divelab/Sys2Bench huggingface dataset:
Question: In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the run rate in the remaining 40 overs to reach the target of 282 runs?
Options:
A)5
B)6.25
C)6.75
D)7
E)7.25
Rationale: Required run rate = 282 - (3.2 x 10)	/40	=	250/40 = 6.25
Option B
Answer: B
Question: X does a work in 15 days. Y does the same work in 30 days. In how many days they together will do the same work?
Options:
A)10
B)12
C)20
D)30
E)15
Rationale: X's 1day's work= 1/15
Y's 1 day's work=1/30
(X+Y)'s 1day's work= (1/15+1/30)=1/10
both together will finish the work in 10 days.
correct option is A
Answer: A
Question: Half of the workers in Palabras bookstore have read the latest book by J. Saramago, and 1/6 of the workers have read the latest book by H. Kureishi. The number of workers that have read neither book is one less than the number of the workers that have read the latest Saramago book and have not read the latest Kureishi book. If there are 150 workers in the Palabras bookstore, how many of them have read both books?
Options:
A)13
B)12
C)9
D)8
E)7
Rationale: There are total 150 workers.
Half of the workers in Palabras bookstore have read the latest book by J. Saramago,
So 75 have read Saramago.
1/6 of the workers have read the latest book by H. Kureishi.
So (1/6) * 150 = 25 have read Kureishi
The number of workers that have read neither book is one less than the number of the workers that have read the latest Saramago book and have not read the latest Kureishi book
If B workers have read both books, 20 - B have read Saramago but not Kureishi.
So, (75 - B - 1) have read neither.
Total = n(A) + n(B) - Both + Neither
150 = 75 + 25 - B + (75 - B - 1)
B = 12
Answer (B)
Answer: B
Question: Eight people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire cost of the car, then the share of each of the remaining persons increased by:
Options:
A)7/8
B)1/8
C)1/3
D)1/7
E)1/9
Rationale: Original share of 1 person =1/8
New share of 1 person =1/7
Increase =1/7 -	1/8	=1/56
Required fraction =	(1/56)/(1/8)=(1/56)*(8/1)	=1/7
Answer is D.
Answer: D
Question: A car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 60 kilometers per hour. At what speed, in kilometers per hour, is the car traveling?
Options:
A)59
B)57
C)59.5
D)58
E)55.5
Rationale: D
75 * T = 1 km => T = 1/60 km/h
V*(T+2/3600) = 1
V (1/60 + 2/3600) = 1 => V = 58 km/h
Answer: D
Question: A and B complete a work in 7 days. A alone can do it in 14 days. If both together can do the work in how many days?
Options:
A)4.6 days
B)4.78 days
C)5.65 days
D)3.77 days
E)5.75 days
Rationale: 1/7 + 1/14 = 3/14
14/3 = 4.6 days
Answer:A
Answer: A
Question: If a * b * c =(√(a + 2)(b + 3)) / (c + 1), find the value of 6 * 15 * 5.
Options:
A)2
B)5
C)11
D)3
E)4
Rationale: 6 * 15 * 5 = (√(6 + 2)(15 + 3) )/ (5 + 1)
= (√8 * 18) / 6
= (√144) / 6
= 12 / 6 = 2
Answer is A
Answer: A
Question: The watch store down the street from Wendy's house has 2 leather watches, 1 gold watch, and 1 silver watch. How many watches does the store have in all?
Options:
A)10
B)19
C)04
D)12
E)07
Rationale: Add the numbers of watches.
2 + 1 + 1 =4.
Answer is C.
Answer: C
Question: A man bought a bike at 40% discount on its original price. He sold it at a 80% increase on the price he bought it. What percent of profit did he make on the original price?
Options:
A)2%
B)8%
C)6%
D)4%
E)10%
Rationale: Original price = 100
CP = 60
S = 60*(180/100) = 108
100 - 108 = 8%
Answer: B
Answer: B
Question: Two isosceles Triangles have equal vertical angles and their areas are in the ratio 4:9. Find the ratio of their corresponding heights .
