divelab/Sys2Bench huggingface dataset:
Question: Raj invested an amount of Rs.17400 for two years. Find the rate of compound interest that will fetch him an amount of Rs.1783.50 at the end of two years?
Options:
A)8% p.a.
B)6% p.a.
C)4% p.a.
D)5% p.a.
E)None of these
Rationale: Let the rate of interest be R% p.a.
17400[1 + R/100]2 = 17400 + 1783.50
[1 + R/100]2 = (17400 + 1783.50)/17400
= 1 + 1025/10000 = 1 + 41/400
= 441/400 = [21/20]2
[1 + R/100] = 21/20
R/100 = 1/20
Therefore R = 5
ANSWER:D
Answer: D
Question: 3 buffaloes eat as much as 4 cows or 2 oxen. At a farm there are 15 buffaloes, 8 oxen and 24 cows. The fodder for these cattle is available for 24days. If 8 more cows & 9 more buffaloes are brought in, how long will the fodder last?
Options:
A)16
B)17
C)19
D)18
E)24
Rationale: Sol. 2 oxen = 3 buffaloes = 4 cows 8 oxen = 16 cows and 15 buffaloes = 20 cows 16 cows + 20 cows + 24 cows = 60 cows Since fodder is available for 60 cows for 24 days
So fodder will be available for (60 + 8 + 12) = 80 cows c 24x60 .0 .
for-^—=18 days.
D
Answer: D
Question: A and B invests Rs.8000 and Rs.9000 in a business. After 4 months, A withdraws half of his capital and 2 months later, B withdraws one-third of his capital. In what ratio should they share the profits at the end of the year?
Options:
A)32:46
B)32:98
C)32:45
D)32:27
E)32:42
Rationale: A : B
(8000*4)+(4000*8) : (9000*6)+(6000*6)
64000 : 90000
32 : 45
Answer:C
Answer: C
Question: A shopkeeper sold an article at $100 with 20% profit. Then find its cost price?
Options:
A)$120
B)$100
C)$91
D)$83
E)$69
Rationale: cost price = selling price *100/(100+profit)
C.P. = 100*100/120 = $83(approximately)
Answer is D
Answer: D
Question: In a two digit number, the digit in the units place is five times the digit in ten's place and sum of the digits is equal to six. What is the number?
Options:
A)15
B)28
C)32
D)36
E)38
Rationale: Solution
Let the ten digits be x. Then,units digit=5x
Therefore x +5x = 6
‹=›6x = 6
‹=›x= 1
So, ten's digit = 1, unit's digit = 5.
Hence, the required number is 15.
Answer A
Answer: A
Question: Half the people on a bus get off at each stop after the first, and no one gets on after the first stop. If only one person gets off at stop number 9, how many people got on at the first stop?
Options:
A)128
B)64
C)32
D)16
E)256
Rationale: 7 - > 1
6 - > 2
5 - > 4
4 - > 8
3 - > 16
2 - > 32
1 - > 64
because people get off after the first stop
=> the formula will be : 2^(n-1) where n is the stop number
in this case n = 9
=> 2^(9-1) = 2^8 = 256
=> answer is E
Answer: E
Question: The length of a rectangular floor is more than its breadth by 200%. If Rs. 240 is required to paint the floor at the rate of Rs. 3 per sq m, then what would be the length of the floor?
Options:
A)65
B)44
C)18
D)15.49
E)14
Rationale: Let the length and the breadth of the floor be l m and b m respectively.
l = b + 200% of b = l + 2b = 3b
Area of the floor = 240/3 = 80 sq m
l b = 80 i.e., l * l/3 = 240
l2 = 240 => l =15.49
Answer:D
Answer: D
Question: A rectangular plot measuring 90 metres by 50 metres is to be enclosed by wire fencing. If the poles of the fence are kept 5 metres apart, how many poles will be needed ?
Options:
A)55
B)56
C)57
D)58
E)None of these
Rationale: Solution
Perimeter of the plot = 2(90 + 50) = 280 m.
∴ Number of poles = [280/5] =56m Answer B
Answer: B
Question: How many ways can 8 friends be arranged around a circular dinner table?
