RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: X and Y are positive integers. If X is a prime factor of Y^2 , which of the following MUST be true?
A.X is even
B.X=Y^2
C.Y/X is even
D.X/Y is less than or equal to 1
Answer: D.X/Y is less than or equal to 1
Explanation: A. x is even --> not necessarily true: x=3=odd x=3=odd and y=3y=3;
B. x=y^2 --> never true, as x=primex=prime then it can not equal to square of another integer;
C. y/x is even --> not necessarily true: if x=3x=3 and y=3y=3 then yx=1=odd yx=1=odd;
D. x/y is less than or equal to 1 --> always true as shown above or by POE;
E. x+1 is also a prime factor of y^2 --> not necessarily true: if x=2x=2 and y=2y=2 then x+1=3x+1=3 and 3 is not a factor of y2=4y2=4.
Answer: D.
Question: Which of the following is the product of two integers whose sum is 13?
A. -42
B. -28
C. 12
D. 26
Answer: C. 12
Explanation: I solved this Question like this,
Let the two integers are x,y
x+y=13 (Given)
xy=? (Needed)
instead of solving this algebraically, Test the Answer choices
C. 12
Do the factorization : (1,12)----> There sum is 13 Bingo!!!!
So, my answer is C...
As the answer is in C, it took me very less time to answer the question. but i think this method is be simple and efficient.
Question: A, B and C invest in the ratio of 3 : 4: 5. The percentage of return on their investments are in the ratio of 6 : 5 : 4. Find the total earnings, If B earns Rs. 150 more than A :
A.2348
B.7250
C.4350
D.1998
Answer: C.4350
Explanation: Explanation:
A B C
investment 3x 4x 5x
Rate of return 6y% 5y% 4y%
Return \inline \frac{18xy}{100} \inline \frac{20xy}{100} \inline \frac{20xy}{100}
Total = (18+20+20) = \inline \frac{58xy}{100}
B's earnings - A's earnings = \inline \frac{2xy}{100} = 150
Total earning = \inline \frac{58xy}{100} = 4350
Answer: C) Rs.4350
Question: If x and y are integers such that x^2= 2y and xy = 32, then x – y = ?
A.-30
B.-20
C.-5
D.-4
Answer: D.-4
Explanation: here x and y are integers .
x^2=2y,xy =32.
substitute (x^2)/2=y in xy => x^3=32*2=>x^3=64.
here X3 is positive ,
X is also positive.
x=4 then y=8.
X-y=-4
so option D is correct
Question: find the number of 6 digit numbers that can be formed using digits 1,2,3,4,5,6 once such that the 6digit number is divisible by its unit digit.
A.648
B.649
C.650
D.651
Answer: A.648
Explanation: when unit digit 1,2,3,5,6 then no. formed will be divisible by the digit at the unit place.
=> 5*5p5 numbers
when unit place is 4, tenth place should be 2 or 6
=> 2*4p4 numbers
total = 5*5p5 + 2*4p4 = 5*5! + 2*4! = 648
ANSWER:A
Question: 3 candidates in an election and received 1136, 7636 and 11628 votes respectively. What % of the total votes did the winningcandidate got in that election?
A.45%
B.47%
C.57%
D.60%
Answer: C.57%
Explanation: Total number of votes polled = (1136 + 7636 + 11628) = 20400
So, Required percentage = 11628/20400 * 100 = 57%
C
Question: In how many ways can 6 apples (identical) be distributed among 3 children? (Some children may get no apples.)
A.32
B.34
C.36
D.28
Answer: D.28
Explanation: Generalised form for n = number of identical objects, and r = number of children is n+r-1Cr-1.
n=6 r= 3
8C2 =28
Answer : D
Question: Two employees A and B are paid a total of Rs. 570 per week by their employer. If A is paid 150 percent of the sum paid to B, how much is B paid per week?