Options:
A) 4/5
B) 5/4
C) 3/2
D) 5/7
E) 2/3
Rationale: We are basically given that the triangles are similar.
In two similar triangles, the ratio of their areas is the square of the ratio of their sides and also, the square of the ratio of their corresponding heights.
Therefore, area/AREA=height^2/HEIGHT^2=4/9--> height/HEIGHT=2/3.
Answer: E.
Answer: E
Question: If the graph of y = f(x) is transformed into the graph of 2y - 6 = - 4 f(x - 3), point (a , b) on the graph of y = f(x) becomes point (A , B) on the graph of 2y - 6 = - 4 f(x - 3) where A and B are given by
Options:
A)A = a - 3, B = b
B)A = a - 3, B = b2
C)A = a + 3, B = -2 b
D)A = a + 3, B = -2 b +3
E)None
Rationale: Solution
We first solve 2y - 6 = - 4 f(x - 3) for y.
y = - 2 f(x - 3) + 3
The graph of y = - 2 f(x - 3) + 3 is that of y = f(x) shifted 3 units to the right, stretched vertically by a factor of 2, reflected on the x axis and shifted up by 3 units. A point of y = f(x) will undergo the same transforamtions. Hence
Point (a , b) on the graph of y = f(x)
Becomes (a + 3 , b) on the graph of y = f(x - 3) : shifted 3 units to the right
Becomes ( a + 3 , 2 b) on the graph of y = 2 f(x - 3) : stretched vertically by 2
Becomes ( a + 3 , - 2 b) on the graph of y = - 2 f(x - 3): reflected on x axis
Becomes ( a + 3 , - 2 b + 3) on the graph of y = - 2 f(x - 3) + 3 : shifted up 3 units
Answer D
Answer: D
Question: A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 1200 m long?
Options:
A)200 Sec
B)240 Sec
C)167 Sec
D)197 Sec
E)179 Sec
Rationale: L = S*T
S= 1200/120
S= 10 m/Sec.
Total length (D)= 2400 m
T = D/S
T = 2400/10
T = 240 Sec
Answer: B
Answer: B
Question: If x is a sum of all even integers on the interval 13...61 and y is their number, what is the GCD (x, y)?
Options:
A) 1
B) 13
C) 26
D) 24
E) 1014
Rationale: x = 14 + 16 + ... + 60 = (largest + smallest)/2 *(# of terms) = (14 + 60)/2*24= 37*24.
GCD of 24 and 37*22 is 24.
Answer: D.
Answer: D
Question: During a trip on an expressway, Jon drove a total of x miles. His average speed on a certain 5-mile section of the expressway was 30 miles per hour, and his average speed for the remainder of the trip was 60 miles per hour. His travel time for the x-mile trip was what percent greater than it would have been if he had traveled at a constant rate of 60 miles per hour for the entire trip?
Options:
A)8.5%
B)50%
C)x/12%
D)60/x%
E)500/x%
Rationale: so Jon drove (x-5) miles at 60mph and 5 miles at 30mph:
(x-5)/60 + (10/60) = (X+5)/60 - current time to drive the whole distance
if the entire trip @60mph than time = x/60
so to get percent [(X+5)/60 ]/[x/60] x100
=(x+5)/x *100
=100+500/x
so increase of 500/x%[/u]=E
Answer: E
Question: A case of candy usually lasts Tomi 42 days when she eats 6 every day. She is going out of the country in 2 weeks so she wants to eat this case in 14 days instead. How many should she eat per day?
Options:
A)15
B)12
C)13
D)17
E)18
Rationale: D1 C1 = D2 C2
So 42*6=14*D2 => 18=D2
Answer:E
Answer: E
Question: Tickets numbered 1 to 10 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn bears a number which is a multiple of 2?