Options:
A)A)16
B)B)48
C)C)96
D)D)5040
E)E)720
Rationale: The number of arrangements of n distinct objects in a row is given by n!n!.
The number of arrangements of n distinct objects in a circle is given by (n−1)!(n−1)!.
The difference between placement in a row and that in a circle is following: if we shift all object by one position, we will get different arrangement in a row but the same relative arrangement in a circle. So, for the number of circular arrangements of n objects we have:
n!n=(n−1)!n!n=(n−1)!.
So, the answer is (8 - 1)! = 7! = 5040.
Answer: D.
Answer: D
Question: The owner of a local jewelry store hired two watchmen to guard his diamonds, but a thief still got in and stole some diamonds. On the way out, the thief met each watchman, one at a time. To each he gave 1/2 of the diamonds he had then, and 2 more besides. He escaped with two diamonds. How many did he steal originally?
Options:
A)20
B)36
C)25
D)None of these
E)Cannot be determined
Rationale: Explanation :
Since, thief escaped with 2 diamonds,
Before 2nd watchman, he had ( 2 + 2 ) x 2 = 8 diamonds.
Before 1st watchman, he had ( 8 + 2 ) x 2 = 20 diamonds.
Answer : A
Answer: A
Question: Find the fraction which has the same ratio to 2/13 that 5/34 has to 7/48.
Options:
A)240/1587
B)240/1545
C)240/1547
D)240/1542
E)240/1512
Rationale: P : 2/13 = 5/34 : 7/48
As the product of the means is equal to the product of the extremes.
P*7/48 = 2/13 * 5/34
P*7/48 = 10/442
P = 480/3094 => P = 240/1547
Answer: C
Answer: C
Question: If 6 women can color 180 m long cloth in 3 days, then 5 women can color 200 m long cloth in?
Options:
A)6 days
B)5 days
C)4 days
D)2 days
E)3 days
Rationale: The length of cloth painted by one woman in one day = 180/ 6× 3 = 10 m
No. of days required to paint 200 m cloth by 5 women = 200/ 5 × 10 = 4 days
Answer : C
Answer: C
Question: If a*b denotes the greatest common divisor of a and b, then ((12*15)*(18*24)) = ?
Options:
A) 24
B) 12
C) 6
D) 4
E) 3
Rationale: The greatest common divisor of 12 and 15 is 3. Hence 12*15 = 3 (note that * here denotes the function not multiplication).
The greatest common divisor of 18 and 24 is 6. Hence 18*24 = 6.
Hence ((12*16)*(18*24)) = 3*6.
The greatest common divisor of 3 and 6 is 3.
Answer; E.
Answer: E
Question: The cost of 4 bags and 12 purses is Rs.620, what is the cost of 10 bags and 30 purses?
Options:
A)Rs.3600
B)Rs.3500
C)Rs.3800
D)Rs.3900
E)Rs.1550
Rationale: Explanation:
Cost of 4 bags + 12 purses = Rs.620
Multiply each term by 5/2, we get,
Cost of 10 bags + 30 purses = Rs.1550.
Answer: Option E
Answer: E
Question: X men can do a work in 120 days. If there were 20 men less, the work would have taken 60 days more. What is the value of X?
Options:
A)60
B)99
C)77
D)55
E)22
Rationale: We have M1 D1 = M2 D2
120X = (X - 20)180
=> 2X = (X - 20) 3 => 2X = 3X - 60
=> X = 60
Answer:a
Answer: A
Question: P and Q invested in a business. They earned some profit which they divided in the ratio of 2:3. If P invested Rs.50, 000, the amount invested by Q is:
Options:
A)Rs. 65,000
B)Rs. 70,000
C)Rs. 75,000
D)Rs. 90,000
E)Rs. 60,000
Rationale: Q invested = 50000/2*3 = 75000
Answer : C
Answer: C
Question: If x and y are positive integers, and x^3*y^4 = 10125, which of the following is the value of xy?
