RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: It costs $3 for the first 30 minutes to make a collect call. After the first 30 minutes it costs $5 per hour. If a certain customer make a collect call lasting for 4 hours and 30 minutes, how much will it cost her?
A.$23
B.$25
C.$80
D.$15
Answer: A.$23
Explanation: 4 hrs 30 min = 270 min
First 30 min ------> $3
Time left is 240 min...
Now, 60 min costs $ 5
1 min costs $ 5/60
240 min costs $ 5/60*240 = $ 20
So, Total cost will be $20 + $3 = $ 23
The answer will be (A) $23
Question: A clock is started at noon. By 10 minutes past 5, the hour hand has turned through
A.145°
B.150°
C.155°
D.160°
Answer: C.155°
Explanation: Solution
Angle traced by hour hand in
12 hrs	=360°
Angle traced by hour hand in
5 hrs 10 min	= 31 / 6 hrs
=[360 / 12 x 31 / 6]
= 155°.
Answer C
Question: By selling 50 meters of cloth. I gain the selling price of 14 meters. Find the gain percent?
A.42 7/7%
B.42 5/8%
C.38 8/9%
D.42 6/8%
Answer: C.38 8/9%
Explanation: SP = CP + g
50 SP = 50 CP + 14 SP
36 SP = 50 CP
36 --- 14 CP gain
100 --- ? => 38 8/9%
Answer: C
Question: Machine A and machine B process the same work at different rates. Machine C processes work as fast as Machines A and B combined. Machine D processes work three times as fast as Machine C; Machine D’s work rate is also exactly four times Machine B’s rate. Assume all four machines work at fixed unchanging rates. If Machine A works alone on a job, it takes 7 hours. If all four machines work together on the same job simultaneously, how many minutes will it take all of them to complete it?
A.8
B.21
C.24
D.27
Answer: B.21
Explanation: C = A + B
D = 3C = 3(A+B) = 4B
Then B = 3A and C = 4A
The combined rate of the four machines is A + 3A + 4A + 12A = 20A
Machine A can complete the work in 420 minutes, so its rate is 1/420 of the work per minute.
The combined rate is 20/420 = 1/21 so the work will be completed in 21 minutes.
The answer is B.
Question: The difference between a number and its three fifth is 50. What is the number?
A.75
B.100
C.125
D.175
Answer: C.125
Explanation: Sol.
Let the numbers be x.
Then, x-3/5x = 50
⇔2/5x = 50⇔ x = (50x5/2) = 125.
Answer C
Question: If x = y+3+4.5x and y = x+18, what is the value of y/x ?
A.-6/5.
B.-7/20.
C.1/4.
D.-20/7.
Answer: D.-20/7.
Explanation: (1) x = y + 3 + 4.5x
Substitute y for y = x + 18 (Eq. we are given)
x = x + 18 + 3 + 4.5x
Combine like terms
x = 5.5x + 21 --> -4.5x = 21 --> x = -14/3
(2) y = x + 18
Substitute x for x = -14/3
y = (-14/3) + 18 = 40/3
(3) x/y = ?
Substitute x and y we found above
y/x = (40/3) /(-14/3) = (40/3) * (-3/14) = -40/14 = -20/7
My answer: D
Question: A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 4 liters per minute. When the tank is full in inlet is opened and due to the leak the tank is empties in 8 hours. The capacity of the tank is?
A.5729
B.5760
C.5729
D.5720
Answer: B.5760
Explanation: 1/x - 1/6 = -1/8
x = 24 hrs
24 * 60 * 4 = 5760
Answer:B
Question: What will be the compound interest on a sum of Rs. 20,000 after 3 years at the rate of 12% p.a.?
A.s.10123.22
B.s.10823.20
C.s.10123.20
D.s. 8098.56
Answer: D.s. 8098.56
Explanation: Explanation:
Amount = [20000 * (1 + 12/100)3]
= 20000 * 28/25 * 28/25 * 28/25 = Rs. 35123.20
C.I. = (35123.20 - 20000) = Rs. 8098.56
Answer:D
Question: A company has 600 employees, 40% of whom are employed Full time. If it hires 100 new employees, 15% of whom are employed part time, what will be the new percent of part time employees in total?
