divelab/Sys2Bench huggingface dataset:
Question: Sarah is driving to the airport. After driving at 15 miles per hour for one hour, she realizes that if she continues at that same average rate she will be an hour late for her flight. She then travels 60 miles per hour for the rest of the trip, and arrives 30 minutes before her flight departs. How many miles did she drive in all?
Options:
A)45
B)175
C)210
D)245
E)280
Rationale: After driving at 15 miles per hourfor one hour, this distance left to cover is d-15. Say this distance is x miles.
Now, we know that the difference in time between covering this distance at 15 miles per hour and 60 miles per hour is 1+ 1/2 = 3/2 hours.
So, we have that x/15 - x/60 = 3/2 --> 4x/60 - x/60 = 3/2 --> 3x/60 = 3/2 --> x = 30.
Total distance = x + 15 = 45 miles.
Answer: A
Answer: A
Question: Six machines at a certain factory operate at the same constant rate. If five of these machines, operating simultaneously, take 30 hours to fill a certain production order, how many fewer hours does it take all six machines, operating simultaneously, to fill the same production order?
Options:
A)3
B)5
C)6
D)16
E)24
Rationale: The total work is 5*30 = 150 machine hours
The time required for six machines is 150/6 = 25 hours, thus 5 fewer hours.
The answer is B.
Answer: B
Question: If x ≠ 0 and (y^2 + xy)/x=y+x, which of the following expressions is equal to its opposite?
Options:
A)x^2
B)x^2 + y^2
C)x^2 - y^2
D)(y + x)^2
E)(x – y)^2
Rationale: (y^2 + xy)/x=y+x
=> y^2 + xy = xy +x^2
=> x^2 - y^2 = 0
Answer C
Answer: C
Question: Convert 800 miles into meters?
Options:
A)1287472
B)845796
C)804670
D)784596
E)864520
Rationale: 1 mile = 1609.34 meters
800mile = 800*1609.34 = 1287472 meters
Answer is A
Answer: A
Question: Out of three consecutive odd numbers eight times the first number is equal to addition of thrice the third number and adding 5 to twice the second . What is the first number?
Options:
A)5
B)6
C)7
D)8
E)9
Rationale: Description :
=> 8x=2(x+2)+5+3(x+4)
=> 3x=21,x=7
=> x+4=11
X=11-4=7
Answer C
Answer: C
Question: A bag contains an equal number of one rupee, 50 paise and 25 paise coins respectively. If the total value is 70, how many coins of each type are there?
Options:
A)20 coins
B)30 coins
C)40 coins
D)25 coins
E)None of these
Rationale: Let number of each type of coin = x. Then,
1 × x + .50 × x + .25x = 70
⇒ 1.75x = 70 ⇒ x = 40 coins
Answer C
Answer: C
Question: Y = {2, 3, 4, 5}
B = {4, 5, 6, 7, 8}
Two integers will be randomly selected from the sets above, one integer from set Y and one integer from set B. What is the probability that the sum of the two integers will equal 9 ?
Options:
A) 0.15
B) 0.20
C) 0.25
D) 0.30
E) 0.33
Rationale: The total number of pairs Y,B possible is 4*5=20. Out of these 20 pairs only 4 sum up to 9: (2, 7); (3, 6), (4, 5) and (5, 4). The probability thus is 4/20=0.2.
Answer: B.
Answer: B
Question: Three friends had dinner at a restaurant. When the bill was received, Akshitha paid 1/4 as much as Veena paid and Veena paid 1/2 as much as Lasya paid. What fraction of the bill did Veena pay ?
Options:
A)3/19
B)3/12
C)3/11
D)3/10
E)4/13
Rationale: Let Veena paid x,
so Akshitha paid x/4 , and Lasya paid 2x,
So total bill paid is given by
x+(x/4) +2x = 1, we get
i.e. x = 4/13
Answer: E
Answer: E
Question: Of the 200 stamps in a collection, 90 are foreign and 70 are more than 10 years old. If 20 stamps are both foreign and more than 10 years old, how many stamps are neither foreign nor more than 10 years old?
