of the car in km/hr?
A.71.28 km/hr
B.47.52 km/hr
C.7.92 km/hr
D.39.6 km/hr
Answer: A.71.28 km/hr
Explanation: Explanatory Answer
The radius of the wheel measures 21 cm.
In one rotation, the wheel will cover a distance which is equal to the circumference of the wheel.
∴ in one rotation this wheel will cover 2 * π * 21 = 132 cm.
In a minute, the distance covered by the wheel = circumference of the wheel * rpm
∴ this wheel will cover a distance of 132 * 900 = 118800 cm in a minute.
In an hour, the wheel will cover a distance of 118800 * 60 = 7128000 cm.
Therefore, the speed of the car = 7128000 cm/hr = 71.28 km/hr
Choice A is the correct answer.
Question: If n is a positive integer and (n+1)(n+3)(n+1)(n+3) is odd, then (n+2)(n+4)(n+2)(n+4) must be a multiple of which one of the following?
A.5
B.6
C.7
D.8
Answer: D.8
Explanation: (n+1)(n+3)(n+1)(n+3) is odd only when both (n+1)(n+1) and (n+3)(n+3) are odd. This is possible only when nn is even.
Hence, n=2mn=2m, where mm is a positive integer. Then,
(n+2)(n+4)=(2m+2)(2m+4)=2(m+1)2(m+2)=4(m+1)(m+2)(n+2)(n+4)=(2m+2)(2m+4)=2(m+1)2(m+2)=4(m+1)(m+2)
=4 * (product of two consecutive positive integers, one which must be even)=4 * (product of two consecutive positive integers, one which must be even) =4 * (an even number), and this equals a number that is at least a multiple of 8=4 * (an even number), and this equals a number that is at least a multiple of 8
Hence, the answer is (D).
Question: A man, a woman and a boy can complete a job in 3, 4 and 12 days respectively. How many boys must assist 1 man and 1 woman to complete the job in 1/4 of a day?
A.22
B.77
C.12
D.41
Answer: D.41
Explanation: (1 man + 1 woman)'s 1 day work = (1/3 + 1/4) = 7/12 Work done by 1 man and 1 woman in 1/4 day = (7/12 * 1/4) = 7/48
Remaining work = (1 - 7/48) = 41/48
Work done by 1 boy in 1/4 day = ( 1/12 * 1/4) = 1/48
Number of boys required = 41/48 * 41 = 41.
Answer: D
Question: A train is 360 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 160 meter length?
A.11 seconds
B.41.6 seconds
C.40 seconds
D.88 seconds
Answer: B.41.6 seconds
Explanation: Speed = 45 Km/hr = 45*(5/18) m/sec = 25/2 m/sec
Total distance = 360+160 = 520 meter
Time = Distance/speed
= 520 * (2/25) = 41.6 seconds
Answer: B
Question: What is the sum of the digits of integer k, if k = (10^40- 79)
A.345
B.340
C.343
D.349
Answer: A.345
Explanation: There are 41 digits in 10^40
When we subtract 79 from it, there will be 40 digits left.
10^40 can be written as 9999999....(40 times) + 1
So,
10^40 - 79 = 9999999....(40 times) + 1 - 79 = 9999999....(40 times) -78
Consider the last 2 digits,
99-78 = 21
The last 2 digits will be 21.
And our number would be 99999......99921 with 2 less 9s after subtraction.
Number of 9s left are 38 and the last two digits are 21
The sum of the digits will be
(38*9) + 2 + 1 =345
Answer:- A
Question: A 600 meter long train crosses a signal post in 40 seconds. How long will it take to cross a 3 kilometer long bridge, at the same speed?
A.4 min
B.8 min
C.9 min
D.6 min
Answer: A.4 min
Explanation: S = 600/40 = 15 mps
S = 3600/15 = 240 sec = 4 min
Answer:A
Question: Simplify: 256 x 256 - 144 x 144
A.761200
B.44800
C.761800
D.761500
Answer: B.44800
Explanation: (256)^2 - (144)^2 = (256 + 144) (256 - 144) = 400 x 112 = 44800
Answer is B
Question: If the integer c is rounded to the nearest hundred, the result represents a 66 2/3 % increase over the value obtained when c is rounded to the nearest ten. which of the following is a possible value of c?