A.1 2/3 %
B.2 2/3 %
C.4 %
D.46.43 %
Answer: D.46.43 %
Explanation: Total employee = 600
Full time Empl = 600 * 40/100 =240
Part time Emp = 600 - 240 = 360
New part time empl = 100 * (15/100)
=15
Total new part time Emp = 15+360= 375
Old part time Emp = 360
Total Emp = 600 + 100 = 700
% of new part-time = (Total employee - new part time)*100 /total emp
= (700-375)*100/700
= 46.43 %
D
Question: A swimmer can swim in still water at 4 km/h. If the speed of the water current is 2 km/h, how many hours will the swimmer take to swim against the current for 5 km?
A.2.0
B.2.5
C.3.0
D.3.5
Answer: B.2.5
Explanation: The swimmer can swim against the current at a speed of 4-2 = 2 km/h.
The time it will take is 5/2 = 2.5 hours.
The answer is B.
Question: An anti aircraft gun can fire four shots at a time. If the probabilities of the first, second, third and the last shot hitting the enemy aircraft are 0.7, 0.6, 0.5 and 0.4, what is the probability that four shots aimed at an enemy aircraft will bring the aircraft down?
A.0.084
B.0.916
C.0.036
D.0.964
Answer: D.0.964
Explanation: Sum of probabilities of each shot= 0.7+0.3*0.6+0.3*0.4*0.5+0.3*0.4*0.5*0.4
=0.964
ANSWER:D
Question: The diameter of the driving wheel of a bus is 140 cm. How many revolution, per minute must the wheel make in order to keep a speed of 66 kmph ?
A.33
B.250
C.138
D.278
Answer: B.250
Explanation: Explanation:
Circumference = No.of revolutions * Distance covered
Distance to be covered in 1 min. = (66 X1000)/60 m = 1100 m.
Circumference of the wheel = 2 x (22/7) x 0.70 m = 4.4 m.
Number of revolutions per min. =(1100/4.4) = 250.
Answer: B) 250
Question: Jackson invested $600,000, dividing it all unequally between Account P and Account Q. At the end of the year, it turned out that Account P had earned 12% interest and Account Q had earned 25% interest. If Jackson earned a total of $60,000 in interest between the two accounts, which of the following is approximately the amount he put in account P?
A.$115,384
B.$120,000
C.$121,072
D.$124,129
Answer: D.$124,129
Explanation: x be the amount invested in account P
0.12*x +(600000-x)*0.25=60,000
15000/.13=x
x=1500000/13=11...=$124,129
hence answer is D
Question: To mail a package, the rate is u cents for the first pound and v cents for each additional pound, where u>v. Two packages weighing 3 pounds and 5 pounds, respectively can be mailed seperately or combined as one package. Which method is cheaper and how much money is saved?
A.Combined, with a saving of u-v cents
B.Combined, with a saving of y-x cents
C.Combined, with a saving of x cents
D.Separately, with a saving of x-y cents
Answer: A.Combined, with a saving of u-v cents
Explanation: This means it costs x cent for the first pound in weight for example, 20 cents for the first pound.
It costs y cents for the every pound in weight above this, for example 10 cents for pound 2 and 10 cents for pound 3.
x is more than y. for example 20 cents vs. 10 cents
3 pounds: x+2y
5 pounds:x+4y
Total: 2x+6y
8 pounds: x+7y
So we are saving:
(2X+6y) - x+7y
= x-y cents
Combined is cheaper as we maximise y and minimize x.
Answer is:
1) Combined, with a saving of x-y cents
Question: Roja and Pooja start moving in the opposite directions from a pole. They are moving at the speeds of 5 km/hr and 3 km/hr respectively. After 4 hours what will be the distance between them?