Options:
A)6
B)10
C)14
D)15
E)21
Rationale: 10125 = 3*3375 = 3^2*1125 = 3^3*375 = 3^4*125 = 3^4*5^3
xy = 3*5 = 15
The answer is D.
Answer: D
Question: Three of the following four are alike in a certain way and hence form a group. Which is the one that does not belong to that group?
Options:
A)Shirt
B)Shoe
C)Ring
D)Cobbler
E)FRR
Rationale: Explanation:
Cobbler is human being while all others are used by human beings.
Answer: D
Answer: D
Question: In a race of 1000 m, A can beat by 100 m, in a race of 800m, B can beat C by 100m. By how many meters will A beat C in a race of 600 m?
Options:
A)927.5 m
B)127.5 m
C)167.5 m
D)128.5 m
E)127.1 m
Rationale: When A runs 1000 m, B runs 900 m and when B runs 800 m, C runs 700 m.
When B runs 900 m, distance that C runs = (900 * 700)/800 = 6300/8 = 787.5 m.
In a race of 1000 m, A beats C by (1000 - 787.5) = 212.5 m to C.
In a race of 600 m, the number of meters by which A beats C = (600 * 212.5)/1000 = 127.5 m.
Answer:B
Answer: B
Question: 'a' and 'b' are positive integers such that their LCM is 20 and their HCF is 1. What is the difference between the minimum and maximum possible values of 'a + b'?
Options:
A)0
B)-24
C)-32
D)-20
E)-12
Rationale: possible values of a and b can be 5,4; 4,5 (which are same for a+b) and 1,20; 20,1 (same result for a+b)
so 9-21 = -12. ans E.
Answer: E
Question: What is the sum of the first 22 natural numbers (starting from 1)?
Options:
A)223
B)233
C)243
D)253
E)263
Rationale: The sum of n natural numbers = n*(n+1) / 2 = 22*23/2 = 253
The answer is D.
Answer: D
Question: Some of the workers at a hedge fund are analysts; the others are not analysts. There are a total of 2x/3 analysts at the hedge fund. A total of x hedge fund workers have an MBA. Furthermore, x/3 analysts have an MBA, y/4 of the hedge fund workers are neither analysts nor have an MBA, and 40 workers are not analysts. If there are y total workers at the hedge fund, x is equal to which of the following?
Options:
A)36
B)50
C)60
D)75
E)80
Rationale: AnalystsNot AnalystsTotal
MBAx/32x/3x
No MBAy/4
Total2x/350y
We are asked for the value of x.
From the table: 2x/3 = y - 40
y - 40 + (y/4) = 40
5y/4 = 80
y = 64
2x/3 = 64 - 40 = 24
x = 72/2 = 36
Answer: A
Answer: A
Question: In a jar there are balls in different colors: blue, red, green and yellow.
The probability of drawing a blue ball is 1/8.
The probability of drawing a red ball is 1/5.
The probability of drawing a green ball is 3/10.
If a jar cannot contain more than 50 balls, how many yellow balls are in the Jar?
Options:
A)20
B)25
C)15
D)30
E)35
Rationale: answer of 1st
just add the given probabilities p(blue)+p(red)+p(green) i.e
1/8+1/5+3/10=5+8+12/40 =25/40
now we know p(blue)+p(red)+p(green)+p(yellow)=1
25/40+p(yellow)=1
p(yellow)=15/40
i.e why yellow balls are 15.
C
Answer: C
Question: An article is bought for Rs.600 and sold for Rs.550, find the loss percent?
Options:
A)8.33%
B)16 7/3%
C)16 2/8%
D)16 2/3%
E)76 2/3%
Rationale: 600 ---- 50
100 ---- ? =>8.33%
Answer:A
Answer: A
Question: The capacity of a cylindrical tank is 246.4 litres. If the height is 4 metres, what is the diameter of the base?
