divelab/Sys2Bench huggingface dataset:
Question: In a sample of associates at a law firm, 25 percent are second-year associates, and 75 percent are not first-year associates. What percentage of the associates at the law firm have been there for more than two years?
Options:
A)0
B)25
C)50
D)75
E)100
Rationale: 75 percent are not first-year associates --> This means 75 percent associates are either two or more than two years
Already, we know % of second-year associates = 25 %
So, % of associates there for more than two years = 75 % - 25 % = 50 % .. => (C).. Is it correct ?
Answer: C
Question: Mike took 5 mock tests before appearing for the GMAT. In each mock test he scored 9 points more than the previous mock test. If he scored 760 on the GMAT and his average score for the mocks and the GMAT was 726.67, what was the difference in the score of his last mock and his GMAT score?
Options:
A)22
B)30
C)40
D)50
E)60
Rationale: One way to do this would be weighted average method..
1) let the average of 5 mocks be x...
so take it as a mix of5 quantitites of xand1 quantity of 760resulting in an average of 726.67...
By alligation/weighted average..
the difference in 760 and 726.67 is 5/6 of difference of 760 and x..
760-726.67 = 5/6 * (760-x)
760-x= 33.33*6/5=40...
so x = 720..
the last of mock test will be 720+9+9=738...
so ans = 760-738=22
A
Answer: A
Question: IF x is an integer greater than 6, then all the following must be divisible by 3 EXCEPT
Options:
A)3x^3
B)x(x+1)(x+2)
C)9x
D)9x^2
E)x+3
Rationale: *any number multiplied by 3, will be divided by 3
for option E if we put value x=7, 7+3=10 is not divisible by 3
Answer : E
Answer: E
Question: A man can row upstream at 25 kmph and downstream at 35 kmph, and then find the speed of the man in still water?
Options:
A)32 kmph
B)34 kmph
C)30 kmph
D)45 kmph
E)65 kmph
Rationale: US = 25
DS = 35
M = (35 + 25)/2 = 30
Answer:C
Answer: C
Question: If 15!/3^x is an integer, what is the greatest possible value of x?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: 15 - 5*3
12 - 4*3
9 - 3*3
6 - 2*3
3 - 1*3
Hence max of 3^6 is allowed. IMO D.
Answer: D
Question: A fence consists of m lengths of fence that are each n feet long. A fence post separates each length of fence by its width of x feet. What is the total length R of the fence including the fence posts on each end?
Options:
A)mn
B)m(n + x)
C)R=m(n + x) + x
D)m(n + x) + 2x
E)2mn
Rationale: Notice that since a fence post separates each length of fence, then there will be m+1 posts, for example if there are m=2 fences, then there will be 3 posts: PFPFP. Thus the total length of the posts is (m+1)x.
The total length of the fence is mn, therefore the total length of the fence including the fence posts on each end is (m+1)x+mn=mx+x+mn=m(n+x)+x.
Answer: C.
Answer: C
Question: A 20% stock yielding 8% is quoted at?
Options:
A)165
B)170
C)250
D)180
E)185
Rationale: Assume that face value = Rs.100 as it is not given
To earn Rs.8, money invested = Rs.100
To earn Rs.20, money invested = 100×20/8 = Rs.250
ie, market value of the stock = Rs.250
Answer is C.
Answer: C
Question: Jim bought edging to go around a circular garden with a radius of 6 feet. Later he decided to
double the diameter of the garden. How many more feet of edging must he buy?
Options:
A)28.84' additional edging
B)48.84' additional edging
C)38.84' additional edging
D)18.84' additional edging
E)37.68' additional edging
Rationale: circumference of small garden = 2 x 3.14 x 6 = 37.68'
double of the circumference of small garden = 2 x 37.68' = 75.36'
More feet to be buy =75.36 - 37.68 = 37.68
Answer : E
Answer: E
Question: Find the amount of rs.7500 at compound interest at 4%per annum for 2 years?