A.32 km
B.20 km
C.65 km
D.18 km
Answer: A.32 km
Explanation: Distance = Relative Speed * Time
= (5 + 3) * 4 =32 km
[ They are travelling in the opposite direction, relative speed
= sum of the speeds].
Answer: A
Question: Set A contains all the even numbers between 6 and 50 inclusive. Set B contains all the even numbers between 106 and 150 inclusive. What is the difference between the sum of elements of set B and the sum of the elements of set A?
A.2300
B.2550
C.5050
D.6275
Answer: A.2300
Explanation: Set A contains 6, 8, ... 50
Set B contains 102 , 104 , 106 ... 150
Number of terms in each set = 23
Difference between corresponding terms in set A and B = 100
Difference between Sum of set B and set A = 100*23 = 2300
Answer A
Question: A clothing store purchased a pair of pants for $90 and was selling it at a price that equaled the purchase price of the pants plus a markup that was 25 percent of the selling price. After some time a clothing store owner decided to decrease the selling price by 20 percent. What was the clothing store's gross profit on this sale?
A.$14
B.$5
C.$10
D.$6
Answer: D.$6
Explanation: Sale Price(SP) = 90 + Markup(MP)
--> Mp = SP-90
and given MP=SP/4 ( 25% is 1/4th)
so SP/4= SP-90
3SP/4= 90
SP=120
Now a discount of 20% is given so NEW SP is .8 *120 =96
Profit=96-90 =6.0$
Answer is D
Question: A = {0, 1, -3, 6, -8}
B = {-1, 2, -4, 7}
If a is a number that is randomly selected from Set A, and b is a number that is randomly selected from Set B, what is the probability that ab > 0?
A.1/4
B.1/3
C.2/5
D.4/9
Answer: C.2/5
Explanation: For the product of 2 numbers to be positive either both of them must be positive or both of them must be negative:
P(positive, positive) = 2/5*2/4 = 4/20;
P(negative, negative) = 2/5*2/4 = 4/20.
P = 4/20 + 4/20 = 8/20 = 2/5.
Answer: C.
Question: If (1 / 3.718) = 0.2689, Then find the value of (1 / 0.0003718).
A.2689
B.2869
C.2968
D.2986
Answer: A.2689
Explanation: (1 / 0.0003718 ) = ( 10000 / 3.718 ) = 10000 * (1 / 3.718) = 10000 * 0.2689 = 2689.
Answer is A.
Question: A certain debt will be paid in 52 installments from January 1 to December 31 of a certain year. Each of the first 22 payments is to be $410; each of the remaining payments is to be $65 more than each of the first 22 payments. What is the average (arithmetic mean) payment that will be made on the debt for the year?
A.447.5
B.450
C.465
D.468
Answer: A.447.5
Explanation: Total number of installments = 52
Payment per installment for the first 22 installments = 410
Payment per installment for the remaining 30 installments = 410+65=475
Average = (22*410 + 30*475)/52 = 447.50
Answer A
Question: The length of a rectangle is reduced by 20%. By what % would the width have to be increased to maintainthe original area?
A.10%
B.21%
C.25%
D.40%
Answer: C.25%
Explanation: Sol. Required change = (20*100)/(100-20)=25%
C
Question: A bag contains 5 red, 6 blue and 2 green balls. If 2 ballsare picked at random, what is the probability that both are red?
A.1/13
B.2/23
C.5/39
D.4/27
Answer: C.5/39
Explanation: P(Both are red),
5C213C2=6C213C2
=10/78=5/39
C
Question: The batting average of a particular batsman is 59 runs in 46 innings. If the difference in his highest and lowest score is 150 runs and his average excluding these two innings is 58 runs, find his highest score.
A.156
B.208
C.210
D.223
Answer: A.156
Explanation: Explanation:
Total runs scored by the batsman = 59*46 = 2714 runs
Now excluding the two innings the runs scored = 58*44 = 2552 runs
Hence the runs scored in the two innings = 2714 – 2552 = 162 runs.