A.64
B.67
C.99
D.133
Answer: A.64
Explanation: We have to check options 1 by 1.
64 rounded to nearest hundred = 100
64 rounded to nearest ten = 60
now difference = 40
the result represents a 66 2/3 % increase over the value obtained when x is rounded to the nearest ten.
therefore 40/60)*100 = 66 2/3 ==>this is the answer.
99 rounded to nearest ten = 100
133 rounded to nearest ten = 130
133 rounded to nearest hundred c= 100=A
Question: At a meeting of the 6 Chiefs of Staff, the Chief of Naval Operations does not want to sit next to the Chief of the National Guard Bureau. How many ways can the Chiefs of Staff be seated around a circular table?
A.56
B.64
C.72
D.80
Answer: C.72
Explanation: 6 people can be arranged around a table in 5! ways.
Consider the two chiefs who will not sit together as a single unit.
The number of ways to arrange 5 units around a table is 4!
We need to multiply this by 2 as the two people can be switched in each arrangement.
The total number of ways to arrange the chiefs is 5! - 2*4! = 3*4! = 72
The answer is C.
Question: If a - b = 3 and
a2+b2=29
, then find the value of ab
A.7
B.8.5
C.10
D.12
Answer: C.10
Explanation: Explanation:
2ab=(a2+b2)−(a−b)2
=> 2ab = 29 - 9 = 20
=> ab = 10
Option C
Question: A, B and C enter into a partnership. A initially invests Rs. 25 lakhs and adds another Rs. 10 lakhs after one year. B initially invests Rs. 35 lakhs and withdraws Rs. 10 lakhs after 2 years and C invests Rs. 30 lakhs. In what ratio should the profits be divided at the end of 3 years ?
A.11:10:15
B.20:17:23
C.19:19:18
D.5:4:9
Answer: C.19:19:18
Explanation: Explanation:
A:B:C =(25 lakhsÃ—Ã—1)+(35 lakhsÃ—Ã—2) :(35 lakhsÃ—Ã—2+25 lakhsÃ—Ã—1) :(30 lakhsÃ—Ã—3)
= 95 lakhs : 95 lakhs : 90 lakhs =19:19:18.
Answer IS C
Question: The average age of 12 men in a group is increased by 2 years when two men whose ages are 20 years and 22 years, are replaced by new members. What is the average age of the new men included?
A.22
B.767
C.77
D.33
Answer: D.33
Explanation: Explanation:
Total age of two men replaced = 20 + 22 = 42 years
Total increase in age on replacement = 2 × 12 = 24 years
Total age two new persons included = 42 + 24 = 66 years
Therefore, Average age of new persons = 66/2 = 33 years
Answer:D
Question: Last week David spent 20 percent of his wages on recreation. This week, his wages are 30 percent less than last weekʼs wages and he spent 20 percent of his wages on recreation. The amount he spends on recreation this week is what percent of the amount he spent on recreation last week
A.75%
B.72%
C.70%
D.73%
Answer: C.70%
Explanation: Say David's wages last week were $100, so he spent 0.20*100=$20 on recreation;
This week's wages is 0.70*100=$70, so he spends 0.2*70=$14 on recreation;
14/20=0.70, hence the amount he spends on recreation this week is 70% of the amount he spent on recreation last week: 20*0.7=14
Answer: C
Question: A can do a work in 12 days. B can do the same work in 24 days. If both A & B are working together in how many days they will finish the work?
A.3
B.5
C.8
D.2
Answer: C.8
Explanation: A rate = 1/12
B rate = 1/24
(A+B) rate = (1/12)+(1/24) = 1/8
A & B finish the work in 8 days
correct option is C
Question: If x and y are even integers, which of the following is an odd integer?
A.xy
B.y^2
C.x+y+3
D.x^2
Answer: C.x+y+3
Explanation: even * even = even
even + odd = odd
Answer : C
Question: The measures of the 2 acute angles of a triangle are in the ratio of 2 : 7. What arethe measures of the 2 angles?