A.s.130
B.s.140
C.s.150
D.s.228
Answer: D.s.228
Explanation: Let the amount paid to A per week = x
and the amount paid to B per week = y
Then x + y = 570
But x = 150% of y = 150y/100 = 15y/10
∴15y/10 + y = 570
⇒ y[15/10 + 1] = 570
⇒ 25y/10 = 570
⇒ 25y = 5700
⇒ y = 5700/25 = Rs.228
D)
Question: If X, Y and Z are consecutive numbers (X>Y>Z). X +2Y +3Z = 5Y + 4. What is the value of Z?
A.6.
B.5.
C.4.
D.3.
Answer: B.5.
Explanation: Let the 3 consecutive integers be k-1 (Z), k (Y) and k+1 (X). Given : X +2Y +3Z = 5Y + 4.
k+1 + 2k + 3k - 3 = 5k+ 4 => k =6.
Thus Z = k-1 = 5.
ANSWER:B
Question: Four students, Jackie, Mandy, Bertrand, and Tao, took a science quiz. If Mandy scored 30% higher than Bertrand did, Tao scored 20% lower than Jackie did, and Jackie scored 40% higher than Mandy did, how much lower did Bertrand score than Tao?
A.50% lower
B.20% lower
C.5% lower
D.40% lower
Answer: A.50% lower
Explanation: In this word problem, the first key is to turn the story into equations:
Mandy scored 30% higher than Bertrand did: M = 0.30 + B
Tao scored 20% lower than Jackie did: T = J - 0.20
Jackie scored 40% higher than Mandy did: J = 0.40 + M
Then, in classic GMAT style, the problem doesn't ask you to solve for a single variable, but instead to solve for the difference between B and T (how much higher did Bertrand score than Tao did?). This means that your goal is to get the equations in terms of B and T so that you can solve for the expression B - T.
Taking the first equation and solving for B, you have B = M - 0.30.
Taking the second equation and solving for T you have T = J - 0.20, and then with the third equation you can replace J with 0.40 + M so that both B and T are in terms of M: T = (0.40 + M) - 0.20.
So if B = M - 0.30 and T = M + 0.20, then:
B - T = (M - 0.30) - (M + 0.20)
B - T = M - 0.30 - M - 0.20 (remove the parentheses by distributing the multiplication)
B - T = -0.50, so the answer is A.
Question: How many times digit 20 is used while writing numbers from 100 to 500?
A.20
B.30
C.15
D.25
Answer: A.20
Explanation: in 100 to 200 there are 5 20's
in 200 to 300 there are 5 20's
in 300 to 400 there are 5 20's
in 400 to 500 there are 5 20's
so, total 20 is 20's
CORRECT OPTION : A
Question: The sale price sarees listed for Rs.400 after successive discount is 10% and 5% is?
A.321
B.276
C.342
D.265
Answer: C.342
Explanation: Explanation:
400*(90/100)*(95/100) = 342
Answer: C
Question: Find the middle one when The sum of three consecutive even numbers is 42?
A.10
B.12
C.14
D.15
Answer: C.14
Explanation: 3 consecutive numbers can be a - 1, a, a + 1
So sum of numbers = 3a = 42.
Hence a = 14.
C
Question: A shopkeeper buys mangoes at the rate of 4 a rupee and sells them at 3 a rupee. Find his net profit or loss percent?
A.31%
B.38 1/3%
C.33 1/3%
D.33%
Answer: C.33 1/3%
Explanation: C
33 1/3%
The total number of mangoes bought by the shopkeeper be 12.
If he buys 4 a rupee, his CP = 3
He selling at 3 a rupee, his SP = 4
Profit = SP - CP = 4 - 3 = 1
Profit Percent = 1/3 * 100 = 33 1/3 %
Question: A train 100 meters long completely crosses a 300-meter long bridge in 40 seconds. What is the speed of the train in km/h?
A.28 km/h
B.32 km/h
C.36 km/h
D.40 km/h
Answer: C.36 km/h
Explanation: speed = distance / time = (100 + 300)/40 = 400/40 (m/s) * 3600/1000 = 36 km/h
The answer is C.
Question: Henrikh lives x blocks from his office. It takes him 1 minute per block to walk to
work and 20 seconds per block to ride his bicycle to work. If it takes him exactly
10 minutes more to walk to work than to ride his bicycle, then x equals
A.4
B.7
C.10
D.15
Answer: D.15
Explanation: The best way would be...