Options:
A)1.4 metres
B)2.8 metres
C)28 metres
D)14 metres
E)none of these
Rationale: Capacity (volume) of a cylindrical tank = πr2h
(Here r = radius and h = height of the tank)
Now, from the question, 246.4 × 0.001 = 22⁄7 × r2 × 4
[∵ 1 litre = 1000 cm3 = 0.001 m3]
or, 0.2464×7/22×4 = r2
or,r = 0.14 m
or,diameter = 2r = 0.28 m
Answer E
Answer: E
Question: The numerator of a certain fraction is 8 less than the denominator. If 3 is added to the numerator and 3 is subtracted from the denominator, the fraction becomes 3/4. Find the original fraction?
Options:
A)2/5
B)7/9
C)3/11
D)8/5
E)9/1
Rationale: Explanation:
The denominator be P, the numerator will be (P - 8).
The fraction will be (P - 8)/P.
Adding 3 to the numerator and subtracting 3 from the denominator, (P - 8 + 3)/(P - 3) = 3/4.
(P - 5)/(P - 3) = 3/4
P = 20 - 9 => P = 11.
The fraction is: 3/11.
ANSWER IS C
Answer: C
Question: Ram purchased a flat at Rs. 1 lakh and Prem purchased a plot of land worth Rs. 1.1 lakh. The respective annual rates at which the prices of the flat and the plot increased were 10% and 5%. After two years they exchanged their belongings and one paid the other the difference. Then
Options:
A)Ram paid Rs. 275 to Prem
B)Ram paid Rs. 475 to Prem
C)Ram paid Rs. 375 to Prem
D)Prem paid Rs. 475 to Ram
E)None of these
Rationale: Explanation :
After 2 years the price of the flat will be (1)(1.10)2 = Rs. 1.21 lakh.
Correspondingly the price of the land will be (1.1)(1.05)2 = Rs. 1.21275 lakh.
Hence, the price of the plot is Rs. (1.21275 – 1.21) lakh = Rs. 275 more than that of the flat. Hence, if they exchange, Ram will have to pay Prem this amount.
Answer : A
Answer: A
Question: How many gallons of milk that is 10 percent butter-fat must be added to 8 gallons of milk that is 50 percent butterfat to obtain milk that is 20 percent butterfat?
Options:
A)6
B)12
C)14
D)24
E)28
Rationale: Equate the fat:
0.1x + 0.5*8 = 0.2(x + 8) --> x = 24.
Answer: D.
Answer: D
Question: If x and y are positive odd integers, then which of the following must also be an odd integer? I. x^(y+2) II. x(y+4) III. (y+1)^(x-1) + 2
Options:
A)II,III only
B)I,II only
C)I only
D)II only
E)III only
Rationale: let x= 5, y= 3
I. 5^5 = > Odd
II. 5*7 = > Odd
III. 4^4 +2= > Even
Answer : B
Answer: B
Question: The present worth of Rs.1404 due in two equal half-yearly instalments at 8% per annum. Simple interest is:
Options:
A)1320
B)1300
C)1325
D)120
E)None of these
Rationale: Explanation:
Required Sum = PW of Rs.702 due 6 months hence +PW of Rs.702 due 1 year hence
=Rs.[100×702/100+(8×12)+100×702/100+(8×1)]
= Rs. 1325
Answer: C
Answer: C
Question: A train overtakes two persons who are walking in the same direction to that of the train at 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. What is the length of the train?
Options:
A)62 m
B)54 m
C)50 m
D)55 m
E)56 m
Rationale: Explanation:
Let x is the length of the train in meter and v is its speed in kmph
x/9 = ( v-2)(10/36) ---(1)
x/10 =( v-4) (10/36) --- (2)
Dividing equation 1 with equation 2
10/9 = (v-2)/(v-4)
=> 10v - 40 = 9v - 18
=> v = 22
Substituting in equation 1, x/9 = 200/36 => x = 9×200/36 = 50 m
Answer: Option C
Answer: C
Question: If Q = {1, 7, 18, 20, 29, 33}, how much less is the mean of the numbers in Q than the median of the numbers in Q?
Options:
A) 1.0
B) 1.5
C) 2.0
D) 2.5
E) 3.0
Rationale: This is a good question to understand the difference between mean and median.