Options:
A)1/3
B)2/5
C)1/2
D)2/3
E)1/4
Rationale: Here, S = {1,2,3,......,9,10}
E= event getting a multiple of 3 = {2,4,6,8,10}
probability = 5/10 = 1/2
correct option is C
Answer: C
Question: What is the dividend. divisor 17, the quotient is 9 and the remainder is 5?
Options:
A)150
B)154
C)158
D)160
E)164
Rationale: D = d * Q + R
D = 17 * 9 + 5
D = 153 + 5
D = 158
C)
Answer: C
Question: A total of 22 men and 35 women were at a party, and the average (arithmetic mean) age of all of the adults at the party was exactly 35 years. If the average age of the men was exactly 38 years, which of the following was closest to the average age, in years, of the women?
Options:
A) 31
B) 31.5
C) 32
D) 32.5
E) 33.1
Rationale: Let Aw = average age of women
Average = (Number of men X average age of men + Number of women X average age of women)/total number of people
35 * 57 = 22 * 38 + 35 * Aw
=>1995 = 836 + 35 Aw
=> 35 Aw = 1159
=>Aw = 33.1
Answer E
Answer: E
Question: In the quadrilateral PQRS d=10 cm, h1=5 cm and
h2=2.5 cm. Find the area
Options:
A)21
B)22
C)37.5
D)24
E)25
Rationale: area of quad.=1/2*any diagonal*(sum of 2 perpendiculars which is drawn on that diagona)
so 1/2*10*(5+2.5)=37.5
ANSWER:C
Answer: C
Question: If (c - a)/(c - b) =1, then (5b - 4a)/(c - a) =
Options:
A)0.5
B)1
C)1.5
D)2
E)2.5
Rationale: Let's say c=3, b=1, a=1 so that our 1st expression holds true. Now, ibsert those numbers in the second expression and we'll get 0.5
Answer A (hopefully )))
Answer: A
Question: If n denotes a number to the left of 0 on the number line such that the square of n is less than 1/9, then the reciprocal of n must be
Options:
A)Less than -3
B)Between -1 and -1/3
C)Between -1/3 and 0
D)Between 0 and 1/3
E)Greater than 3
Rationale: n^2 < 1/9
abs(n) < 1/3
Since n<0, then 0 > n > -1/3
1/n < -3
The answer is A.
Answer: A
Question: What is 0.02 percent of 12,356?
Options:
A)0.247
B)2.47
C)24.7
D)0.0247
E)0.00247
Rationale: Since, Percent=1/100, what=something(s), and is:=. We can write the question as s=0.02(1/100)12,356. The answer is 2.47. Hence, the correct answer is B.
Answer: B
Question: What annual payment will discharge a debt of Rs. 1025 due in 2 years at the rate of 5% compound interest?
Options:
A)993.2
B)551.25
C)534.33
D)543.33
E)646.33
Rationale: Explanation:
Let each installment be Rs. x. Then,
x/(1 + 5/100) + x/(1 + 5/100)2 = 1025
820x + 1025 * 441
x = 551.25
So, value of each installment = Rs. 551.25
Answer: Option B
Answer: B
Question: A man engaged a servant on the condition that he would pay him Rs.900 and a uniform after 1year service. He served only for 9 months and receiveduniform and Rs.650, find the price of the uniform?
Options:
A)Rs.90
B)Rs.100
C)Rs.130
D)Rs.170
E)Rs.190
Rationale: 9/12 = 3/4 * 900 = 675
650
-------------
25
1/4 -------- 25
1 --------- ? => Rs.100
B
Answer: B
Question: A completes 80% of a work in 20 days. Then B also joins and A and B together finish the remaining work in 3 days. How long does it need for B if he alone completes the work?