Per km, he takes 40 secs extra if he walks
So he will take 10 mins or 10*60 secs in 10*60/40 =15 km
ANSWER:D
Question: A cube is painted red on all faces. It is then cut into 27 equal smaller cubes. How many cubes are painted on only 2 faces?
A.12
B.8
C.6
D.10
Answer: A.12
Explanation: The mini-cubes with 2 painted sides are ALL on the edge of the cube, in the "middle" of the edge.
There are 4 in front, 4 in back and 4 more on the "strip" that runs around the left/top/right/bottom of the cube.
4 + 4 + 4 = 12.
Answer A
Question: Which of the following is equal to the value of 2^6 + 2^6 + 3^6 + 3^6 + 3^6 ?
A.2^7
B.2^7 + 3^7
C.3^7
D.2^8 + 3^8
Answer: B.2^7 + 3^7
Explanation: 2^6 + 2^6 + 3^6 + 3^6 + 3^6
= 2 (2^6) + 3 (3^6)
= 2^1 (2^6) + 3^1 (3^6)
= 2^(1+6) + 3^(1+6)
= 2^7 + 3^7
Ans: B
Question: For how many integer values of n will the value of the expression 4n + 7 be an integer greater than 1 and less than 40?
A.10
B.12
C.14
D.16
Answer: A.10
Explanation: 4n+7 > 1
4n> -6
n > -(3/2)
n> -1.5 (n = -1, 0, 1 ,2 3........ upto infinity)
From second constraint
4n+7 < 40
4n< 33
n < 8. 25
n = (-infinity, .......-3, -2, -1, 0, 1, 2, .........upto 8)
Combining the two
-1.5 < n<8.25
n = 1 to 8 (48 integers)
and n = -1 and 0
so 10 integers.
A
Question: Points A, B, C, and D, in that order, lie on a line. If AB = 3 cm, AC = 4 cm, and BD = 9 cm, what is CD, in centimeters?
A. 1
B. 8
C. 3
D. 4
Answer: B. 8
Explanation: Putting a value to each point, lets use the following:
A - 0
B - 3 (AB = 3)
C - 4 (AC = 4)
D - 12 (BD = 9)
CD is 12-4 = 8.
Ans 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.22 sec
C.27 sec
D.17 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: A and B enter into a partnership with capitals in the ratio 2 : 3. At the end of 9 months, A withdraws from the business. If their profits are in the ratio 1 : 2, how long did B invest his capital?
A.12 months
B.8 months
C.10 months
D.14 months
Answer: A.12 months
Explanation: Explanation:
Let the initial investment of A and B be Rs. 2x and Rs. 3x respectively.
Let B invested for a period of y months.
Then, ratio of capitals of A and B
= (2x × 9) : (3x × y) = 1 : 2
=> 18x/(3x × y) = 1/2
=> 6/y = 1/2
=> y = 12
Hence, B's investment is for 12 months.
Answer: Option A
Question: Carol, Belle and Andrew are business partners. Carol's capital is Rs.12000. If his share of a profit of Rs.1000 is Rs.380 and Andrew's share is Rs.250, what is Belle's capital?
A.116847.21
B.14684.21
C.21684.21
D.11684.21
Answer: D.11684.21
Explanation: 380 + 250 = 630
1000 - 630 = 370
380 ---- 12000
370 ---- ? => 11684.21
ANSWER:D
Question: 12x − 12 = 12y
5y + 5x = 15
Which of the following is the number of solutions to the system of equations shown above?
A.More than three
B.Exactly three
C.Exactly two
D.Exactly one
Answer: D.Exactly one
Explanation: => 12x - 12y = 12
=> x- y =1 -- 1
5y + 5x = 15
=>x + y = 3 -- 2
From equation 1 and 2 , we get
2x = 2
=> x=1
y=1
Therefore , the given system will have Exactly one solution
Answer : D
Question: On dividing 109 by a number, the quotient is 9 and the remainder is 1. Find the divisor
A.12
B.14
C.16
D.18
Answer: A.12
Explanation: d = (D-R)/Q
= (109 - 1)/9
= 108/9 = 12
A)
Question: A person can swim in still water at 4 km/h. If the speed of water 2 km/h, how many hours will the man take to swim back against the current for 6km?