Mean: Average of all the numbers. (Sum of all the elements divided by the number of elements)
Median: Arrange the elements of the set in increasing order. If the number of terms is odd, the middle term is the median. If the number of terms is even, the average of middle two terms is the median
Coming to this question,
Mean = (1 + 7 + 18 + 20 + 29 + 33)/6 = 18
Median = (18 + 20)/2 = 19
Difference = 1
Option A
Answer: A
Question: 4 persons a, b, c, d are to be lined up in a row. If a, b, and c adhere always together, how many possible cases are there?
Options:
A)12
B)36
C)48
D)72
E)144
Rationale: firstly it is not GEOMETRY but COMBINATIONS, so changing the TAG accordingly..
total 4 are there..
take a,b, and c as one,so total =2..
these 2 can be arranged in 2! ways..
a,b, and c can be arranged within themselves in 3! ways ..
TOTAL = 2!*3!=12
A
Answer: A
Question: At Company X, senior sales representatives visit the home office once every 20 days, and junior sales representatives visit the home office once every 15 days. The number of visits that a junior sales representative makes in a 2-year period is approximately what percent greater than the number of visits that a senior representative makes in the same period?
Options:
A)10%
B)25%
C)33%
D)50%
E)67%
Rationale: Each 60-day period, senior representatives visit the home office 3 times while junior representatives visit 4 times, thus 33% more.
The answer is C.
Answer: C
Question: Otto and Han are driving at constant speeds in opposite directions on a straight highway. At a certain time they are driving toward each other and are 10 miles apart. One and a half hours later, they are again 10 miles apart, driving away from each other. If Otto drives at a speed of x miles per hour, then, in terms of x, Han drives at a speed of how many miles per hour?
Options:
A)a) 13.33-x
B)b) 40-x
C)c) 80-2x
D)d) 120-x
E)e) 40-x/2
Rationale: Let's say the two cars have speeds V1 and V2. The fact that they are moving in opposite direction means that their relative speed is (V1 + V2). In other words, any gap between them will be changing in size at a rate of (V1 + V2). It doesn't matter whether they are moving toward each other or away from each other. If they are approaching each other, the gap between them is decreasing at a rate of (V1 + V2). If they are moving away from each other, the gap between them is increasing at a rate of (V1 + V2). Either way, the number for the rate of change remains the same.
Here, the two cars approach a distance 10 mi, then move away from each other another distance of 10 miles. That's a total distance of 20 miles in 1.5 hr, which gives a rate of:
R = (20 mi)/(1.5) = 13.33 mph
That's the rate of change of the gap, so it must equal the sum of the speeds of the two cars.
One of the speeds is x, and let's call the other y. We want y.
x + y = 13.33
y = 13.33 - x
Answer =(A)
Answer: A
Question: At 11:00 a.m., Tom begins traveling on a certain bike path from Riverdale at a constant rate of 10 mph. If, at 3:00 p.m., Jim begins traveling from Riverdale on the same path at a constant rate of 20 mph, at what time will he catch up to Peter?
Options:
A)6:00 p.m.
B)7:00 p.m.
C)8:00 p.m.
D)9:00 p.m.
E)10:00 p.m.
Rationale: By the time Jim starts, Tom has already covered = 4 hr * 10 mph = 40 miles
Relative speed = 20- 10 = 10mph
To catch up, Jim needs to cover 40 miles which can be covered in = 40/10= 4 hours
If Jim leaves at 3 pm, he will catch Tom at 7 pm
Answer: B
Answer: B
Question: A train 125 m long pass a telegraph pole in 5 seconds. Find the speed of the train
Options:
A)90 km/hr
B)68.4 km/hr
C)72 km/hr
D)79.2 km/hr
E)None
Rationale: Sol.
Speed = [125/5] m/sec = [25 * 18/5] km/hr = 90 km/hr.
Answer A
Answer: A
Question: Express 25 mps in kmph?
Options:
A)77 kmph
B)55 kmph
C)90 kmph
D)56 kmph
E)17 kmph
Rationale: 25 * 18/5 = 90 kmph
Answer: C
Answer: C
Question: How many shots of 1cm radius can be prepared from a sphere of 3cm radius?