Options:
A)8112
B)9110
C)7160
D)6210
E)8021
Rationale: Compound interest=[7500*(1+(4/100))^2]
=7500*((104/100)^2)
=(7500*104*104)/(100*100)
=Rs.8112
Option A
Answer: A
Question: 10^196 - 10^9 = Which of the following best approximates the value of the expression above?
Options:
A)10^186
B)10^196
C)10^100
D)10^150
E)10^170
Rationale: 10^196 - 10^9 =
Which of the following best approximates the value of the expression above?
Yes, answer 10^196 is correct. Note that we need approximate value of the given expression and as 10^(196) is much larger number than 10^(9) then 10^(9) is pretty much negligible in this case: 10^(196)-10^(9)=~10^(196).
Answer : B
Answer: B
Question: After decreasing 20% in the price of an article costs Rs.600. Find the actual cost of an article?
Options:
A)775
B)620
C)53
D)530
E)220
Rationale: CP* (80/100) = 600
CP= 7.75 * 100 => CP = 775
Answer: A
Answer: A
Question: The cost price of 25 books is the same as the selling price of ’X’ books. If the profit is 25%, then the value of X is ?
Options:
A)12.8
B)18
C)16
D)15
E)14
Rationale: let S.P. of X books = Rs 100 = C.P. of 25 books
Therefore, C.P. of one book = Rs 6.25
Profit = 25 %
Therefore, S.P of one book = 7.8
S.P of X articles = 7.8 X
7.8 X = 100 => X = 12.8
ANSWER:A
Answer: A
Question: total dinning bill of 3 people was $139.00 and 10% tip divided the bill evenly ?what is the bill amount each person shared .
Options:
A)21.84
B)50.96
C)53.84
D)24.84
E)50.26
Rationale: dinner bill of 3 person = 139 + 10% tip
so,
10% of 139 = (139*10)/100 = 13.9
So, the actual total amount = 139+13.9 = $ 152.9
so per head bill = 152.9/3 = $ 50.96
ANSWER:B
Answer: B
Question: The cash difference between the selling prices of an article at a profit of 2% and 6% is Rs. 3. The ratio of the two selling prices is?
Options:
A)52:56
B)52:53
C)52:50
D)22:56
E)51:53
Rationale: Let C.P. of the article be Rs. x.
Then, required ratio = 102% of x / 106% of x
= 102/106 = 51/53 = 51:53
Answer: E
Answer: E
Question: Which of the following Equation is NOT equivalent to 25x^2 = y^2 - 16?Which of the following Equation is NOT equivalent to 25x^2 = y^2 - 16?
Options:
A)25x^2 + 4 = y^2
B)75x^2 = 3y^2 - 12
C)25x^2 = (y + 2)(y - 2)
D)5x = y - 4
E)x^2 = (y^2 - 4)/25
Rationale: 1) Take the original equation and try to manipulate it so that it becomes 4 of the 5 answers
2) Take each answer choice and see if you can manipulate it to make it into the original equation.
With Answer D, we have...
5X = Y - 2
If we square both sides, we end up with....
(5X)^2 = (Y-4)^2
(5X)(5X) = (Y-4)(Y-4)
25X^2 = Y^2 - 8Y + 16
This is NOT a match for the original equation, so it's the answer that is NOT equivalent. D
Answer: D
Question: A vessel of capacity 45 litres is fully filled with pure milk. Nine litres of milk is removed from the vessel and replaced with water. Nine litres of the solution thus formed is removed and replaced with water. Find the quantity of pure milk in the final milk solution?
Options:
A)28.8
B)72.9
C)38.3
D)78.3
E)79.3
Rationale: Explanation:
Let the initial quantity of milk in vessel be T litres.
Let us say y litres of the mixture is taken out and replaced by water for n times, alternatively.
Quantity of milk finally in the vessel is then given by [(T - y)/T]^n * T
For the given problem, T = 45, y = 9 and n = 2.
Hence, quantity of milk finally in the vessel
= [(45 - 9)/45]^2 (45) = 28.8 litres.