A.3
B.4
C.5
D.6
Answer: A.3
Explanation: M = 4
S = 2
US = 4 - 2 = 2
D = 6
T = 6/2 = 3 Answer:A
Question: A bag contains 4 black, 5 yellow and 6 green balls. Three balls are drawn at random from the bag. What is the probability that all of them are yellow?
A.2/91
B.1/81
C.1/8
D.2/81
Answer: A.2/91
Explanation: Total number of balls = 4 + 5 + 6 = 15
Let S be the sample space.
n(S) = Total number of ways of drawing 3 balls out of 15 = 15C3
Let E = Event of drawing 3 balls, all of them are yellow.
n(E) = Number of ways of drawing 3 balls, all of them are yellow
= Number of ways of drawing 3 balls from the total 5 = 5C3
(∵ there are 5 yellow balls in the total balls)
P(E) = n(E)/n(S)
=5C3/15C3=5C2/15C3 [∵ nCr = nC(n - r). So 5C3 = 5C2. Applying this for the ease of calculation]
=(5×4/2×1)/(15×14×13/3×2×1)=5×4/(15×14×13/3)=5×4/5×14×13=4/14×13=2/7×13=2/91
ANSWER:A
Question: Which of the following is equal to (n – 3)2*square* if
n = 11?
A.(n + 6)(n – 6)
B.(n + 5)(n – 7)
C.(n + 4)(n – 8)
D.(n + 3)(n – 9)
Answer: B.(n + 5)(n – 7)
Explanation: If n = 11, then:
(n – 3)2 = (11 – 3)2 = 82 = 64
Substitute 11 for n into each answer until you find one that equals 64:
(n + 6)(n – 6) = (17)(5) = 85
(n + 5)(n – 7) = (16)(4) = 64 You’ve found a match
correct answer B)(n + 5)(n – 7)
Question: Rs. 5000 is divided into three parts A, B and C. How much A is more than C if their ratio is 1/5:1/5:1/10?
A.1000
B.992
C.772
D.552
Answer: A.1000
Explanation: 1/5:1/5:1/10 = 2:2:1
1/5*5000 = 1000
2000-1000 = 1000
Answer: A
Question: The ratio of the ages of Maala and Kala is 4 : 3. The total of their ages is 2.8 decades. The proportion of their ages after 0.8 decades will be [1 Decade = 10 years]
A.4:3
B.12:11
C.7:4
D.6:5
Answer: D.6:5
Explanation: Explanation:
Let, Maala’s age = 4A and Kala’s age = 3A
Then 4A + 3A = 28
A = 4
Maala’s age = 16 years
and Kala’s age = 12 years
Proportion of their ages after 8 is = (16 + 8) : (12 + 8)
= 24 : 20
= 6 : 5 .. Answer: D
Question: It is being given that (232 + 1) is completely divisible by a whole number. Which of the following numbers is completely divisible by this number?
A.(2 16 + 1)
B.(2 16 - 1)
C.(7 x 2 23)
D.(2 96 + 1)
Answer: D.(2 96 + 1)
Explanation: Explanation:
Let 232 = x. Then, (232 + 1) = (x + 1).
Let (x + 1) be completely divisible by the natural number N. Then,
(296 + 1) = [(232)3 + 1] = (x3 + 1) = (x + 1)(x2 - x + 1), which is completely divisible by N, since (x + 1) is divisible by N.
ANSWER IS D
Question: A six-sided die is rolled once. What is the probability that the number rolled is an even number greater than 5?
A.2 / 3
B.1 / 6
C.3 / 3
D.4 / 5
Answer: B.1 / 6
Explanation: Only 6 so, 1 / 6
correct answer B
Question: Two trains are moving in the same direction at 72 kmph and 36 kmph. The faster train crosses a man in the slower train in 12 seconds. Find the length of the faster train?