Let the highest score be x, hence the lowest score = x – 150
x + (x - 150) = 162
2x = 312
x = 156 runs
ANSWER A
Question: How many two digit numbers are there such that the product of their digits after reducing it to the smallest form is a prime number? for example if we take 98 then 9*8=72, 72=7*2=14, 14=1*4=4. Consider only 4 prime no.s (2,3,5,7)
A.16
B.17
C.18
D.19
Answer: C.18
Explanation: we know prime no. are 2 ,3 , 5, 7
mulply by 1 is prime no
2 = 21(2*1)=73(7*3)
2 = 21 (2*1)=37(3*7)
2= 12(1*2)=43(4*3)or34(3*4)
or26(2*6)or62(6*2)
.
.
.similarly for all prime no then u will got it....
12,13,15,17,21,26,31,34,35,37,43,51,53,57,62,71,73,75
ans is 18
ANSWER:C
Question: What is the difference between the C.I. on Rs. 5000 for 1 1/2 years at 4% per annum compounded yearly and half-yearly?
A.Rs.2.04
B.Rs.2.08
C.Rs.2.02
D.Rs.2.83
Answer: A.Rs.2.04
Explanation: C.I. when interest is compounded yearly
= [5000 * (1 + 4/100) * (1 + (1/2 * 4)/100]
= 5000 * 26/25 * 51/50 = Rs. 5304
C.I. when interest is compounded half-yearly
= [5000 * (1 + 2/100)2]
= (5000 * 51/50 * 51/50 * 51/50)
= Rs. 5306.04 Difference
= (5306.04 - 5304)
= Rs.2.04.
Answer: A
Question: A certain NYC taxi driver has decided to start charging a rate of r cents per person per mile. How much, in dollars, would it cost 3 people to travel x miles if he decides to give them a 50% discount?
A.3xr/2
B.3x/200r
C.3r/200x
D.3xr/200
Answer: D.3xr/200
Explanation: r/100 dollars per person per mile
one person going x miles will be charged rx/100
50% discount = rx/200
3 such people = 3rx/200 ;
ANSWER:D
Question: How many of the following numbers are divisible by 132?
396, 462, 792, 965, 2178, 5184, 6336
A.3
B.5
C.6
D.7
Answer: A.3
Explanation: Explanation:
A number is divisible by 132, if it is divisible by each one of 11, 3 and 4.
Clearly, 965 is not divisible by 3. None of 462 and 2178 is divisible by 4.
Also, 5184 is not divisible by 11.
Each one of remaining 3 is divisible by each one of 11, 3 and 4 and therefore, by 132.
Answer: A
Question: In the coordinate plane, one of the vertices of a square is the point (-5, -4). If the diagonals of that square intersect at point (3, 2), what is the area of that square?
A.100
B.225
C.169
D.256
Answer: D.256
Explanation: One point (-5-4), Intersection (3,2) so the distance from the first point -5-3=-8 is the midpoint of the square --> whole side 16, 16*16=256
D
Question: A train 125 m long passes a man, running at 8 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:
A.35 km/hr
B.53 km/hr
C.45 km/hr
D.65 km/hr
Answer: B.53 km/hr
Explanation: Speed of the train relative to man
= (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr
= 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed
= (x - 8) km/hr. x - 8 = 45 ==> x = 53 km/hr.
Answer: B
Question: Right triangle ABC is to be drawn in the xy-plane so that the right angle is at A and AB is parallel to the y-axis. If the x- and y-coordinates of A, B, and C are to be integers that are consistent with the inequalities -3 ≤ x ≤ 2 and 4 ≤ y ≤ 9 , then how many different triangles can be drawn that will meet these conditions?
A.54
B.432
C.2,160
D.2,916
Answer: B.432
Explanation: We have the rectangle with dimensions 9*3 (9 horizontal dots and 3 vertical). AB is parallel to y-axis and AC is parallel to x-axis.