Answer: Option A
Answer: A
Question: Three distinct single digit no A,B,C are in G.P. If abs(x) for real x is the absolute value of x(x if x is positive or zero, and x if x is negative),then the no. of different possible values of abs(A+B-C) is
Options:
A)6
B)4
C)3
D)5
E)2
Rationale: if a=1,r=2 then a=1,b=2,c=4 then abs(a+b-c)=1
if a=1,r=3 then a=1,a=3,a=9 then abs(1+3-9)=5
if a=2,r=2, then a=2,b=4,c=8 then abs(2+4-8)=2
if a=1,r=-2 then a=1,b=-2,c=4 the abs(1-2-4)=5
if a=1,r=-3 then a=1,b=-3,c=9 then abs(1-3-9)=11
if a=2,r=-2 then a=2,b=-4,c=-8 then abs(2-4-8)=10
so total 5 abs() values
ANSWER:D
Answer: D
Question: 15 men can complete a piece of work in 25 days. In how many days can 20 men complete that piece of work?
Options:
A)55 days
B)18.75 days
C)20 days
D)88 days
E)44 days
Rationale: 15 * 25 = 20 * x => x
= 18.75 days
Answer: B
Answer: B
Question: What is the sum of the digits of integer k, if k = (10^45- 46)
Options:
A)356
B)366
C)363
D)396
E)408
Rationale: There are 46 digits in 10^45
When we subtract 46 from it, there will be 45 digits left.
10^45 can be written as 9999999....(45 times) + 1
So,
10^45 - 46 = 9999999....(45 times) + 1 - 46 = 9999999....(45 times) -45
Consider the last 2 digits,
99-45 = 54
The last 2 digits will be 54.
And our number would be 99999......99954 with 2 less 9s after subtraction.
Number of 9s left are 43 and the last two digits are 54
The sum of the digits will be
(43*9) + 5 + 4 =396
Answer:- D
Answer: D
Question: A grocery store bought some mangoes at a rate of 5 for a dollar. They were separated into two stacks, one of which was sold at a rate of 5 for a dollar and the other at a rate of 5 for a dollar. What was the ratio of the number of mangoes in the two stacks if the store broke even after having sold all of its mangoes?
Options:
A)1:1
B)1:5
C)2:3
D)1:2
E)2:5
Rationale: The cost price of a mango = 1/5 dollars.
The selling price of a mango from the first stack = 1/3 dollars --> the profit from one mango = 1/5 - 1/5 = 0 dollars.
The selling price of a mango from the second stack = 1/5 dollars --> the loss from one mango = 1/5 - 1/5 = 0 dollars.
no profit as whole 1:1
Answer: A.
Answer: A
Question: Given
A+B+C=100
60A+40B+C=2000
Find A+B=?
Options:
A)76
B)74
C)40
D)44
E)can't determine
Rationale: (60A+40B+C=2000)-(A+B+C=100)
59A+39B=1900
So if we take A+B=40 so if A=17 and B=23 then 17+23=40 and 59*17+39*23=1900
it satisfy the condition so correct answer is=40
ANSWER:C
Answer: C
Question: A batsman scored 120 runs which included 3 boundaries and 8 sixes. What percent of his total score did he make by running between the wickets.
Options:
A)40%
B)50%
C)60%
D)70%
E)80%
Rationale: Explanation:
Number of runs made by running = 110 - (3 x 4 + 8 x 6)
= 120 - (60)
= 60
Now, we need to calculate 60 is what percent of 120.
=> 60/120 * 100 = 50 %
Answer: Option B
Answer: B
Question: The average of a couple was 18Yrs when they were married 20Yrs ago.The avg age of
the couple and a child, who was born during the interval, is 26Yrs now. How old is the
child now ?
Options:
A)2 Yrs
B)4 Yrs
C)3 Yrs
D)1 Yrs
E)None of these
Rationale: (a+b-20-20)/2=18;
a+b=76;
a+b+c/3=26;
solving both c=2
ANSWER:A
Answer: A
Question: If x and y are positive integers such that x/y=33.375, which of the following could be the remainder when x is divided by y?