Options:
A)33
B)88
C)27
D)88
E)99
Rationale: 4/3 π * 3 * 3 * 3 = 4/3 π * 1 * 1 * 1 * x
x = 27
Answer: C
Answer: C
Question: If a quarter kg of potato costs 60 paise, how many paise does 200 gm cost?
Options:
A)65 paise
B)70 paise
C)52 paise
D)48 paise
E)None of these
Rationale: Explanation :
Let 200 gm potato costs x paise
Cost of ¼ Kg potato = 60 Paise
=> Cost of 250 gm potato = 60 Paise (∵ 1 Kg = 1000 gm => ¼ Kg = 1000/4 gm = 250 gm)
More quantity, More Paise (direct proportion)
Hence we can write as
Quantity200:250}::x:60
⇒200×60=250×x⇒4×60=5×x⇒4×12=x⇒x=48 . Answer : Option D
Answer: D
Question: What will come in place of the x in the following Number series? 5,28,57,88,125
Options:
A)120
B)145
C)166
D)170
E)189
Rationale: 28=23+5
57=29+28
88=31+57
125=37+88
166=41+125
=166
C
Answer: C
Question: If m is an odd integer and n an even integer, which of the following is definitely odd?
Options:
A)(2m+n)(m-n)
B)(m+n2)+(m+n2)
C)m2+mn+n2
D)m +n
E)None
Rationale: m+n because the sum of an even and an odd number is always an odd number.
Ex: 3 is an odd number and 6 is an even number. Now, 3+6=9, is an odd number.
ANSWER:D
Answer: D
Question: Daniel is playing a dice game in which a dice is rolled 5 times. If a number turns up exactly 3 times then the game is won. Daniel has thrown the dice two times and got number 4 both times. What is the probability that Daniel will win the game ?
Note: the dice is an unbiased die with numbers 1 to 6
Options:
A)1/216
B)75/216
C)80/216
D)90/216
E)100/216
Rationale: Probability of any number from 1 to 6 = 1/6.
Given that you already have 2 4s , leaving you with 3 more slots to determine if you will win or not.
2 scenarios for a win:
Scenario 1: 4 4 T N N , with T= 4 , N= not 4
Probability of this scenario = 1*1*(1/6)*(5/6)*(5*6)*3!/2!=75/216 .... (3!/2! to show the arrangement of TNN in 3 slots)
Scenario 2: 4 4 N N N , with N = any particular number but 4 and in this case for a 'win' all 'N's are the same number.
Probability of this scenario = 1*1*(5/6)*(1/6)*(1/6) = 5/216 ...(with 1/6 shows the probability of choosing that same number out of 6 possible)
Thus the final probability = 75/216 + 5/216 = 80/216
C is the correct answer.
Answer: C
Question: The price of commodity X increases by 30 cents every year, while the price of commodity Y increases by 20 cents every year. If in 2001, the price of commodity X was $4.20 and the price of commodity Y was $4.40, in which year will commodity X cost 70 cents more than the commodity Y?
Options:
A)2010
B)2011
C)2012
D)2013
E)2014
Rationale: The cost of commodity X increases by 10 cents per year relative to commodity Y.
The price of X must gain 20 + 70 = 90 cents on commodity Y, which will take 9 years.
The answer is A.
Answer: A
Question: In a certain game, a large container is filled with red, yellow, green, and blue beads worth, respectively, 7, 5, 3, and 2 points each. A number of beads are then removed from the container. If the product of the point values of the removed beads is 30,870,000, how many red beads were removed?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: 30,870,000
= 2^4 * 5^4 * 3087
= 2^4 * 3 * 5^4 * 1029
= 2^4 * 3^2 * 5^4 * 343
= 2^4 * 3^2 * 5^4 * 7^3
The answer is C.
Answer: C
Question: In the xy-coordinate system, what is the slope of the line that goes through the origin and is equidistant from the two points P = (4, 6) and Q = (6, 2)?