Choose the (x,y) coordinates for vertex A: 9C1*3C1;
Choose the x coordinate for vertex C (as y coordinate is fixed by A): 8C1, (9-1=8 as 1 horizontal dot is already occupied by A);
Choose the y coordinate for vertex B (as x coordinate is fixed by A): 2C1, (3-1=2 as 1 vertical dot is already occupied by A).
9C1*3C1*8C1*2C1=432.
Answer: B.
Question: What is the % change in the area of a rectangle when its length increases by 10% and its width decreases by 10%?
A.0%
B.20% increase
C.20% decrease
D.1% decrease
Answer: D.1% decrease
Explanation: Explanatory Answer
Whenever you encounter problems like this, use a numerical example and then proceed.
For ease of computation, it is safe in most cases, to assume the length to be 100 units and the width to be 100 units.
(Remember, a square is a rectangle too and the problem works the same way when you assume different values for length and width. Computation becomes a bit tedious with different values for length and width)
Area of a rectangle = length * width = 100 * 100 = 10,000 sq units.
When the length increases by 10%, the new length becomes 110 units.
And as the width decreases by 10%, new width becomes 90 units.
Therefore, New area = 110 * 90 = 9900 sq units.
New area is 100 sq units lesser than the original area.
% change in area = ((change in area)/(original area)) * 100
= (100/10,000)*100 = 1% decrease in area
The correct choice is (D)
Question: How many digits will be there to the right of the decimal point in the product of 95.75 and .02554?
A.5
B.6
C.7
D.8
Answer: B.6
Explanation: Solution
Som of decimal places	= 7.
Since the last digit to the extreme right will be zero ( ∴ 5 x 4 = 20), so there will be 6 significant digits to the right of the decimal point.
Answer B
Question: The product of the prime integers between 53 and 60, inclusive, is:
A.50! – 40!
B.178,239
C.2,303
D.2,021
Answer: B.178,239
Explanation: only prime number bet ween 53 and 60 inclusive are 53, 57, 59
thus 53*57 * 59= 178,239
Ans: B
Question: If (4 - x)/(4 + x) = x, what is the value of x^2 + 5x - 4?
A.0
B.2
C.4
D.6
Answer: A.0
Explanation: (4-x) = x*(4+x)
(4-x) = 4x+x^2
0 = x^2+5x-4
The answer is A.
Question: Rohan spends 40% of his salary on food, 20% on house rent, 10% on entertainment and 10% on conveyance. If his savings at the end of a month are Rs. 3000. then his monthly salary is
A.Rs. 15000
B.Rs. 12000
C.Rs. 9000
D.Rs. 6000
Answer: A.Rs. 15000
Explanation: Sol.
Saving = [100 - (40 + 20 + 10 + 10]% = 20%.
Let the monthly salary be Rs. x.
Then, 20% of x = 3000
â‡” 20 / 100x = 3000
â‡” x = 3000 Ã— 5 = 15000.
Answer A
Question: In a two digit number, if it is known that its units digit exceeds its ten's digit by 2 and that the product of the given number and the sum of its digits is equal to 144, then the number is
A.42
B.46
C.22
D.24
Answer: D.24
Explanation: Sol.
Let the ten's digit be x.
Then, units digit = x + 2.
Number = 10x + (x+2) = 11x + 2;
Sum of digits = x + (x+2) = 2x +2.
∴ (11x +2)(2x+2) = 144
⇔ 22x2 + 26x - 140 = 0
⇔ 11x2 + 13x - 70 = 0
⇔ (x - 2)(11x+35) = 0 ⇔ x =2.
Hence, required number = 11x + 2 = 24.
Answer D
Question: Suresh can complete a job in 15 hours. Ashutosh alone can complete the same job in 35 hours. Suresh works for 9 hours and then the remaining job is completed by Ashutosh. How many hours will it take Ashutosh to complete the remaining job alone?