Options:
A)8
B)21
C)25
D)44
E)47
Rationale: The answer is B - 21 because 21/0.375 yields an integer (= 56) and none of the other options does
x/y = Integer + Remainder
=> x/y = 33 + 0.375
Multiplying both sides by 56,
56(x/y) = 56*33 + 21
ALTERNATIVELY,you may calculate as follows:
x/y = 33.375
=> x/y = 33375/1000 = 267/8 = (33*8 + 3)/8
Multiply both sides by 7 to get
x/y = (33*56 + 21)/8 which can be written as 33*56/8 + 21/8
Once we know that we can get 3 as a remainder, we can select the answer choice that is a multiple of 3 (21 in this case)
The answer is therefore choice (B)
Answer: B
Question: An artist wishes to paint a circular region on a square poster that is 3 feet on a side. If the area of the circular region is to be 1/2 the area of the poster, what must be the radius of the circular region in feet?
Options:
A)1/pi
B)sqrt(2/pi)
C)sqrt(4.5/pi)
D)2/sqrt(pi)
E)pi/2
Rationale: Area of the poster is 3x3 = 9
1/2 the area = 4.5
pi*r^2 = 4.5
r^2 = 4.5/pi
r = sqrt(4.5/pi) answer (C)
Answer: C
Question: Train A is stopped at a railway station and train B is passing the train A with a speed of 62kph. Train A and B are having lengths of 200m and 185m respectively. How long it will take the train B to pass train A?
Options:
A)14.45
B)19.82
C)22.36
D)28.38
E)31.91
Rationale: Relative speed of train B with respect to train A = 62-0=62kph=17.22m/s
Distance needs to be covered by train B=200+185=385m
Time taken by the train B to pass train A = 385/17.22 = 22.36s
Answer: C
Answer: C
Question: A man purchases 8 pens for Rs.9 and sells 9 pens for Rs.8, how much profit or loss does he make?
Options:
A)20.88%loss
B)20.98%loss
C)20.78%loss
D)20.38%loss
E)10.98%loss
Rationale: 81 ---- 17
100 ----- ? è 20.98%loss
Answer:B
Answer: B
Question: Paul's income is 40% less than Rex's income, Quentin's income is 20% less than Paul's income, and Sam's income is 40% less than Paul's income. If Rex gave 60% of his income to Sam and 40% of his income to Quentin, sam's new income would be what fraction of Quentin's new income?
Options:
A)	11/12
B)	12/11
C)	13/19
D)	12/19
E)	11/19
Rationale: MAKE R = 10
P = 0.6R = 6
Q = 0.8P = 4.8
S= 0.6P = 3.6
FOR THAT WE GET S = 9.6
AND Q 8.8
SO 9.6/8.8= 1.2/1.1
Ans:B
Answer: B
Question: Out of first 20 natural numbers, one number is selected at random. The probability that it is either an even number or a prime number is -.
Options:
A)1/2
B)16/19
C)4/5
D)17/20
E)3/5
Rationale: n(S) = 20
n(Even no) = 10 = n(E)
n(Prime no) = 8 = n(P)
P(EᴜP) = 10/20 + 8/20 - 1/20 = 17/20
ANSWER:D
Answer: D
Question: Find the odd man out 17, 39, 171, 347
Options:
A)18
B)18
C)83
D)82
E)39
Rationale: 6 x 2+5=17
17 x 2+5=39
39 x 2+5=83
83 x 2+5=171
ANSWER:C
Answer: C
Question: The radius of a semi circle is 6.3 cm then its perimeter is?
Options:
A)32.7
B)32.4
C)32.5
D)32.9
E)32.2
Rationale: 36/7 r = 6.3
=32.4
Answer: B
Answer: B
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 72,030,000, how many red beads were removed?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: 72,030,000
= 2^4 * 5^4 * 7203
= 2^4 * 3 * 5^4 * 2401
= 2^4 * 3 * 5^4 * 7 * 343
= 2^4 * 3 * 5^4 * 7^4
The answer is D.