Options:
A)60
B)80
C)100
D)130
E)150
Rationale: 20 stamps are both foreign and more than 10 years old.
70 stamps are foreign only.
50 stamps are 10 years old only.
The number of remaining stamps is 200 - (20+70+50) = 60
The answer is A.
Answer: A
Question: The ratio of the age of a man and his wife is 4:3. At the time of marriage the ratio was 5:3 and After 4 years this ratio will become 9:7. How many years ago were they married?
Options:
A)8
B)9
C)10
D)11
E)12
Rationale: Let the present age of the man and his wife be 4x and 3x respectively.
After 4 years this ratio will become 9:7
⇒(4x+4):(3x+4)=9:7⇒7(4x+4)=9(3x+4)⇒28x+28=27x+36⇒x=8
Present age of the man =4x=4×8=32
Present age of his wife =3x=3×8=24
Assume that they got married before t years. Then,
(32−t):(24−t)=5:3⇒3(32−t)=5(24−t)⇒96−3t=120−5t⇒2t=24⇒t=242=12
Answer is E.
Answer: E
Question: If a = -0.2, which of the following is true?
Options:
A)a < a^2 < a^3
B)a^2 < a^3 < a
C)a < a^3 < a^2
D)a^2 < a < a^3
E)a^3 < a < a^2
Rationale: a=-0.2;
a^2=0.04;
a^3=-0.008;
Answer : C
Answer: C
Question: total race distance 2100
A flight beat B flight by 420 when wind is in the race direction,it beats B by 300 when opposite.find the still fight speeds
Options:
A)300
B)360
C)400
D)450
E)480
Rationale: (420+300)/2=360
ANSWER:B
Answer: B
Question: Jodi is given the perimeter of a rectangle. She also knows
that the length is twice as many meters as the width. Using the formula for finding the perimeter
of a rectangle, find the dimensions of the rectangle
Options:
A)31 meters wide and 62 meters long.
B)21 meters wide and 42 meters long.
C)41 meters wide and 82 meters long.
D)11 meters wide and 22 meters long.
E)51 meters wide and 102 meters long.
Rationale: The formula for finding the perimeter of a rectangle is P 2l 2w, where l length and
w width
In this case, let x represent the width and 2x the length.
Now substitute the information you have into the formula and solve.
P 2l 2w
126 2(2x) 2(x)
126 4x 2x
126 6x
21 x
Answer: The rectangular garden is 21 meters wide and 42 meters long.
Check: Make sure the dimensions meet the condition of the problem. Substitute the dimensions
into the perimeter formula: P 2(21) 2(42) 42 84 126 meters. The answer is correct.
correct answer B
Answer: B
Question: Lindsay can paint 1/x of a certain room in one hour. If Lindsay and Joseph, working together at their respective rates, can paint the room in six hours, what fraction of the room can Joseph paint in 20 minutes?
Options:
A)1/6x
B)x/(x-3)
C)(x-6)/18x
D)x/(x-6)
E)(x-6)/x
Rationale: Let J be Joseph's rate per hour.
1/x + J = 1/6 of a room per hour
J = 1/6 - 1/x, of a room per hour
In 20 minutes, Joseph can paint 1/3*(1/6-1/x) = 1/18-1/3x = (x-6)/18x
The answer is C.
Answer: C
Question: The ratio of boarders to day students at a school was originally 5 to 12. However, after a number of new boarders join the initial 330 boarders, the ratio changed to 1 to 2. If no boarders became day students and vice versa, and no students left the school, how many new boarders joined the school?
Options:
A)48
B)66
C)72
D)80
E)84
Rationale: Let x be the number of new boarders.
The ratio changed from 5:12 up to 1:2 = 6:12.
330 / (330+x) = 5/6
x = 66
The answer is B.
Answer: B
Question: A pool can be filled in 4 hours and drained in 5 hours. The valve that fills the pool was opened at 9:00 am and some time later the drain that empties the pool was also opened. If the pool was filled by 6:00 pm and not earlier, when was the drain opened?
Options:
A)10:45 am
B)11:45 am
C)12:45 pm
D)1:45 pm
E)2:45 pm
Rationale: The filling rate is 1/4 and the draining rate is 1/5.