A.270
B.288
C.266
D.120
Answer: D.120
Explanation: Relative speed = (72 - 36) * 5/18 = 2 * 5 = 10 mps.
Distance covered in 12 sec = 27 * 10 = 270 m.
The length of the faster train = 120 m.
Answer: D
Question: The greatest possible length which can be used to measure exactly the lengths 7 m, 3 m 85 cm, 12 m 95 cm is
A.16 cm
B.25 cm
C.30 cm
D.35 cm
Answer: D.35 cm
Explanation: Explanation:
So by now, you must be knowing this is a question of HCF, right.
H.C.F. of (700 cm, 385 cm, 1295 cm) = 35 cm.
Option D
Question: What is the sum of all 3 digit numbers that leave a remainder of '2' when divided by 7?
A.70,592
B.64,850
C.64,749
D.149,700
Answer: A.70,592
Explanation: Find the number , Upon Sum of 3 Digits of a number Gives a Reminder 2 when it is Divided by 7
Seeing the Options After Dividing an Finding the Reminder of 2
My Answer was A
Question: A person walks at a speed of 4 km/hr and runs at a speed of 8 km/hr. How many hours will the person require to cover a distance of 4 km, if the person completes half of the distance by walking and the other half by running?
A.0.25
B.0.5
C.0.75
D.1
Answer: C.0.75
Explanation: time = 2/4 + 2/8 = 6/8 = 0.75 hours
The answer is C.
Question: A card is drawn from a pack of 52 cards. The probability of getting a queen of club or a king of heart is
A.1/13
B.2/13
C.1/26
D.1/52
Answer: C.1/26
Explanation: Explanation:
Total number of cases = 52
Favourable cases = 2
Probability = 2/56 = 1/26
Answer: Option C
Question: What is the remainder when the number Q=14^2 * 15^8 is divided by 5?
A.0
B.1
C.2
D.4
Answer: A.0
Explanation: 14^2 has units digit 6
15^8 has units digit 5
Thus Q=14^2*15^8 has units digit 0 and will be divisible by 5. The remainder will be zero
Answer: (A)
Question: In an electric circuit, three resistors with resistances 2 ohms, 5 ohms and 6 ohms are connected in parallel. In this case, if R is the combined resistance of these three resistors, then the reciprocal of R is equal to the sum of the reciprocals resistors. What is R value?
A.13/15 ohms
B.15/13 ohms
C.5/8 ohms
D.3/7 ohms
Answer: A.13/15 ohms
Explanation: The wording is a bit confusing, though basically we are told that 1/R = 1/2 + 1/5 + 1/6, from which it follows that R=13/15ohms
Option: A
Question: An amount of Rs.3120 was divided among A, B and C, in the ratio 1/2 : 1/3 : 1/4. Find the share of A?
A.1320
B.1196
C.1210
D.1440
Answer: D.1440
Explanation: Let the shares of A, B and C be a, b and c respectively.
a : b : c = 1/2 : 1/3 : 1/4
Let us express each term with a common denominator which is the last number divisible by the denominators of each term i.e., 12.
a : b : c = 6/12 : 4/12 : 3/12 = 6 : 4 : 3.
Share of A = 6/13 * 3120 = Rs. 1440
Answer: D
Question: Ann and Bob drive separately to a meeting. Ann's average driving speed is greater than Bob's avergae driving speed by one-third of Bob's average driving speed, and Ann drives twice as many miles as Bob. What is the ratio Q of the number of hours Ann spends driving to the meeting to the number of hours Bob spends driving to the meeting?
A.8:3
B.3:2
C.4:3
D.2:3
Answer: B.3:2
Explanation: Say the rate of Bob is 3mph and he covers 6 miles then he needs 6/3=2 hours to do that.
Now, in this case the rate of Ann would be 3+3*1/3=4mph and the distance she covers would be 6*2=12 miles, so she needs 12/4=3 hours for that.
The ratio Q of Ann's time to Bob's time is 3:2.
Answer: B.
Question: The sum of four consecutive even numbers is 292. What would be the smallest number?
