divelab/Sys2Bench huggingface dataset:
Question: In a certain state, the ratio of registered Republicans to registered Democrats is 3 to 2, and every registered voter is either a Republican or a Democrat. If 75 percent of the Republicans and 15 percent of the Democrats are expected to vote for Candidate X, and everyone else is expected to vote for Candidate Y, by what percent is Candidate X expected to win the election?
Options:
A)2%
B)5%
C)8%
D)10%
E)15%
Rationale: Since we were expected to find a percentage figure - It thought that it might be easier to pick a 'smart number' to represent the total number of voters (republicans and democrats). Therefore, I picked 100 (as the total number of voters) and thus 3:2 ==60:40 represents the number ratio of Republicans:Democrats. If 75% of Republicans (which is (60*0.75) = 45) and 15% of Democrats (40*0.15 = 6) voted for candidate X, means that out of total of 100 voters; 51 (45 + 6) voters voted for candidate X and 49 voted for candidate Y. Thus we can infer that candidate X is expected to win the election by 2 (51-49) votes. Therefore candidate X is expected to win the election by (2/100) votes which is equivalent to 2%.
I think the answer is A.
Answer: A
Question: A man spends 50% of his income on food, 15% on children education and 50% of the remaining on house rent. What percent of his income he is left with?
Options:
A)17.5%
B)16%
C)15.4%
D)12.6%
E)13.5%
Rationale: Let the total income be x
then, income left = (100-50)% of x - [100-(50+15)]% of x = 50% of 35% of x = 17.5% of x
Answer is A
Answer: A
Question: There are 12 points in a given plane, no three of which are on the same line. If one of the points is represented as 'A', then how many triangles can be determined with the 12 points that contain the point A?
Options:
A)55
B)105
C)182
D)210
E)455
Rationale: Any 2 points out 11 points will create triangle with third point A, so the answer is 11C2=55.
Answer: A.
Answer: A
Question: The monthly income of Suman in the year 2009 was approximately what percentage of the monthly income of Jyothi in the year 2010?
Options:
A)22
B)27
C)26
D)29
E)21
Rationale: Answer:C
Answer: C
Question: Two cars cover the same distance at the speed of 60 and 64 kmps respectively. Find the distance traveled by them if the slower car takes 1 hour more than the faster car.
Options:
A)906
B)900
C)960
D)450
E)280
Rationale: Explanation:
Distance= speed * Time
60(x + 1) = 64x
X = 15
60 * 16 = 960 km
Answer: C
Answer: C
Question: The length of rectangle is thrice its breadth and its perimeter is 96 m, find the area of the rectangle?
Options:
A)432
B)197
C)279
D)269
E)207
Rationale: 2(3x + x) = 96
l = 36 b = 12
lb = 36 * 12 = 432
Answer: A
Answer: A
Question: The letters B,G,I,N and R are rearranged to form the word 'Bring'. Find its probability.
Options:
A)1/120
B)1/235
C)1/24
D)1/76
E)1/53
Rationale: Explanation :
There are total 5 letters. The probability that B gets the first position is 1/5.
The probability that G is in the second position is 1/4.
Likewise, probability for I,N and G are 1/3, 1/2 and 1/1.
Hence, the required probability is:-
=> (1/5) x (1/4) x (1/3) x (1/2) x 1.
=> 1/120.
Answer : A
Answer: A
Question: What is the 25th digit to the right of the decimal point in the decimal form of 6/11?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: Explanation:
To determine the greatest possible number of members, first recognize that each member had to contribute the lowest amount given. Build an inequality for the individual contributions and the total amount collected, with n=the number of members in the club, and solve for n.
12n≤599
n≤49 11/12
Since n represents individual people it must be a whole number. Thus the greatest number of people is 49.
Answer: Option C
Answer: C
Question: On Thursday Mabel handled 90 transactions. Anthony handled 10% more transactions than Mabel, Cal handled 2/3rds of the transactions that Anthony handled, and Jade handled 19 more transactions than Cal. How much transactions did Jade handled?