A.4
B.5
C.14
D.12
Answer: C.14
Explanation: The part of job that Suresh completes in 9 hours
= 9â„15 = 3â„5
Remaining job = 1 - 3â„5 = 2â„5
Remaining job can be done by Ashutosh in 2â„5 Ã— 35 = 14 hours
Answer C
Question: In how many ways can 7 boys be seated in a circular order?
A.110
B.230
C.720
D.420
Answer: C.720
Explanation: Number of arrangements possible
=(7−1)!=6!=6x5x4x3x2x1=720
Answer: C
Question: If y is 70 percent greater than x, then x is what percent less than y?
A.41%
B.47%
C.55%
D.63%
Answer: A.41%
Explanation: y = 1.7x
x = y/1.7 = 10y/17 = y - (7/17)*y
7/17 is about 41%.
The answer is A.
Question: Find k if 56 / k = 4.
A.16
B.17
C.18
D.14
Answer: D.14
Explanation: Since 56 /k = 4 and 56/ 14 = 4, then
k = 14 correct answer D
Question: The circumferences of two circles are 264 meters and 352 meters. Find the difference between the areas of the larger and the smaller circles?
A.4329
B.2799
C.4312
D.2799
Answer: C.4312
Explanation: Let the radii of the smaller and the larger circles be s m and l m respectively.
2∏s = 264 and 2∏l = 352
s = 264/2∏ and l = 352/2∏
Difference between the areas = ∏l2 - ∏s2
= ∏{1762/∏2 - 1322/∏2}
= 1762/∏ - 1322/∏
= (176 - 132)(176 + 132)/∏
= (44)(308)/(22/7) = (2)(308)(7) = 4312 sq m
Answer: C
Question: A certain sum of money at simple interest amounted Rs.840 in 10 years at 3% per annum, find the sum?
A.277
B.262
C.298
D.646
Answer: D.646
Explanation: 840 = P [1 + (10*3)/100]
P = 646
Answer: D
Question: Find the least number must be subtracted from 62575 so that remaining number is divisible by 99.
A.93
B.7
C.54
D.9
Answer: B.7
Explanation: On dividing 62571 by 99 we get the remainder 7, so 7 should be subtracted. Answer is
B
Question: A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 18 km/hr. What is the length of the platform?
A.80
B.240
C.288
D.277
Answer: A.80
Explanation: Speed = 18 * 5/18 = 5 m/sec.
Length of the train =5 * 20 = 100 m.
Let the length of the platform be x m . Then,
(x + 100)/36 = 5 => x = 80 m.
Answer: A
Question: How many ways are there to split a group of 6 girls into two groups of 3 girls each? (The order of the groups does not matter)
A.35
B.10
C.40
D.20
Answer: B.10
Explanation: the combination is 6C3 /2
= 6!/3!*3!*2 = 20/2 =10
B
Question: A certain sum amounts to Rs.1725 in 3 years and Rs.1875 in 5 years. Find the rate % per annum?
A.9%
B.5%
C.3%
D.1%
Answer: B.5%
Explanation: 3 --- 1725
5 --- 1875
--------------
2 --- 150
N = 1 I = 75 R = ?
P = 1725 - 225 = 1500
75 = (1500*1*R)/100
R = 5%
Answer: B
Question: In how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together?
A.120028 ways
B.120860 ways
C.120960 ways
D.120920 ways
Answer: C.120960 ways
Explanation: In the word 'MATHEMATICS', we treat the vowels AEAI as one letter.
Thus, we have MTHMTCS (AEAI).
Now, we have to arrange 8 letters, out of which M occurs twice, T occurs twice and the rest are different.
Number of ways of arranging these letters =	8!/(2!)(2!)	= 10080.
Now, AEAI has 4 letters in which A occurs 2 times and the rest are different.
Number of ways of arranging these letters =	4!/2!	= 12.
Required number of words = (10080 x 12) = 120960.
Answer:C
Question: The probability that A speaks truth is 3/5 and that of B speaking truth is 4/7. What is the probability that they agree in stating the same fact?
A.18/35
B.18/37
C.18/39
D.18/33
Answer: A.18/35
Explanation: If both agree stating the same fact, either both of them speak truth of both speak false.