A.20°
B.70°
C.110°
D.120°
Answer: B.70°
Explanation: If the ratio of the two angles is 2:7, then the measures of two angles can be written as 2x and 7x. Also the two acute angles of a triangle is equal to 90°. Hence
2x + 7x = 90
9x = 90
x = 10
Measures of the two acute angles are
2x = 2 × 10 = 20°
7x = 7 × 10 = 70°
B
Question: If y is the smallest positive integer such that 11,025 multiplied by y is the square of an integer, then y must be
A.2
B.4
C.6
D.7
Answer: B.4
Explanation: i just tried plugging in the numbers and found out that
4*11025 = 44, 100, which is a square of 210
B
Question: #p is defined as 2p+20 for any number p. What is p, if #(#(#p))=4?
A.–108
B.–44
C.10
D.-17
Answer: D.-17
Explanation: #p = 2p+20 --->#(#p) = 2(2p+20)+20 = 4p+60 and thus #(4p+60) = 2(4p+60)+20 = 8p+140 = 4 ---> 8p= -136 ---> p = -17, D is the correct answer.
Question: If Tim had lunch at $60.50 and he gave 20% tip, how much did he spend?
A.$30.60
B.$72.60
C.$70.60
D.$40.60
Answer: B.$72.60
Explanation: The tip is 20% of what he paid for lunch. Hence
tip = 20% of 60.50 = (20/100)*60.50 = $12.1
Total spent
60.50 + 12.1 = $72.6
correct answer B
Question: Solve the equation:
(2x - 1)2 – x(10x + 1) = x(1 – x)(1 + x) – (2 – x)3
A.1
B.1/2
C.2
D.2/1
Answer: B.1/2
Explanation: Solution:
(2x - 1)2 – x(10x + 1) = x(1 – x)(1 + x) – (2 – x)3 <=>
4x2 - 4x + 1 -10x2 – x = x – x3 - 8 + 12x - 6x2 + x3 <=>
18x = 9 <=> x = 1/2
Answer B
Question: If a , b, and c are integers and a∗b2/ca∗b2/cis a positive even integer, which of the following must
be true?
I. ab is even
II. ab > 0
III. c is even
A.l
B.ll only
C.l and ll
D.l and lll
Answer: A.l
Explanation: Given: a∗b2c=even>0a∗b2c=even>0 --> ab2=c∗even=evenab2=c∗even=even --> either aa is even or bb or both.
I. abab is even --> according to the above this must be true;
II. ab>0ab>0 --> not necessarily true, bb could be positive as well as negative (for example a=1a=1, c=1c=1 and b=−2b=−2);
III. cc is even --> not necessarily true, see above example.
Answer: A (I only).
Question: Of the 40 electronics components that a factory must manufacture, 30 percent would be most e¢ ciently manufactured by Machine A and the remaining 70 percent would be most efficiently manufactured by Machine B, though either machine could manufacture any of the 40 components. If 70 percent of the components were manufactured by Machine A and the remainder were manufactured by Machine B, what is thehighest possible number of components that were manufactured by the machine that would manufacture them the most efficiently?
A. 30
B. 32
C. 60
D. 35
Answer: C. 60
Explanation: A can manufacture 30 % of 40 efficiently, which is 12.
B can manufacure 70 % of 40 efficiently, which is 28.
Now 80 % of 40 are produced by A. This means 32 parts. Since A can produce 12 efficiently, all 32 are produced efficiently. Rest (8) is produced by B, which can produce max. 28 parts efficiently.
Hence parts that were produced efficiently = 32+28 = 60. (C).
Question: What is the 36th digit to the right of the decimal point in the decimal expansion of 1/37?
A. 0
B. 2
C. 4
D. 7
Answer: D. 7
Explanation: 1/37=0.027027... So, we have a repeating cycle of 027. Every third digit (3rd, 6th, 9th, ...) to the right of the decimal point is 7, thus 36th digit to the right of the decimal point is also 7.
Answer: D.
Question: The simple interest and the true discount on a certain sum for a given time and at a given rate are Rs. 85 and Rs. 78 respectively. The sum is:
A.1360
B.1450
C.1600
D.947
Answer: D.947
Explanation: Sol.
Sum = S.I. * T.D. / (S.I)-(T.D.) = 85 * 78 / (85 - 78) = Rs.947.
Answer D
Question: A person distributed 20% of his income to his 3 children each. He deposited 30% of his income to his wife's account. He donated 5% of remaining amount to an orphan house.Finally he has $60000. Find his total income?