A.33
B.88
C.70
D.123
Answer: C.70
Explanation: Let the four consecutive even numbers be 2(x - 2), 2(x - 1), 2x, 2(x + 1)
Their sum = 8x - 4 = 292 => x = 37
Smallest number is: 2(x - 2) = 70.
Answer: C
Question: The sum R of the arithmetic sequence a, a+d, a+2d,..., a+(n-1)d is give by Rn = (n/2)*(2a + n-1)d. What is the sum of the integers 1 to 100 inclusive, with the even integers between 25 and 63 omitted.
A.4345
B.4302
C.4258
D.4214
Answer: D.4214
Explanation: a method to do it under one minutes is to take advantage of the choices given...
lets work on the last digit aswe have different units digit in each choice...
total sum of 1 to 100 inclusive will have 0 as the last digit..
this is so because the resultant will be 10*(sum of all single digits)... and since we are multiplying by 10,units digit will be 0...
now for single digit in sum R of even number from 25 to 63..
25 to 65 will have 4 times sum of single digit even int, 4*(2+4+6+8+0)=4*20..
here too the units digit is 0, but 64 has to be excluded from the total..
two ways from here on..
1) we are subtracting 0 from 0
so units digit should be 0, but we have to add 64..
so last/units digit =4..
2)we subtract 64 from sum of even int..
so units digit=80-4=76..
or units digit =6...
so our answer should have units digit as 10-6=4..
only D has 4 as units digit..
ans D
Question: A batsman scored 140 runs which included 3 boundaries and 8 sixes. What percent of his total score did he make by running between the wickets?
A.45(4/11) %
B.45 %
C.45(5/11) %
D.57(1/7) %
Answer: D.57(1/7) %
Explanation: Explanation :
Total runs scored = 140
Total runs scored from boundaries and sixes = 3 x 4 + 8 x 6 = 60
Total runs scored by running between the wickets = 140 - 60 = 80
Required % = (80/140) × 100 = 400/7 = 57(1/7)%
Answer : Option D
Question: How many seconds will a 500 meter long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
A.288
B.266
C.500
D.277
Answer: C.500
Explanation: Let length of tunnel is x meter
Distance = 800+x meter
Time = 1 minute = 60 seconds
Speed = 78 km/hr = 78*5/18 m/s = 65/3 m/s
Distance = Speed*Time
800+x = (65/3) * 60
800+x = 20 * 65 = 1300
x = 1300 - 800 = 500 meters.Answer:C
Question: The speed at which a man can row a boat in still water is 9 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 60 metres?
A.16 seconds
B.34 seconds
C.14 seconds
D.18 seconds
Answer: D.18 seconds
Explanation: Speed of the boat downstream = 9 + 3 = 12 kmph
= 12 * 5/18 = 10/3 m/s
Hence time taken to cover 60 m = 60*3/10
= 18 seconds.
Answer: D
Question: If Tim had lunch at $50.50 and he gave 20% tip, how much did he spend?
A.$33.95
B.$47.47
C.$28.40
D.$60.60
Answer: D.$60.60
Explanation: The tip is 20% of what he paid for lunch. Hence
tip = 20% of 50.50 = (20/100)*50.50 = 101/100 = $10.10
Total spent
50.50 + 10.10 = $60.60
correct answer D
Question: A large no. N =1234567891011121314…99899100. What will be the remainder when 1st 100 digits of N is divided by 9?
A.2
B.3
C.5
D.7
Answer: C.5
Explanation: Hence the first 100 digits of N goes like this 1234567891011121314.......5253545
We need to find the sum of the above number to check for divisibility by 9.
From 1 to 50, each of the digits 1 to 4 occurs 14 times, digit 5 occurs 6 times and each of 6 to 9 occurs 5 times
Sum of digits from 1 to 4 = 10
Sum of digits from 6 to 9 = 30
Therefore, sum of digits from 1 to 50 = 10 * 15 + 5 * 6 + 30 * 5 = 330
Sum of digits from 51 to 54 plus a 5 = 5 * 4 + ( 1 + 2 + 3 + 4) + 5 = 20 + 15 = 35
Total sum = 330 + 35 = 365
When 365 is divided by 9, we get 5 as the remainder!