Options:
A)80
B)81
C)82
D)83
E)85
Rationale: Solution:
Mabel handled 90 transactions
Anthony handled 10% more transactions than Mabel
Anthony = 90 + 90 × 10%
= 90 + 90 × 0.10
= 90 + 9
= 99
Cal handled 2/3rds of the transactions than Anthony handled
Cal = 2/3 × 99
= 66
Jade handled 19 more transactions than Cal.
Jade = 66 + 19
= 85
Jade handled = 85 transactions.
Answer: E
Answer: E
Question: Subtracting 10% from X is the same as multiplying X by what number?
Options:
A)70%
B)90%
C)50%
D)97%
E)10%
Rationale: X - (10/100) X = X * ?
? = 90%
Answer: B
Answer: B
Question: In the simple subtraction problem below some single digits are replaced by letters .Fined the value of 7A+5D+6CD?
Options:
A)288
B)3799
C)277
D)278
E)7A+5D+6CD=240
Rationale: 15 - 7 = 8 So D = 8
10 + (C -1) - 8 = 4 So C = 3
10 + (5-1) - B = 7 So B = 7
(A-1) - 1 = 6 So A = 8
7A + 5D + 6CD = 56 + 40 + 144 = 240
Answer:E
Answer: E
Question: Caleb spends $74.50 on 50 hamburgers for the marching band. If single burgers cost $1.00 each and double burgers cost $1.50 each, how many double burgers did he buy?
Options:
A)5
B)10
C)20
D)40
E)49
Rationale: Solution -
Lets say, Single hamburgersxand Double hamburgersy
Given that,
x+y=50 and 1x+1.5y=74.50. By solving the equations y=49. ANS E.
Answer: E
Question: A girl has exactly 6 quarters, 6 dimes, and 10 nickels in her pocket. If she withdraws a number of these coins at random, how many coins would she have to withdraw to ensure that she has at least a 50 percent chance of withdrawing at least one quarter?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: When the probability of NOT drawing a quarter is 50% or less, then the probability of drawing a quarter is at least 50%.
P(not drawing a quarter with 2 coins) = 16/22 * 15/21 = 40/77 > 50%
P(not drawing a quarter with 3 coins) = 40/77 * 14/20 = 4/11 < 50%
The answer is C.
Answer: C
Question: In a ratio which is equal to 4:6, if the antecedent is 20, then the consequent is?
Options:
A)72
B)85
C)30
D)51
E)45
Rationale: We have 4/6 = 20/x
4x = 20*6
x = 30
consequent = 30
Answer is C
Answer: C
Question: A certain team has 14 members, including Joey. A three-member relay team will be selected as follows: one of the 14 members is to be chosen at random to run first, one of the remaining 13 members is to be chosen at random to run second, and one of the remaining 12 members is to be chosen at random to run third. What is the probability that Joey will be chosen to run second or third?
Options:
A)1/3
B)2/5
C)1/6
D)1/7
E)5/14
Rationale: Each member has an equal probability to run second (1/14) or third (1/14).
The probability that Joey runs second or third is 1/14 + 1/14 = 1/7
The answer is D.
Answer: D
Question: When a plot is sold for Rs. 18,700, the owner loses 15%. At what price must that plot be sold in order to gain 15%?
Options:
A)Rs. 21,000
B)Rs. 22,500
C)Rs. 25,300
D)Rs. 25,800
E)Rs. 55,800
Rationale: Explanation :
Let the C.P. of the plot = Rs. x
Given that x - 15% of x = 18700.
=> (85/100) * x = 18700
=> x = 22000
So the cost price (C.P.) of the plot = Rs. 22000
S.P. of plot for 15% profit = 22000 + 15% of 22000 = 22000*(115/100) = 25300
Answer : C
Answer: C
Question: The ratio of a to b is 4 to 5, where a and b are positive. If x equals a increased by 25 percent of a, and m equals b decreased by 60 percent of b, what is the value of m/x?