Options:
A)37 ½ days
B)22 days
C)31 days
D)20 days
E)24 days
Rationale: Explanation :
Work done by A in 20 days = 80/100 = 8/10 = 4/5
Work done by A in 1 day = (4/5) / 20 = 4/100 = 1/25 --- (1)
Work done by A and B in 3 days = 20/100 = 1/5 (Because remaining 20% is done in 3 days by A and B)
Work done by A and B in 1 day = 1/15 ---(2)
Work done by B in 1 day = 1/15 – 1/25 = 2/75
=> B can complete the work in 75/2 days = 37 ½ days
Answer : Option A
Answer: A
Question: A certain factory produces buttons and buckles at a uniform weight. If the total weight of 2 buttons and 2 buckles is one third of 11 buckles and 3 buttons, then the weight of 3 buttons and 3 buckles is how many times that of 5 buckles and 6 buttons?
Options:
A)7/15
B)4/9
C)6/11
D)5/9
E)8/15
Rationale: Let x be the weight of a button and let y be the weight of a buckle.
2x + 2y = (1/3)(3x+11y)
3x = 5y
x = 5y/3
3x + 3y = a(6x+5y)
8y = a(15y)
a = 8/15
The answer is E.
Answer: E
Question: Dacid obtained 76, 65, 82, 67 and 85 marks (out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks?
Options:
A)79
B)99
C)88
D)88
E)75
Rationale: Average = (76 + 65 + 82 + 67 + 85)/5
= 375/5 = 75.
Answer:E
Answer: E
Question: In what ratio mental A at Rs.68 per kg be mixed with another metal at Rs.96 per kg so that cost of alloy (mixture) is Rs.82 per kg?
Options:
A)5:8
B)4:7
C)3:7
D)1:1
E)9:8
Rationale: (96-82)/(82-68)=14/14=1/1
ANSWER:D
Answer: D
Question: A boat can travel with a speed of 16 km/hr in still water. If the rate of stream is 5 km/hr, then find the time taken by the boat to cover distance of 63 km downstream.
Options:
A)3 hours
B)5 hours
C)6 hours
D)7 hours
E)8 hours
Rationale: Explanation:
It is very important to check, if the boat speed given is in still water or with water or against water. Because if we neglect it we will not reach on right answer. I just mentioned here because mostly mistakes in this chapter are of this kind only.
Lets see the question now.
Speed downstream = (16 + 5) = 21 kmph
Time = distance/speed = 63/21 = 3 hours
Option A
Answer: A
Question: A sum of Rs.1460 is divided into 13 students so that each boy gets Rs.120 while each girl gets Rs.100. Find the number of boys and number of girls
Options:
A)8B, 5G
B)5B, 8G
C)4B, 9G
D)9B, 4G
E)9B, 5G
Rationale: 120B+100G=1460-----i
B+G=13-------ii
from i
100B+20B+100G=1460
100(B+G)+20B=1460
100(13)+20B=1460
By simplifing we get
B=8;G=5
ANSWER:A
Answer: A
Question: (1/10)18 - (1/10)20 = ?
Options:
A)99/1020
B)99/10
C)0.9
D)0.8
E)None of the above
Rationale: (1/10)(18-20) = -2/10 = -0.2
ANSWER:E
Answer: E
Question: A man can swim in still water at 4.5 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?
Options:
A)2:0
B)3:4
C)4:9
D)1.5
E)1:5
Rationale: M = 4.5
S = x
DS = 4.5 + x
US = 4.5 + x
4.5 + x = (4.5 - x)2
4.5 + x = 9 -2x
3x = 4.5
x = 1.5
Answer: D
Answer: D
Question: A train covers a distance of 12 km in 10 min. If it takes 11 sec to pass a telegraph post, then the length of the train is?
Options:
A)298
B)220
C)120
D)776
E)991
Rationale: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec.
Length of the train = 20 * 11
= 220 m.