Answer: D
Question: A card game called “high-low” divides a deck of 52 playing cards into 2 types, “high” cards and “low” cards. There are an equal number of “high” cards and “low” cards in the deck and “high” cards are worth 2 points, while “low” cards are worth 1 point. If you draw cards one at a time, how many ways can you draw “high” and “low” cards to earn 5 points if you must draw exactly 3 “low” cards?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: To get a 5, you need one high and three lows (you could have had 2 highs and one low, but the constraint is that you must have three low cards)
HLLL = 4!3! =4
4! is the number of ways you can arrange these four spaces. divide by 3! because you you repeat three low cards
ANS:D
Answer: D
Question: A and B invest in a business in the ratio 3 : 2. If 5% of the total profit goes to charity and A's share is Rs. 855. the total profit is
Options:
A)Rs. 1425
B)Rs. 1500
C)Rs.1537
D)Rs.1576
E)None
Rationale: Solution
Let the total profit be Rs.100
After playing to charity, A's share	= Rs. (95 x 3/5)
If A's share is Rs.57, total profit	= Rs. 100.
If A's share is 855, total profit	= (100/57 x 855)
‹=›1500
Answer B
Answer: B
Question: Evaluate: 35 - 12*3*2 = ?
Options:
A)62
B)52
C)32
D)27
E)22
Rationale: According to order of operations, 12?3?2 (division and multiplication) is done first from left to right
12**2 = 4* 2 = 8
Hence
35 - 12*3*2 = 35 - 8 = 27
correct answer D
Answer: D
Question: In how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together?
Options:
A)10080
B)4989600
C)120960
D)180960
E)None of these
Rationale: The given words contain 8 letter MTHMTCS(AEAT), so 8!.
Then the 4 vowels can be formed differently, 4!.
But there are three words have repeated in the given words. So it should be divided by 2!*2!*2!.
Hence the solution is (8! * 4!) / (2! * 2! * 2!) = 120960
ANSWER:C
Answer: C
Question: In a Lake, there is a patch of lily pads. Every day, the patch doubles in size. It takes 34 days for the patch to cover the entire lake, how many days would it take the patch to cover half of the lake?
Options:
A)33
B)2^4*3
C)24
D)38
E)47
Rationale: Working backward from the day it's covered:
day 34: fully covered
day 33: half covered
So 33 days
ANSWER:A
Answer: A
Question: Murali travelled from city A to city B at a speed of 4 kmph and from city B to city C at 6 kmph. What is the average speed of Murali from A to C given that the ratio of distances between A to B and B to C is 2 : 3?
A. 48 kmph
Options:
A)33
B)5
C)28
D)7
E)16
Rationale: Let the distances between city A to B and B to C be 2x km and 3x km respectively.
Total time taken to cover from A to C
= (2x)/4 + (3x)/6 = (6x + 6x)/12 = 12x/12 = x Average speed = (2x + 3x)/(x) = 5 kmph.
Answer: B
Answer: B
Question: There are 134 toys coloured red and white in a box. Two red toys are removed from the lot and now there are twice as many red ones as white ones. How many of red colour toys are there now?
Options:
A)76
B)86
C)90
D)88
E)78
Rationale: r+w=134
Two red toys are removed from the lot and now there are twice red ones as white ones
r-2=2w sub 1st one we get
134-w-2=2w
132=3w
w=44
r=88
actually red will be 90
now 88
ANSWER:D
Answer: D
Question: 8 and 2 are the first two terms in a geometric sequence. What is the arithmetic difference between the 3rd term and the 4th term?
Options:
A)(3) * (1/4)^3
B)(6) * (1/4)^3
C)(6) * (1/8)^3
D)(6) - (1/4)^3
E)(6) / (1/4)^3
Rationale: Common ratio = 2/8 =1/4
3rd term = 8*(1/4)^3
4th term = 8*(1/4)^4
Difference = 8 * ((1/4)^3 - (1/4)^4)
= 8 * (1/4)^3 *(1 - (1/4))
= 8 * (1/4)^3 * (3/4)
= (1/4)^3 * (3/4) * 8
= (6) * (1/4)^3
B
Answer: B
Question: A person crosses a 600 m long street in 5 minutes. What is his speed in km per hour?