Options:
A)1/3
B)2/5
C)3/4
D)3/2
E)2/3
Rationale: a/b = 4/5
m/x = (2/5)*5 / (5/4)*4 = 2/5
The answer is B.
Answer: B
Question: The sum of two consecutive integers is 61. Find the numbers.
Options:
A)17, 18
B)30,31
C)5, 6
D)1, 2
E)8, 9
Rationale: n + (n + 1) = 61
2n + 1 = 61
2n = 60
n = 30
Answer: B
Answer: B
Question: Average between 2 sets of numbers is closer to the set with more no's?
Options:
A)70
B)80
C)90
D)92
E)94
Rationale: If on a test three people answered 90% of the questions correctly and two people answered 80% correctly, then the average for the group is not 85% but rather 3×90+2×805=4305=86.3×90+2×805=4305=86.
Here, 90 has a weight of 3 => it occurs 3 times.
Whereas 80 has a weight of 2 => it occurs 2 times.
So the average is closer to 90 than to 80 as we have just calculated.
B
Answer: B
Question: If the wheel is 14 cm then the number of revolutions to cover a distance of 1408 cm is?
Options:
A)A)16
B)B)10
C)C)14
D)D)12
E)E)11
Rationale: 2 * 22/7 * 14 * x = 1408 => x = 16
ANSWER:A
Answer: A
Question: If it takes a machine 4⁄5 minute to produce one item, how many items will it produce in 2 hours?
Options:
A)1⁄3
B)150
C)80
D)120
E)180
Rationale: 1 item takes 4/5 min so it takes 120 min to produce x
4x/5=120 the x=150
Answer:B
Answer: B
Question: If points A and B are (4+1) units apart, which of the following can have only one possible value?
I. The area of a square region with side AB
II. The circumference of a circle passing through points A and B
III. The area of a rectangular region with diagonal AB
Options:
A)I only
B)II only
C)III only
D)I and II only
E)I and III only
Rationale: I. The area of a square region with side AB --> side=AB=(4+1) or 5 --> the area of a square is 5^2=25, so only one possible value;
II. The circumference of a circle passing through points A and B --> circle is not defined by only two points, hence the circumference of a circle passing through points A and B can take infinitely many values. For example consider when AB=diameter and when points A and B are not the endpoints of the diameter;
III. The area of a rectangular region with diagonal AB --> consider the case when AB is the diagonal of a square (the area is 25/2) and the case when AB is the diagonal of a rectangle with the sides equal to 3 and 4 (the area 12).
Answer: A.
Answer: A
Question: In a party attended by 10 persons, each clinch their glass with every other. How many glass clinches?
Options:
A)45
B)52
C)53
D)54
E)55
Rationale: Total no. of person = 11
Total no. of glass clinches = n(n-1)/2
=10*9/2
= 45
ANSWER:A
Answer: A
Question: If the positive integer y is divisible by 3, 8, and 12, then which of the following must y be divisible by?
I. 24
II. 36
III. 48
Options:
A)I only
B)II only
C)I and II only
D)II and III only
E)I, II, and III
Rationale: y needs to be divisible by 3, 8 and 12. This means that it must be the LCM of 3, 8 and 12 or a multiple of the LCM. The LCM is the smallest number which is divisible by all 3 numbers.
LCM of 3, 8 and 12 will be 3*8 = 24
Now y must be either 24 or a multiple of 24. In any case it will always be divisible by 24.
Will it be divisible by 36 necessarily? No. Say if y is 24, it will not be divisible by 36.
Will it be divisible by 48 necessarily? No. Say if y is 24, it will not be divisible by 48.
Answer (A)
Answer: A
Question: How many possible integer values are there for x if |6x - 3| < 6 ?