Correct Answer: 5
C
Question: If two dice are thrown together, the probability of getting an even number on one die and an odd number on the other is?
A.1/6
B.1/2
C.1/9
D.1/1
Answer: B.1/2
Explanation: The number of exhaustive outcomes is 36.
Let E be the event of getting an even number on one die and an odd number on the other. Let the event of getting either both even or both odd then
= 18/36 = 1/2
P(E) = 1 - 1/2 =1/2.
Answer: B
Question: Running at the same rate, 8 identical machines can produce 560 paperclips a minute. At this rate, how many paperclips could 10 machines produce in 6 minutes?
A.1344
B.4200
C.8400
D.50400
Answer: B.4200
Explanation: 8 machines produce 560 in 1 min
8 machines produce 560* 6 in 6 min
10 machine produce 560*6*(10/8) in 6 minutes
560*6*10/8=4200 answer is B.
Question: Sanoop bought 8 t-shirts at an average price (arithmetic mean) of Rs.526. If Sanoop returned 3 t-shirts to the retailer, and the average price of the remaining t-shirts was Rs.505, then what is the average price, of the three returned t-shirts?
A.560
B.561
C.562
D.563
Answer: B.561
Explanation: Total price of 8 t-shirts= 8*526=4208
Total price of 5 t-shirts=5*505=2525
Total price of 3 t-shirts=4208-2525=1683
Average price of 3 t-shirts=1683/3=561
Correct option Answer:B
Question: If a function f is defined by f(x)= 2x/(x-1) for all non zero numbers x. If f(a) = 4 and f(ab) = 6 then b= ?
A.3/2
B.1/2
C.7/2
D.3/4
Answer: D.3/4
Explanation: Given that f(x) =2x/(x-1) and f(a) = 4, then f(a) =2a/(a-1)=4 ===> 2a = 4a -4 => a =2, then backsolve using the answer choices:
f(ab) = f(2b) = 6
A) 3/2 ===> f(2*3/2) = f(3) = 2*3/(3-1) = 6/ 2 = 3
B) 1/2 ===> f((2*1/2) = f(1) = 2*1/(1-1) = undefined
C) 7/2 ===> f(2*7/2) = f(7) = 2*7/(7-1) = 14/6 = 7/3
D) 3/4 ===> f(2*3/4) = f(3/2) (2*3/2)/(3/2-1) = 3/(1/2) = 6 WINS
E) 1/4 ===> f(2*-1/4) = f(1/2) = (2*1/2)/(1/2-1) = 1/-1/2 = -2
Answer: D
Question: Train X and train Y pass one another traveling in opposite directions. Twenty four minutes later they are 100 miles apart. If train X’s constant speed is 30 miles per hour greater than train Y’s, how far does train X travel during that time?
A.28
B.40
C.56
D.72
Answer: C.56
Explanation: Let the rate of the Train Y be R
Then the rate of the Train X will be R+30 (given)
As per relative rate concept, the rate at which they are increasing the distance between them is R+(R+30) [add the rates] i.e. 2R+30
d=100 and t = 24 min i.e 24/60 hr
using RTD table, (2R+30) * 24/60 = 100 ==> R= 110 miles/hr
So the rate of train X is 140 miles/hr (since R+30)
The distance traveled by Train X in 24 min is R*T = 140 * 24/60 = 56 miles (C)
Question: At a company, the average wage of male employees is $9.97 per hour, and the average wage of female employees is $10.37 per hour. If the average wage of all employees is $10.12 per hour, what is the ratio of the number of male employees to the number of female employees?
A.1 to 2
B.2 to 3
C.3 to 2
D.5 to 3
Answer: D.5 to 3
Explanation: Average hourly wage of male employees = 9.97 $
Average hourly wage of female employees = 10.37 $
Average hourly wage of all employees = 10.12 $
Let number of male employees = m
number of female employees = f
10.12 = (9.97m + 10.37f ) / m+f
=>10.12m + 10.12f = 9.97m + 10.37f
=> .15m = .25f
=> m/f = .25/.15 = 5/3
Answer D