Options:
A)3.6
B)7.2
C)8.4
D)10
E)9
Rationale: Speed=(600/5 * 60) m/sec
= 2 m/sec.
Converting m/sec to km/hr
=(2*18/5) km/hr
= 7.2 km/hr.
Answer : B.
Answer: B
Question: Due to 10% decrease in the price of sugar and John can buy 5kg more sugar in Rs100 , then find the CP of sugar?
Options:
A)Rs. 1(2/9)
B)Rs. 2(2/7)
C)Rs. 2(2/11)
D)Rs. 2(2/13)
E)Rs. 2(1/9)
Rationale: Here r = 10 % ,x = 100 and A = 5 kg
Actual price of sugar = 10*100/((100-10 )*5) = Rs. 2(2/9)
B
Answer: B
Question: A man invests Rs. 3,000 at the rate of 5% per annum. How much more should he invest at the rate of 8%, so that he can earn a total of 6% per annum?
Options:
A)Rs. 1200
B)Rs. 1300
C)Rs. 1500
D)Rs. 2000
E)None of these
Rationale: Explanation :
Interest on Rs.3000 at 5% per annum = ( 3000 × 5 × 1) / 100 = Rs. 150
Let his additional investment at 8% = x
Interest on Rs.x at 8% per annum = ( x × 8 × 1 ) / 100 = 2x/25.
To earn 6% per annum for the total, interest = (3000 + x) × 6 × 1/100.
=> 150 + 2x/25 = (3000 + x) × 6 × 1/100.
=> 15000 + 8x = (3000 + x) × 6.
=> 15000 + 8x = 18000 + 6x.
=> 2x=3000.
=> x=1500.
Answer : C
Answer: C
Question: If we have 12 people in a meeting, in how many ways they can sit around a table?
Options:
A)11*10!
B)9*8!
C)8*7!
D)7*6!
E)6*5!
Rationale: If there arenpeople sitting around a table, there are(n-1)!possible arrangements:
Here, n=12
(n-1)!=11!=11*10!
Ans:A
Answer: A
Question: A cistern is normally filled in 8 hours but takes two hours longer to fill because of a leak in its bottom. If the cistern is full, the leak will empty it in?
Options:
A)33
B)88
C)40
D)99
E)11
Rationale: 1/8 - 1/x = 1/10
x = 40
Answer: C
Answer: C
Question: An arithemetic sequence of numbers begins p, 2p + 2, 4p + 3... What is the 12th member of this sequence?
Options:
A)A)37
B)B)40
C)+ 13
D)D)34
E)+ 13
Rationale: Common difference of an arithmetic series is constant.
2p+2-p=4p+3-2p-2
p=1
1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37
Ans:D
Answer: D
Question: Evaluate 75 / .05
Options:
A)1400
B)1500
C)1505
D)None of these
E)1506
Rationale: Explanation:
75/.05 = 7500/5 = 1500
Option B
Answer: B
Question: Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 5 sec. What is the length of the fast train?
Options:
A)22
B)23
C)25
D)27 7/9
E)27
Rationale: Relative speed = (40 - 20) = 20 km/hr.
= 20 * 5/ 18 = 50/9 m/sec.
Length of faster train = 50/9 * 5 = 250/9 = 27 7/9 m.
Answer: Option D
Answer: D
Question: A man sells a horse for Rs.800 and loses something, if he had sold it for Rs.980, his gain would have been double the former loss. Find the cost price of the horse?
Options:
A)337
B)278
C)288
D)860
E)721
Rationale: CP = SP + 1CP = SP - g
800 + x = 980 - 2x
3x = 180 => x = 60
CP = 800 + 60 = 860
Answer: D
Answer: D
Question: What is the remainder when 570 is divided by 6?
Options:
A)1
B)5
C)4
D)0
E)2
Rationale: Explanation:
52 = 25, on division by 6, the remainder is 1.