Answer:B
Answer: B
Question: On January 1, 2010, Dolly invests 30% of his retirement savings in Antarctic largecap stocks, 30% in Antarctic midcaps, and 40% in Antarctic smallcaps. In 2010, largecaps rise 10%, midcaps rise 20%, and smallcaps rise 15% in the Antarctic stock market; however, in 2011, largecaps fall 20% and midcaps fall 10%, while smallcaps rise x% in Antarctica. If, on January 1, 2012, Dolly has the same total amount of retirement savings as he did two years before, then x is between
Options:
A)10 and 20
B)20 and 30
C)30 and 40
D)40 and 50
E)50 and 60
Rationale: Pick a smart number for the total retirement savings Dolly starts with—say, $10,000. (If you pick $100, you’ll wind up needing to track decimals, so give yourself more zeros to start with.)
Here are the starting values:
L = $3000
M = $3000
S = $4000
Apply the first year’s changes, so that you have these numbers on 1/1/2012:
Newer L = $3000 + 10% = $3300
Newer M = $3000 + 20% = $3600
Newer S = $4000 + 15% = $4600
Now apply the second year’s changes to L and M:
Newest L = $3300– 20% = $3300– $660 = $2640
Newest M = $3600– 10% = $3600– $360 = $3240
Add these to get $5880. So the newest S must be $10,000 (the target final total of Dolly’s retirement savings) minus $5880, $4120
The dollar change in S from 1/1/12 to 1/1/13 is $4600 – $480 = $4120. So the question is this: what percent change does $480 represent, from a starting point of $4600? Since $4600 is a nasty divisor, switch to benchmarks:
10% of $4600 = $460.
So 20% is just double that, or $920.
And so on.
From this $480 lies between $460 and $920
The correct answer is A.
Answer: A
Question: One fourth of a solution that was 10% sugar by weight was replaced by a second solution resulting in a solution that was 16 percent sugar by weight. The second solution was what percent sugar by weight?
Options:
A)34%
B)24%
C)22%
D)18%
E)8.5%
Rationale: et 100 be the total volume.
total salt = 10
salt taken out = 10/4 = 2.5
to make solution 16%, total salt = 16
salt added = 16-7.5 = 8.5
solution had = 8.5/25*100 = 34% sugar
ANSWER:A
Answer: A
Question: If a positive odd integer N has p positive factors, how many positive factors will N have ?
Options:
A)p
B)2p
C)P+1
D)2p+1
E)Cannot be determined
Rationale: I have added some extra text to make this question more GMAT-like:
Let's TEST some values of N
Try N = 3
The factors of 3 are {1, 3}. Here, p =2
So, 2N = (2)(3) = 6
The factors of 6 are {1, 2, 3, 6}. So, we have a total of4
Now check the answer choices:
A) p =2No good. We want an output of4. ELIMINATE
B) 2p = (2)(2) = 4. PERFECT! KEEP B
C) P+1 =2+ 1 = 3 No good. We want an output of4. ELIMINATE
D) 2p+1 = (2)(2) + 1 = 5 No good. We want an output of4. ELIMINATE
E) Cannot be determined. POSSIBLE. KEEP E
Let's TEST another value of N
Try N = 7
The factors of 7 are {1, 7}. Here, p =2
So, 2N = (2)(7) = 14
The factors of 14 are {1, 2, 7, 14}. So, we have a total of4
Now check the REMAINING answer choices:
B) 2p = (2)(2) =4. PERFECT! KEEP B
E) Cannot be determined. POSSIBLE. KEEP E
Let's TEST one more (non-prime) value of N
Try N = 9
The factors of 9 are {1, 3, 9}. Here, p =3
So, 2N = (2)(9) = 18
The factors of 18 are {1, 2, 3, 6, 9}. So, we have a total of6
Now check the REMAINING answer choices:
B) 2p = (2)(3) =6. PERFECT! KEEP B
E) Cannot be determined. POSSIBLE. KEEP E
At this point, it SEEMS LIKELY that the correct answer is C
Answer: C
Question: A man sells two articles for Rs.3600 each and he gains 42% on the first and loses 42% on the next. Find his total gain or loss?
Options:
A)9% loss
B)400
C)4000
D)17.64%loss
E)8% LOSS
Rationale: (42*42)/100 = 17.64%loss
ANSWER:D
Answer: D
Question: January 1, 2008 is Thursday. What day of the week lies on Jan 1, 2009?