A.A)1200000
B.B)562000
C.C)800000
D.D)500000
Answer: A.A)1200000
Explanation: 3 children got = 3*20% = 60%
wife got = 30%
orphan house = 5%
total = 60+30+5 = 95%
remaining = 100-95 = 5%
5% = 60000
100% = 60000*100/5 = $1200000
Answer is A
Question: In particular old age home, 60% are suffering from diabetic and at the same time 80% are suffering from blood pressure.If suppose 75% are suffering from diabetic,what percentage of old people suffering from blood pressure at the same old age home?
A.23
B.16
C.26
D.36
Answer: D.36
Explanation: given : % of people suffering from diabetics = 60%; % of people suffering from blood pressure = 80% (ie ) 0.8
total =75*100; Those who are suffering from diabetics= 75 - 60 = 15; Those who are suffering from blood pressure =
100 - 80=20; so those who are suffering from blood pressure =0.8*20=16; Total number of people suffering from blood pressure = 20+16 = 36. Answer: D
Question: If P/6 = Q/7 = R/8 then find P:R:Q
A.1:2:3
B.6:8:7
C.2:4:9
D.4:9:7
Answer: B.6:8:7
Explanation: Let P/6 = Q/7 = R/8 = K
P = 6K
Q = 7K
R = 8K
P:R:Q = 6:8:7
Answer is B
Question: ABCD is a square. E and F are the midpoints of sides CD and BC, respectively. What is the ratio of the shaded region area to the unshaded region?
A.1:1
B.2:1
C.3:1
D.5:3
Answer: D.5:3
Explanation: Let's join the midpoints as shown in the figure then we'll get four small squares...
AODX be 1 and similarly all squares..and we can split the unit 1 into half and half as per the mid points...
Then shaded will be 1+1/2+1/2+1/2 = 5/2
and unshaded is 1/2+1/2+1/2 = 3/2..
shaded : unshaded is 5:3..
ANS option D.
Question: The average of five consecutive odd numbers is 51. What is the difference between the highest and lowest number?
A.3
B.7
C.8
D.11
Answer: C.8
Explanation: Explanation:
Let the numbers be x, x + 2, x + 4, x + 6 and x + 8.
Then, [x + (x + 2) + (x + 4) + (x + 6) + (x + 8)] / 5 = 51
5x + 20 = 255
x = 47
So, required difference = (47 + 8) – 47 = 8
ANSWER C
Question: In a city, the streets are aligned in a grid, where the east-west roads are called 1st Rd, 2nd Rd, 3rd Rd, etc, increasing in number as one moves northward. The north-south roads are called 1st Ave, 2nd Ave, 3rd Ave, etc, increasing in number as one moves eastward. If Bill needs to walk from the corner of 2nd Rd and 3rd Ave to the corner of 10th Rd and 5th Ave in the shortest possible time, how many different routes could he take?
A.45
B.60
C.75
D.90
Answer: A.45
Explanation: Bills needs to walk 8 blocks north and 2 blocks east.
One possible solution is NNNNNNNNEE.
There are 10C8 = 45 possible solutions.
The answer is A.
Question: How many numbers between 11 and 90 are divisible by 7?
A.7
B.9
C.11
D.8
Answer: C.11
Explanation: The required numbers are 14, 21, 28, 35, .... 77, 84.
This is an A.P. with a = 14 and d = (21 - 14) = 7.
Let it contain n terms.
Then, T^n = 84 => a + (n - 1) d = 84
=> 14 + (n - 1) x 7 = 84 or n = 11.
Answer is C.
Question: HCF of 2472,1284 and a third number 'n'is 12.If their LCM is 8*9*5*103*107.then the number 'n'is.
A.160
B.170
C.180
D.190
Answer: C.180
Explanation: 2472=8*3*103
1284=4*3*107
so n = 4*3*x
dividing by hcf
2472/12=2*103
1284/12=107
lcm/12=2*3*5*103*107
x=lcm/first*second
x=2*3*5*103*107/2*103*107=3*5=15
number is = 15*12=180
ANSWER:C
Question: Arya starts cycling along the boundaries of the squares. She starts from a point A and after 90 minutes she reached to point C diagonally opposite to A. If she is travelling with 20km/hr, then find the area of square field.