The combined rate of filling and draining is 1/4 - 1/5 = 1/20.
Let x be the number of hours before the drain was opened.
x/4 + (9-x)/20 = 1
5x + 9 - x = 20
4x = 11
x = 2.75
The answer is 11:45 am.
The answer is B.
Answer: B
Question: If the wheel is 28 cm then the number of revolutions to cover a distance of 1056 cm is?
Options:
A)3
B)5
C)26
D)12
E)6
Rationale: 2 * 22/7 * 28 * x = 1056
=> x = 6
Answer: E
Answer: E
Question: AB + CD = SSS, where AB and CD are two-digit numbers and SSS is a three digit number; A, B, C, and D are distinct positive integers. In the addition problem above, what is the value of C?
Options:
A) 1
B) 3
C) 7
D) 9
E) Cannot be determined
Rationale: AB and CD are two digit integers, their sum can give us only one three digit integer of a kind of SSS it's 111.
So, A=1. 1B+CD=111
Now, C can not be less than 9, because no to digit integer with first digit 1 (mean that it's<20) can be added to two digit integer less than 90 to have the sum 111 (if CD<90 meaning C<9 CD+1B<111) --> C=9
Answer: D.
Answer: D
Question: Raja spends 60% of his monthly income on household items, 10% of his monthly income on buying cloths, 10% of his monthly income on medicines and saves the remaining amount which is Rs. 5000. Find his monthly income.
Options:
A)Rs. 40000
B)Rs. 36000
C)Rs. 50000
D)Rs. 25000
E)None of these
Rationale: Savings 20% - 5000
Expenditure 80% - 20000
Total - 25000
Answer : D
Answer: D
Question: 51 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work?
Options:
A)10
B)13
C)14
D)15
E)17
Rationale: According to the chain rule,
M1 x T1 = M2 x T2
Therefore, 51 x 12 x 5 = 30 x 6 x X
X = 17
Hence, the number of days = 17.
ANSWER:E
Answer: E
Question: A right triangle has sides of a, b, and 13, respectively, where a and b are both integers. What is the value of (a + b)?
Options:
A)160
B)169
C)162
D)164
E)166
Rationale: LET a= hypotenuse , b =base ,13 = perpendicular . therefore a^2 -b^2 =1^2 or (a+b)(a-b) = 169
a+b =169/a-b ' a-b cannot be zero ..therefore a+ b =144 where a-b is equal to 1
B
Answer: B
Question: If 5/(a - 5) = -7/(a + 7), then a = ?
Options:
A)-31/6
B)-35/6
C)-33/6
D)-29/6
E)-37/6
Rationale: Multiply all terms of the given equation by (a - 5)(a + 7), simplify and solve
(a - 5)(a + 7)[ 5/(a - 5) ] = (a - 5)(a + 7) [ -7/(a + 7) ]
5 (a + 7) = -7 (a - 5)
a = -35/6
correct answer B
Answer: B
Question: You collect baseball cards. Suppose you start out with 16. Since you're nice, you give John 3 baseball cards. How many baseball cards do you have at the end?
Options:
A)11
B)12
C)13
D)14
E)15
Rationale: Solution
Start with 16 baseball cards.
John takes 3 baseball cards from you: 16 - 3 = 13 baseball cards.
So you have 13 at the end.
Correct answer : C
Answer: C
Question: Convert 60miles into yards?
Options:
A)105600 yards
B)35200 yards
C)39520 yards
D)42560 yards
E)41520 yards
Rationale: 1 mile = 1760 yards
60 miles = 60*1760 = 105600 yards
Answer is A
Answer: A
Question: If 2 men or 3 women can reap a field in 10 days how long will 4 men and 5 women take to reap it?
Options:
A)2/25
B)11/30
C)3/60
D)5/42
E)7/12
Rationale: Explanation:
2 men reap 1/10 field in 1 day
1 man reap 1/(2 x 10)
3 women reap 1/10 field in 1 day
1 woman reap 1/(10 x 3)
4 men and 5 women reap 4/(2 x 10)+ 5/(3 x 10)) =11/30 in 1 day
4 men and 5 women will reap the field in 11/30 days
Answer: Option B
Answer: B
Question: Find the length of the wire required to go 14 times round a square field containing 5625 m2.