Options:
A)Saturday
B)Wednesday
C)Thursday
D)Tuesday
E)Monday
Rationale: Explanation:
Number of odd days in 2008 = 2 (since it is a leap year)
(we have taken the complete year 2008 because we need to find out the odd days from 01-Jan-2008 to 31-Dec-2008, that is the whole year 2008)
Given that January 1, 2008 is Thursday.
Hence January 1, 2009 = (Thursday + 2 odd days) = Saturday
Answer: Option A
Answer: A
Question: Robert spent $30 in buying raw materials, $105 in buying machinery and 10% of the total amount he had as cash with him. What was the total amount?
Options:
A)A)$150
B)B)$210
C)C)$250
D)D)$160
E)E)$200
Rationale: Let the total amount be x
then, (100-10)% of x = 30+105
90% of x = 135
90x/100 = 135
x = $150
Answer is A
Answer: A
Question: A and B started a business investing Rs. 60,000 and Rs 45,000 respectively. In what ratio the profit earned after 2 years be divided between A and B respectively?
Options:
A)3:2
B)4 : 3
C)18:20
D)1:4
E)18:4
Rationale: A: B = 60000 : 45000 = 4 : 3
ANSWER:B
Answer: B
Question: AB + CD = AAA, where AB and CD are two-digit numbers and AAA 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 AAA 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: A certain company reported that the revenue on sales increased 40 % from 2000 to 2003, and increased 90 % from 2000 to 2005. What was the approximate percent increase in revenue for this store from 2003 to 2005?
Options:
A) 50 %
B) 36 %
C) 30 %
D) 32 %
E) 29 %
Rationale: Assume the revenue in 2000 to be 100. Then in 2003 it would be 140 and and in 2005 190, so from 2003 to 2005 it increased by (190-140)/140=50/140=~29%.
Answer: B
Answer: B
Question: On dividing 123 by a number, the quotient is 7 and the remainder is 4. Find the divisor.
Options:
A)15
B)16
C)17
D)18
E)19
Rationale: d = (D-R)/Q
= (123 - 4)/7
= 119/7 = 17
C
Answer: C
Question: A can do a work in 6 days , B can do a work in 8 days and C can do it in 12 days. B left work after 6 days. For how many number of days should A and C should work together to complete the remaining work ?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: b work 1/8 * 6=3/4
remaining work =1-3/4=1/4
a and c work together =1/6+1/12=3/12=1/4
take reciprocial 4 * remaining work =4 *1/4=1
ANSWER:A
Answer: A
Question: David invested certain amount in three different schemes A, B and C with the rate of interest 10% p.a., 12% p.a. and 15% p.a. respectively. If the total interest accrued in one year was Rs. 3200 and the amount invested in Scheme C was 150% of the amount invested in Scheme A and 240% of the amount invested in Scheme B, what was the amount invested in Scheme B?
Options:
A)Rs.5000
B)Rs.2000
C)Rs.6000
D)Rs.3000
E)Rs.4000
Rationale: Explanation :
Let x , y and x be his investments in A, B and C respectively. Then
Then, Interest on x at 10% for 1 year
+ Interest on y at 12% for 1 year
+ Interest on z at 15% for 1 year
= 3200
x×10×1/100+y×12×1/100+z×15×1/100=3200
⇒10x+12y+15z=320000−−−(1)
Amount invested in Scheme C was 240% of the amount invested in Scheme B
=>z=240y/100=60y/25=12/y5−−−(2)
Amount invested in Scheme C was 150% of the amount invested in Scheme A
=>z=150x/100=3x/2
=>x=2z/3=2/3×12y/5=8y/5−−−(3)
From(1),(2) and (3),
10x + 12y + 15z = 320000
10(8y/5)+12y+15(12y/5)=320000
16y+12y+36y=320000
64y=320000
y=320000/64=10000/2=5000
i.e.,Amount invested in Scheme B = Rs.5000
Answer : Option A
Answer: A
Question: What is the greatest value of n such that 4^n is a factor of 23! ?