53 = 125, on division by 6, the remainder is 5.
54 = 625, on division by 6, the remainder is 1.
55 = 3125, on division by 6, the remainder is 5.
Hence, for 5 (2x) on division by 6, the remainder is 1, and for 5(2x-1) on division by 6, the remainder is 5.
Therefore, for 570, on division by 6, the remainder is 1.
ANSWER: A
Answer: A
Question: a,b,c are positive numbers such that they are in increasing Geometric progression then how many such numbers are there in (loga+logb+logc)/6 =log6
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: given that a,b,c are in gp
so b/a=c/b =>b^2=ac
(loga+logb+logc)/6=log6
=>log(abc)=6*log6
=>log(ac*b)=log(6^6)
=>log(b^3)=log(6^6)
=>b^3=6^6=>b^3=(6^2)^3
=>b=6^2=36
it means a=2,c=18 or a=3 c=12 or a=4 c=9 or a=6 c=6.
hence there are four such numbers
ANSWER:D
Answer: D
Question: List I: 2, 4, 6, 8 List II: x,2, 4, 6, 8
Options:
A)7
B)5
C)9
D)11
E)13
Rationale: List I has even number of terms, thus its median is the average of two middle terms (when arranged in ascending/descending order), so median=(4+6)/2=5.
List II has odd number of terms, thus its median is the middle term (when arranged in ascending/descending order). As no other number in the list equal to 5, then x=5.
Answer: B
Answer: B
Question: Two trains T1 and T2 start simultaneously from two stations X and Y respectively towards each other. If
they are 85 km apart both 3 and 6 hours after start, then find the distance between the two stations.
Options:
A)255km
B)210km
C)220km
D)180km
E)200km
Rationale: In first 3 hours T1 travels R km and T2 travels S km.
After 6 hours they traveled R+S+85+ 85
2(R+S ) = R+S +170
R+S = 170
Hence distance between XY is R+S+ 85 = 170 +85 =255
Answer : A
Answer: A
Question: In a series of football matches, the probability that Team P wins a match against Team Q is 1/4 and the probability that the match ends in a draw is 1/6. If the two teams play five matches, what is the probability that all five matches end in a draw?
Options:
A)1/4436
B)1/5546
C)1/6656
D)1/7776
E)1/8886
Rationale: P(5 draws)=(1/6)^5=1/7776
The answer is D.
Answer: D
Question: For a light that has an intensity of 60 candles at its source, the intensity in candles, S, of the light at a point d d feet from the source is given by the formula S=60k/d^2 60, where k is a constant. If the intensity of the light is 40 candles at a distance of 6 feet from the source, what is the intensity of the light at a distance of 30 feet from the source?
Options:
A)3/10 candles
B)1/2 candles
C)8/5 candles
D)2 candles
E)3 candles
Rationale: ANS = 3/10
S= 60k/d^2
At 6 feet
40 = 60k/36 so k = 24
At 30 feet
S = 60 *24/30^2 = 8/5
C
Answer: C
Question: Jemma takes 2 hours to swim the 4 miles from buoy A to buoy B. Tired from her swim, she then continues to buoy C at half her previous speed. If buoy C is 6 miles away from buoy B, how many more hours will pass before Jemma reaches Buoy C?
Options:
A)4
B)5
C)6
D)7
E)8
Rationale: Time taken for Jemma to reach buoy B is 2 hours.
The distance between the buoys is 4 miles.
Distance travelled/time taken = Average speed
Hence the average speed to travel the distance is 2m/hr
Now, she would have to travel 6 miles .
However as she is tired the speed is half or 1m/hr
Hence, it will take her 6 hours
(Option C)
Answer: C
Question: The average salary of the employees in a office is Rs.120/month.The avg salary of officers is Rs.470 and of non officers is Rs 110. If the no.of officers is 15,then find the No of nonofficers in the office.
Options:
A)400
B)420
C)430
D)450
E)525
Rationale: Let no. of non- officers be x
15 * 470 + x * 110 = (x + 15) 120
x = 525
E
Answer: E