Options:
A)15840
B)3388
C)4200
D)8766
E)66711
Rationale: a2 = 5625 => a = 75
4a = 300
300 * 14 = 4200
Answer: C
Answer: C
Question: The volume of the greatest sphere that can be cut off from a cylindrical log of wood of base radius 1 cm and height 5 cm is :
Options:
A)3/4∏
B)4/3∏
C)5∏
D)5/9∏
E)None
Rationale: Sol.
Required volume = Volume of a sphere of radius 1 cm
=[4/3 ∏ * 1 * 1 * 1]cm³ = 4/3 ∏cm³
Answer B
Answer: B
Question: Ashok secured average of 75 marks in 6 subjects. If the average of marks in 5 subjects is 74, how many marks did he secure in the 6th subject?
Options:
A)38
B)27
C)99
D)17
E)80
Rationale: Explanation:
Number of subjects = 6
Average of marks in 6 subjects = 75
Therefore total marks in 6 subjects = 75 * 6 = 450
Now, No. of subjects = 5
Total marks in 5 subjects = 74 * 5 = 370
Therefore marks in 6th subject = 450 – 370 = 80
ANSWER: E
Answer: E
Question: The time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 39 kmph, find the speed of the stream?
Options:
A)12 kmph
B)13 kmph
C)14 kmph
D)15 kmph
E)16 kmph
Rationale: The ratio of the times taken is 2:1.
The ratio of the speed of the boat in still water to the speed of the stream = (2+1)/(2-1) = 3/1 = 3:1
Speed of the stream = 39/3 = 13 kmph
ANSWER:B
Answer: B
Question: What is the probability of getting a sum 9 from two throws of dice.
Options:
A)1/3
B)1/9
C)1/12
D)2/9
E)None of these
Rationale: Explanation:
Total number of cases = 6*6 = 36
Favoured cases = [(3,6), (4,5), (6,3), (5,4)] = 4
So probability = 4/36 = 1/9
Option B
Answer: B
Question: The smallest 3 digit prime number is
Options:
A)A)113
B)B)103
C)C)109
D)D)101
E)E)None
Rationale: The smallest 3-digit number is 100, which is divisible by 2.
100 is not a prime number.
101 < 11 and 101 is not divisible by any of the prime numbers 2, 3, 5, 7, 11.
101 is a prime number.
Hence 101 is the smallest 3-digit prime number.
D)
Answer: D
Question: P and Q need 8 days to complete a work. Q and R need 12 days to complete the same work. But P, Q and R together can finish it in 6 days. How many days will be needed if P and R together do it?
Options:
A)3
B)8
C)12
D)4
E)6
Rationale: Explanation :
Let work done by P in 1 day = p
work done by Q in 1 day =q
Work done by R in 1 day = r
p + q = 1/8 ---(1)
q + r= 1/12	---(2)
p+ q+ r = 1/6	---(3)
(3) – (2) => p = 1/6 - 1/12 = 1/12
(3) – (1) => r = 1/6 – 1/8 = 1/24
p + r = 1/12 + 1/24 = 3/24 = 1/8
=> P and R will finish the work in 8 days
Answer : Option B
Answer: B
Question: How many integers from 101 to 200, inclusive, are divisible by 3 but not divisible by 7?
Options:
A)20
B)25
C)28
D)30
E)40
Rationale: We should find # of integers divisible by 3 but not by 3*7=21.
# of multiples of 21 in the range from 101 to 200, inclusive is (189-105)/21+1=5;
33-5=28.
Answer: C.
Answer: C
Question: Country X imposes a two-tiered tax on imported cars: the first tier imposes a tax of 25% of the car's price up to a certain price level. If the car's price is higher than the first tier's level, the tax on the portion of the price that exceeds this value is 15%. If Ron imported a $30,000 imported car and ended up paying $5500 in taxes, what is the first tier's price level?