Probability = 3/5 * 4/7 + 2/5 * 3/7
= 12/35 + 6/35
= 18/35
Answer:A
Question: The L.C.M of two numbers is 2310 and their H.C.F is 30. If one number is 330 the Other is
A.330
B.300
C.210
D.250
Answer: C.210
Explanation: The other number
= L.C.M * H.C.F/given number
= 2310*30/330 = 210
Answer is C.
Question: If the selling price of 50 articles is equal to the cost price of 40 articles, then the loss or gain percent is:
A.20% loss
B.20% gain
C.25% loss
D.25% gain
Answer: A.20% loss
Explanation: Let C.P. of each article be Re. 1.
Then, C.P. of 50 articles = Rs. 50;
S.P. of 50 articles = Rs. 40.
Loss % = 10/50 * 100 = 20%
ANSWER:A
Question: The set X consists of the following terms: {4,44,444,4444,.....}, where the nth term has n 4's in it for example 10th term is 4444444444. What is the hundreds digit of the sum of the first 35 terms of set X?
A.1
B.3
C.5
D.7
Answer: D.7
Explanation: 35*4 + 34*40 + 33*400 = 140 + 1360 + 13200 = 14700
The hundreds digit is 7.
The answer is D.
Question: If log10 5 + log10 (5x + 1) = log10 (x + 5) + 1, then x is equal to:
A.15
B.8
C.9
D.3
Answer: D.3
Explanation: Explanation:
log10 5 + log10 (5x + 1) = log10 (x + 5) + 1
log10 5 + log10 (5x + 1) = log10 (x + 5) + log10 10
log10 [5 (5x + 1)] = log10 [10(x + 5)]
5(5x + 1) = 10(x + 5)
5x + 1 = 2x + 10
3x = 9
x = 3.
answer D
Question: One water pump can fill half of a certain empty tank in 6 hours. Another pump can fill half of the same tank in 6.5 hours. Working together, how long will it take these two pumps to fill the entire tank?
A.6 7/13
B.1 5/8
C.3 1/4
D.6 6/25
Answer: D.6 6/25
Explanation: One pump can fill a tank in 6 hours and another in 6.5 hours
so the rate at which both can half fill the tank is (1/6+1/6.5) => 25/78
Thus half of the tank can be filled in 78/25
so for filling the complete tank => 78/25*2 = 156/25 = 6 6/25
ANSWER:D
Question: Annika hikes at a constant rate of 10 minutes per kilometer. She has hiked 2.5 kilometers east from the start of a hiking trail when she realizes that she has to be back at the start of the trail in 35 minutes. If Annika continues east, then turns around and retraces her path to reach the start of the trail in exactly 35 minutes, for how many kilometers total did she hike east?
A.3.625
B.3.5
C.3
D.4
Answer: C.3
Explanation: Set up two R x T =D cases.
1. 1/10 km/ min x T = 2.5
from which T= 25 mins.
We know total journey time now is 35 +25 = 60
The rate is the same ie 1/10km/min.
set up second R x T =D case.
1/10 km/min x 60 = 6 km
Now the total journey would be halved as distance would be same in each direction. 6/2 =3
C
Question: A and B invested in a business in the ratio 7 : 11, in the annual profit they donated 10% of the profit to a charity, and after donating, A received Rs.12600 as his share in the profit, then what amount is donated to the charity ?
A.Rs.2500
B.Rs.1800
C.Rs.3600
D.Rs.1260
Answer: C.Rs.3600
Explanation: Ratio of investments of A and B = 7 : 11 = [18 units].
A received = Rs.12600.
Total profit = 12600 / 7 × 18 = Rs.324000.
Profit after donation = Rs.32400 which is [Profit – 10% = 90% of the actual profit].
Profit before donation = 32400 / 90 × 100 = Rs.36000.
Actual profit = Rs.360000 => Donation = Rs.36000 × 10 / 100 = Rs.3600
Option C