A.125
B.225
C.325
D.425
Answer: B.225
Explanation: Explanation :
D = 20*3/2 = 30 km. So side of square is 15km, so area – 225km^2
Answer – B
Question: The length of a rectangle is increased by 25% and its breadth is decreased by 20%. What is the effect on its area?
A.10000
B.10008
C.10005
D.10004
Answer: A.10000
Explanation: 100 * 100 = 10000
125 * 80 = 10000
No change
Answer:A
Question: A certain junior class has 1000 students and a certain senior class has 800 students. Among these students, there are 60 siblings pairs each consisting of 1 junior and 1 senior. If 1 student is to be selected at random from each class, what is the probability that the 2 students selected will be a sibling pair?
A.3/40000
B.1/3600
C.9/2000
D.1/60
Answer: A.3/40000
Explanation: There are 60 siblings in junior class and 60 their pair siblings in the senior class. We want to determine probability of choosing one sibling from junior class and its pair from senior.
What is the probability of choosing ANY sibling from junior class? 60/1000 (as there are 60 of them).
What is the probability of choosing PAIR OF CHOSEN SIBLING in senior class? As in senior class there is only one pair of chosen sibling it would be 1/800 (as there is only one sibling pair of chosen one).
So the probability of that the 2 students selected will be a sibling pair is: 60/1000∗1/800=3/40000
Answer: A.
Question: If r ≠ 1 and if sr/(s - r) = 1, what is the value of s in terms of r?
A.(r+1)/r
B.(r - 1)/r
C.r/(r + 1)
D.r/(1-r)
Answer: D.r/(1-r)
Explanation: This question comes with a particular 'quirk' (one that you probably won't see on Test Day). The GMAT won't test you on the concept of undefined numbers (re: numbers divided by 0), so any time that this concept is a possibility, the question writers have to add a restriction that removes the option that a 0 could occur in the denominator.
Here, we're told that B CANNOT = 1, which is a bit strange because that restriction doesn't seem to impact the original equation much. In fact, it impacts JUST ONE of the answer choices - so you have to ask WHY that restriction is even there. It's actually because that one answer is the correct one.
Final Answer:
D
Question: Worker W produces n units in 5 hours. Workers V and W work independently but at the same time, produce n units in 2 hours. How long would it take V alone to produce n units?
A.8/3 hours
B.10/3 hours
C.11/3 hours
D.12/3 hours
Answer: B.10/3 hours
Explanation: w's 1 hours production=n/5
(w+v)'s 1 hours production=n/2
v's 1 hours production
n/5+V=n/2
v's 1 hours production=n/2-n/5
=3n/10
n/(10/3)
ans=10/3 hours
ANSWER:B
Question: A computer manufacturer produces a certain electronic component at a cost of $50 per component. Shipping costs for delivering the components are $8 per unit. Further, the manufacturer has costs of $16,000 a month related to the electronic component regardless of how many it produces. If the manufacturer produces and sells 200 components a month, what is the lowest price it can sell them for such that the costs don't exceed the revenues?
A.135
B.129
C.131
D.138
Answer: D.138
Explanation: $16000 is a fixed cost
Each component is $58 ($50 to produce, $8 to ship)
Manufacturer will be producing and selling 200 components
so therefore the equation to find price would be
200*p = 16000+(200*50)+(200*8)
p = (16000+10000+1600)/200
p = 138
Answer: D
Question: A fruit drink is made of orange, watermelon, and grape juice, where 35 percent of the drink is orange juice and 35 percent is watermelon juice. If the drink is made with 45 ounces of grape juice, how many ounces is the drink total?
A.120
B.140
C.150
D.180
Answer: C.150
Explanation: Let the total number of ounces in the drink be x.
% of orange = 35%
% of watermelon = 35%
% of grape = 100% - 70% = 30%
0.30x = 45
x = 150
Therefore there are a total of 150 ounces in the drink.
The answer is C.
Question: Find 44 % of 240
A.96
B.105.6
C.86
D.74
Answer: B.105.6
Explanation: We know that R % of m is equal to R/100 × m.
So, we have 44 % of 240
44/100 × 240
=105.6
Answer:B