Options:
A)$10000
B)$11000
C)$12000
D)$10500
E)$11500
Rationale: Let T be the tier price, P be total price = 30000
Per the given conditions:
0.25T + 0.15(P-T) = 5500
0.25T+0.15*30000-0.15T =5500
0.10T +4500 =5500
0.10T = 5500-4500 = 1000
T = 1000/0.10 =10000
Answer A
Answer: A
Question: In how many years will a sum of money doubles itself at 5% per annum on simple interest?
Options:
A)22 years
B)20 years
C)22 years
D)31years
E)13years
Rationale: Explanation:
P = (P*5*R)/100
R = 20%
Answer: Option B
Answer: B
Question: One fourth of one third of two fifth of a number is 15. What will be40% of that number
Options:
A)140
B)150
C)180
D)200
E)250
Rationale: Explanation:
(1/4) * (1/3) * (2/5) * x = 15 then x = 15 * 30 = 450
40% of 450 = 180
Answer: Option C
Answer: C
Question: If a merchant makes a profit of 20% based on the selling price of an article, what percent does the merchant makes on the cost?
Options:
A)20
B)40
C)25
D)50
E)None of These
Rationale: Let say Selling price will be Rs100,
20% profit means Cost price will be Rs80 and Rs20 is profit
now we have to find what percent of 80 will be 20 : X% * 80 = 20
X will be 25%
ANSWER:C
Answer: C
Question: Today my car meter reads as 72827 kms. I notes that this is a palindrome. How many minimum kms i need to travel so my car meter find another palindrom.
Options:
A)100 kms
B)115 kms
C)110 kms
D)160 kms
E)120 kms
Rationale: D
160 kms
72827+160 = 72827 , a palindrome
Answer: D
Question: Train A is 13 miles ahead of Train B, which is traveling the same direction along the same route as Train A. If Train A is traveling at an average speed of 37 miles per hour and Train B is traveling at an average speed of 43 miles per hour, how long will it take Train B to overtake and drive 17 miles ahead of Train A?
Options:
A)4 hours
B)2 hours
C)2 hours 30 minutes
D)5 hours
E)3 hours 20 minutes
Rationale: Relative speed = 43-37 = 6 miles per hour
Dist required = 13+17 = 30 miles
Time taken to overtake = 30/6 = 5 hours. D is the answer.
Answer: D
Question: A tank holds x gallons of a saltwater solution that is 20% salt by volume. One Fourth of the water is evaporated, leaving all of the salt. When 5 Gallons of water and 10 gallons of salt are added, the resulting mixture is 33 1/3 % salt by volume. What is the value of x?
Options:
A)37.5
B)75
C)100
D)150
E)175
Rationale: Nope, 150. I can only get it by following PR's backsolving explanation. I hate that.
Original mixture has 20% salt and 80% water.
Total = x
Out of which Salt = 0.2x and water = 0.8x
Now, 1/4 water evaporates and all salt remains.
So what remains is 0.2x salt and 0.6x water.
Now 10 gallons salt is added and 5 gallons of water is added.
So salt now becomes -> (0.2x + 10) and water --> (0.6x+5)
Amount of salt is 33.33% of total. So amount of water is 66.66%. So salt is half of the volume of water.
So (0.2x+10) = (0.6x+5)/2 = 0.4X+20 = 0.6X+5 =>0.2X=15
Solving, x = 75
Answer : B
Answer: B
Question: In the line xy plane line m has the equation y = 3x - 10, then the line m passes through which of the following points?
Options:
A)(3, 1)
B)(3, 4)
C)(4, 2)
D)(6, 9)
E)(6, 15)
Rationale: Yes it is y=3x-8....extremely sorry for mistake....
IF that's the case then answer is C
y=3x-8
2=3X4-10
2=12-10
2=2 (satisfied)
Answer: C
Question: How many diagonals does a polygon with 13 sides have, if one of its vertices does not connect to any diagonal?
Options:
A)65
B)62
C)58
D)54
E)60
Rationale: If I calculate it using the formulae, #diagonals = n (n-3)/2Each vertex sends of n-3 diagonals
n= 13-1 then 12*(12-3)/2 = 54
Correct Option:D
Answer: D
Question: The greatest possible length which can be used to measure exactly the length 6m, 4m 20cm, 4m is
Options:
A)20
B)27
C)35
D)87
E)98
Rationale: Explanation:
Required Length = H.C.F of 600 cm, 420 cm and 400 c
= 20 cm.