Options:
A)0.8
B)1.0
C)1.2
D)1.4
E)1.6
Rationale: First, get the middle coordinate between (4,6) and (6,2).
x = 4 + (6-4)/2 = 5
y = 2 + (6-2)/2 = 4
Second, get the slope of (5,4) and (0,0). m = 4-0 / 5-0 = 4/5 = 0.8
Answer: A
Answer: A
Question: Of the total amount that Jill spent on a shopping trip, excluding taxes, she spent 50 percent on clothing, 20 percent on food, and 30 percent on other items. If Jill paid a 4 percent tax on the clothing, no tax on the food, and an 8 percent tax on all other items, then the total tax that she paid was what percent of the total amount that she spent, excluding taxes?
Options:
A)2.8%
B)3.6%
C)4.4%
D)5.2%
E)6.0%
Rationale: Let amount spent by Jill = 100
Clothing=50, Food=20, others=30
Tax on clothing= 2
Tax on others=2.4
Percentage= 4.4/100 4.4%
Answer: C
Answer: C
Question: The ratio of a to b to c is 2 to 3 to 4, and a, b, c are positive integers. If the average (arithmetic mean) of the three numbers is 51, what is the value of a?
Options:
A)24
B)25
C)28
D)32
E)34
Rationale: Let a=2k, b=3k, and c=4k.
a+b+c = 2k+3k+4k = 9k
Since the average is 51:
9k/3 = 51
3k = 51
k=17
Then a=34.
The answer is E.
Answer: E
Question: Two pipes can fill a tank in 12 minutes and 20 minutes respectively. Both pipes are opened together and after some time the first pipe is closed and the tank is full in totally 10 minutes. For how many minutes was first pipe open?
Options:
A)8 minutes
B)6 minutes
C)7 minutes
D)10 minutes
E)9 minutes
Rationale: Second pipe is opened for 10 minutes. So , part of tank filled by the second pipe = 10/20=1/2.
So, 1 -1/2 = 1/2 tank is filled by first pipe.
First pipe can fill 1/2 of tank in 1 * 12/2 = 6minutes.
So, the first pipe is opened for 6minutes.
ANSWER:B
Answer: B
Question: If Rani earns a raise of between 5% and 11%, non-inclusive, by what fraction could her salary have increased?
Options:
A)1/4
B)1/5
C)1/70
D)1/10
E)1/20
Rationale: Perhaps it is also easy to just translate the % into fractions:
6%: 6/100 = 3/50
7%: 7/100
8%: 8/100 = 4/50 =2/25
9%: 9/100
10%:10/100=1/10
Only 1/10 exists in the answer choices, so ANS D
Answer: D
Question: How many days will there be from 29th January,1996 to 15th May,1996(both days included)?
Options:
A)102
B)103
C)111
D)120
E)108
Rationale: Explanation:
Number of days from 29-Jan-1996 to 15-May-1996 (both days included)
= 3(Jan) + 29(Feb) + 31 (Mar) + 30(Apr)+ 15(May) = 108
Answer: Option E
Answer: E
Question: The parameter of a square is double the perimeter of a rectangle. The area of the rectangle is 480 sq cm. Find the area of the square.
Options:
A)488
B)776
C)481
D)480
E)412
Rationale: Let the side of the square be a cm. Let the length and the breadth of the rectangle be l cm and b cm respectively.
4a = 2(l + b)
2a = l + b
l . b = 480
We cannot find ( l + b) only with the help of l . b. Therefore a cannot be found .
Area of the square cannot be found.Answer:D
Answer: D
Question: There are 36 people in a certain community who belong to the local golf club, tennis club or both clubs. If twice as many people belong to the tennis club as belong to the golf club, what could be the number of people who belong to both clubs?
Options:
A)4
B)7
C)17
D)21
E)27
Rationale: let's find the range of Both and hence the range of x. Minimum value of Both: Say there is no overlap in the two sets. 36 = x + 2xx = 12In this case Both = 0 Maximum value of Both: Say there is maximum overlap between the two sets. One set has x so it could be a subset of the set 2x.36 = 2xx = 18 So Both lies between 0 and 18 Only option (C) satisfies this condition. ANSWER:C
Answer: C