Options:
A)8
B)4
C)7
D)5
E)9
Rationale: Pretty simple, really.
If m = 9, then 4m = 36, which is 18x2, both of which are included in 23!
Since 9 is the largest number here, its the answer.
Answer is E
Answer: E
Question: In what ratio should a variety of rice costing $6 per kg be mixed with another variety of rice costing $8.75 per kg to obtain a mixture costing $7.50 per kg?
Options:
A)4/7
B)5/6
C)5/9
D)4/8
E)3/8
Rationale: B
5/6
Let us say the ratio of the quantities of cheaper and dearer varieties = x : y
By the rule of allegation, x/y = (87.5 - 7.50) / (7.50 - 6) = 5/6
Answer: B
Question: Pipe A can fill a tank in 6 hours, pipe B in 12 hours and pipe C in 36 hours. If all the pipes are open,in how many hours will the tank be filled ?
Options:
A)3.2
B)3
C)3.3
D)3.5
E)3.6
Rationale: 1/6+1/12+1/36=10/36=1/3.6. so 3.6 hrs
ANSWER:E
Answer: E
Question: A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same time during which the tank is filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe. Time required by the first pipe to fill the tank is
Options:
A)30 hours
B)15 hours
C)10 hours
D)6 hours
E)7 hours
Rationale: Explanation:
Suppose the first pipe alone can fill the tank in x hours. Then,
second pipe alone can fill the tank in (X-5)hours,
third pipe alone can fill the tank in(xâˆ’5)-4=(xâˆ’9)hours.
Part filled by first pipe and second pipe together in 1 hr= Part filled by third pipe in 1 hr
We can not take the value (xâˆ’3)because,(xâˆ’9)becomes negative which is not possible, because the third pipe can fill the tank in(xâˆ’9) hours.
Hence, x=15
ANSWER IS B
Answer: B
Question: The average of 10 numbers is calculated as 16. It is discovered later on that while calculating the average, the number 55 was incorrectly read as 25, and this incorrect number was used in the calculation. What is the correct average?
Options:
A)17
B)19
C)25
D)31
E)46
Rationale: The total sum of the numbers should be increased by 30.
Then the average will increase by 30/10 = 3.
The correct average is 19.
The answer is B.
Answer: B
Question: The factorial expression 10!/5! is divisible by which of the following integers?
Options:
A)5
B)31
C)21
D)11
E)19
Rationale: 10!/5! => 10 x 9 x 8 x 7 x 6
(A) 5 Can divide 10
(B) 31 None of the Multiplicands present
(C) 21 None of the Multiplicands present
(D) 11 None of the Multiplicands present
(E) 19 None of the Multiplicands present
Hence answer will be (A)
Answer: A
Question: If from a group of 5 people, an old member is replaced by a new one, the average age is same as it was 3 years ago. What is the difference between the ages of the old member and the new one?
Options:
A)12
B)15
C)11
D)18
E)16
Rationale: Explanation:
The present average age is (x + 3) when the old member is present and it equals to x when an old member is replaced by a new one.
The difference in the ages of the old member and the new one is equal to the difference in the total age before and after the replacement = 15 years.
ANSWER: B
Answer: B
Question: The ratio of the present ages of Sunitha and Vinitha is 4:5. Six years hence the ratio of their ages will be 14:17. What will be the ratio of their ages 12 years hence ?
Options:
A)15:19
B)13:15
C)16:19
D)17:19
E)14: 16
Rationale: Suppose the present ages of sunitha and vinitha be 4x and 5x years respectively.
six years hence
4x + 6 / 5x + 6 = 14/17
or 68x + 102 = 70x + 84
or x= 9
Ratio of ages of sunita and vinita after 12 years
4x + 12 : 5x + 12 = 48 : 57 = 16 : 19 ANSWER :C
Answer: C