Answer: A) 20 cm
Answer: A
Question: Look at this series: 544, 509, 474, 439, ... What number should come next?
Options:
A)414
B)404
C)420
D)445
E)500
Rationale: Option A
Explanation:
This is a simple subtraction series. Each number is 35 less than the previous number.
ANSWER B
Answer: B
Question: Two couples and one single person are seated at random in a row of five chairs. What is the probability that neither of the couples sits together in adjacent chairs?
Options:
A)1/5
B)1/4
C)3/8
D)2/5
E)1/2
Rationale: Let A be any person from Couple A and B be any person from Couple B.
There are only two cases how the single person could be distributed to split the couples:
(1) * A1 * B1 * A2 * B2 *
(2) A1 B1 * A2 B2
where * denotes the possible seating arrangements for the single person.
(1) There are 5∗2!∗2!∗2!=40 different seating arrangements. We multiply by 2! because there are two options for couple A and two options for couple B to be seated. Furthermore, couple B could be seated to the left of A. Consider these possibilities:
* A2 * B1 * A1 * B2 *
* A1 * B2 * A3 * B1 *
* B1 * A1 * B2 * A2 *
etc.
(2) There are 2!∗2!∗2!=8 different seating arrangements. Same reason as above. Consider these possibilities:
A2 B1 * A1 B2
B1 A1 * B2 A2
etc.
Overall we have 40+8=48 possible arrangements and 5!=120 ways to arrange 5 people. The probability is 48/120=2/5
Answer: D.
Answer: D
Question: A certain football coach allows his quarterback to call three plays in a row. If the quarterback can choose from 3 passing plays, 4 running plays, and 2 trick plays, how many different N arrangements of plays can be run, if the same play can’t be run more than once?
Options:
A)24
B)125
C)243
D)504
E)729
Rationale: Number of N ways to choose the first play: 9
Second play: 8
Third:7
9*8*7= 504.D
Answer: D
Question: What is the next number in this Sequence ?
6, 14, 36, 98, 276, ?
Options:
A)657
B)794
C)453
D)564
E)123
Rationale: B
794
The nth term in the series is given by the sum of x^n for x in the range 1 to 3, i.e. 1^n + 2^n + 3^n.
Thus the first term is 1^1 + 2^1 + 3^1 = 1 + 2 + 3 = 6,
the second term is 1^2 + 2^2 + 3^2 = 1 + 4 + 9 = 14,
and so on.
The sixth term is then 1^6 + 2^6 + 3^6 = 1 + 64 + 729 = 794.
Answer: B
Question: The product of x and y is a constant. If the value of x is increased by 80%, by what percentage must the value of y be decreased?
Options:
A)45%
B)55%
C)35%
D)40%
E)44.44%
Rationale: x*y = constt.
Let x = y = 100 in beginning
i.e. x*y = 100*100 = 10000
x (100) ---becomes---> 1.8x (180)
i.e. 180*New 'y' = 10000
i.e. New 'y' = 10000/180 = 55.55
i.e. y decreases from 100 to 55.55 i.e. Decrease of 44.44%
Answer: option E
Answer: E
Question: How many sides does the polygon have if the sum of the interior angles measures up to 360 degrees?
Options:
A)4
B)6
C)3
D)7
E)None of these
Rationale: 4 sides...answer A
Answer: A
Question: A began a business with Rs. 85,000. He was joined afterwards by B with Rs. 42,500. For how much period does B join, if the profits at the end of the year are divided in the ratio of 3 : 1?
Options:
A)8 months
B)6 months
C)4 months
D)2 months
E)None
Rationale: Sol.
Suppose B joined for x months. Then, 85000 * 12 / 42500 * x = 3/1 or
x = 85000 * 12 / 42500 * 3 = 8.
So, B joined for 8 months.
Answer A
Answer: A
Question: If 2x+3y+z=55,x-y=4 and y - x + z=12,then what are the values of x , y and z?
Options:
A)7,11,8
B)5,8,9
C)4,2,5
D)3,9,8
E)None of them
Rationale: The given equations are:
2x+3y+z=55 …(i); x + z - y=4 …(ii); y -x + z =12 …(iii)
Subtracting (ii) from (i), we get: x+4y=51 …(iv)
Subtracting (iii) from (i), we get: 3x+2y=43 …(v)
Multiplying (v) by 2 and subtracting (iv) from it, we get: 5x=35 or x=7.
Putting x=7 in (iv), we get: 4y=44 or y=11.
Putting x=7,y=11 in (i), we get: z=8
Answer is A.
Answer: A
Question: If a man travels f miles an hour for h hours and r miles an hour for s hours, what is his average rate in miles per hour for the entire distance traveled?
Options:
A)fh + rs
B)(fh + rs)/2
C)h/f + s/r
D)(fh + rs)/(h - s)
E)(fh + rs)/(h + s)
Rationale: Average Speed = Total Distance /Total Time Taken
Total Distance travelled in t hours = fh
Total Distance travelled in s hours = rs
Total Time taken = h+s
Therefore , Average Speed = (fh+hs)/(h+s)
Answer E
Answer: E
Question: X and Y started a business by investing Rs.36000 and Rs.42000 respectively after 4 months Z joined in the business with an investment of Rs.48000, then find share of Z in the profit of Rs.14300 ?
Options:
A)3200
B)4000
C)3250
D)4160
E)3985
Rationale: Ratio of investment, as investments is for different time.
Investment x Number of units of time.
Ratio of investments X : Y : Z = 36000 : 42000 : 48000 => 6 : 7 : 8.
X = 6 x 12 Months = 72, Y = 7 x 12 = 84, Z = 8 X 8 = 64 => 18 : 21 : 16.
Ratio of investments => X : Y : Z = 18 : 21 : 16.
Investment Ratio = Profit sharing Ratio.
Z = 14300 Ã— 16/55 = Rs.4160.
Share of Z in the profit is Rs.4160.
Option D
Answer: D
Question: 2x<4y<0 which of the following is the greatest?
Options:
A)3x+3y
B)-(5x+4y)
C)2x-2y
D)x-3y
E)0
Rationale: Plugging in -1 for both x and y we get
A. 3x+3y =-6
B. -(5x+4y) =9
C. 2x-2y=0
D. x-3y =2
E. 0 =0
Answer: B
Answer: B
Question: In what ratio should a variety of rice costing Rs. 5 per kg be mixed with another variety of rice costing Rs. 8.75 per kg to obtain a mixture costing Rs. 7.50 per kg?
Options:
A)1/2
B)5/9
C)5/1
D)5/3
E)7/6
Rationale: Let us say the ratio of the quantities of cheaper and dearer varieties
= x : y
By the rule of allegation, x/y
= (8.75 - 7.50) / (7.50 - 5) =1/2
Answer: A
Answer: A
Question: A car travels first 160 km at 75 km/hr and the next 160 km at 80 km/hr. What is the average speed for the first 320 km of the tour?
Options:
A)71.11
B)71.12
C)71.1
D)71.17
E)77.42
Rationale: Car travels first 160 km at 75 km/hr
Time taken to travel first 160 km = distancespeed=160/75
Car travels next160 km at 80 km/hr
Time taken to travel next 160 km = distancespeed=160/80
Total distance traveled = 160+160=2×160
Total time taken = 160/75+160/80
Average speed = Total distance traveled/Total time taken=320/(160/75+160/80)=77.42 km/hr
Answer:E
Answer: E
Question: The positive number a is q percent greater than the positive number b, which is y percent less than a itself. If a is increased by y percent, and the result is then decreased by q percent to produce a positive number c, which of the following could be true?
I. c > a
II. c = a
III. c < a
Options:
A)I only
B)II only
C)III only
D)I and II only
E)II and III only
Rationale: Let q = 10% then y = 100/11 %
let b = 100 then a = 110
after increasing a by y and decreasing b yq we get c= 108
therefore c<a
C it is answer
Answer: C