Options:
A)One
B)Two
C)Three
D)Four
E)Five
Rationale: Solution: |6x-3| < 6
let 6x=a therefore we have |a-3| < 6 ==> read this as origin is at +3 and we have to move +6 to the right and -6 to the left
(the less than sign represents that the a must be within boundaries )
(3-6)----------3----------(3+6)
now, we have -3<a<9
but a =6x ==> -3<6x<9
dividing all values by +4 we have -0.5 <x < 1.5
Now question says Integer values (not rational ) therefore we have 0,1
Hence 2 B
Answer: B
Question: If |x - 8| = x, then x=?
Options:
A)8
B)4
C)-4
D)0
E)2
Rationale: |x - 8| = x ...(given)
x^2 - 16x + 64 = x^2
0*x^2 + 16*x -64 = 0 ....(by solving above eq. we get) , x = 4 ===> Ans - B
Answer: B
Question: At what rate percent per annum will a sum of money double in 8 years.
Options:
A)12.5%
B)13.5%
C)11.5%
D)14.5%
E)24.5%
Rationale: Explanation:
Let principal = P, Then, S.I.=P and Time=8 years
Rate = [(100 x P)/ (P x 8)]% = 12.5% per annum.
Answer: A
Answer: A
Question: The L.C.M of two numbers is 48. The numbers are in the ratio 1:2. The sum of numbers is:
Options:
A)28
B)30
C)40
D)50
E)72
Rationale: Let the numbers be 1x and 2x.
Then, their L.C.M = 2x. So, 2x = 48 or x = 24.
The numbers are 24 and 48.
Hence, required sum = (24 + 48) = 72.
ANSWER:E
Answer: E
Question: 225 metres long yard, 26 trees are palnted at equal distances, one tree being at each end of the yard. What is the distance between 2consecutive trees
Options:
A)10
B)12
C)15
D)17
E)18
Rationale: 26 trees have 25 gaps between them,
Required distance (225/25) = 10
A
Answer: A
Question: How many multiples of 5 are there between 5 to 100?
Options:
A)9
B)18
C)17
D)none of these
E)Cannot be determined
Rationale: Explanation :
As you know, multiples of 5 are integers having 0 or 5 in the digit to the extreme right (i.e. the units place).
So the numbers are 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95.
Answer : B
Answer: B
Question: If V is the product of the integers from 1 to 30, inclusive, what is the greatest integer k for which 3^k is a factor of V?
Options:
A)10
B)12
C)14
D)16
E)18
Rationale: V = 30!
8
V = 30 x 29 x 28 x 27 x 26 x 25 x 24 x 24 x 22 x 21 x 20 x 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 09 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
Out of these 30 , 27 , 24 , 21 , 18, 15 , 12 , 09 , 06 , 3 are factors of 3
3 x 10 , 3 x 3 x 3 , 3 x 8 , 3 x 3 x 2, 3 x 5 , 3 x 4 , 3 x 3 x 3 , 3 x 2 , 3
So we have a total of 14 three's ...
Therefore the maximum value of K can be 14 (C)
Answer: C
Question: Which of the following is the equation of the line in the xy-plane that has slope 0
(I) x = 3
(II) y = 3
(III) x + y = 0
Options:
A)II
B)I
C)III
D)I&II
E)II&III
Rationale: y =mx+c therefore y-c= mx then m =(y-c)/x
m=0 means y = c constant ..= II
A
Answer: A
Question: The cost of the paint is rs.20 per kg. if 1kg of paint covers 15 sq.ft, how much will it cost to paint outside of a cube having 5 feet each side
Options:
A)Rs.200
B)Rs.672
C)Rs.546
D)Rs.876
E)None of these
Rationale: Explanation:
surface area of a cube= 6 x 5^2 = 150 sq.ft
quantity of paint required=(150/15)=10 kg
cost of painting= 20 x 10 = Rs.200
Answer: A
Answer: A
Question: Find the average of first 30 natural numbers.
Options:
A)20.5
B)15.5
C)19.5
D)19
E)17
Rationale: Exp. Sum of first n natural numbers = n( n+1)/2
So, sum of first 30 natural numbers = 30*31/2 = 465
Required average =465/30 =15.5
Answer:B
Answer: B
Question: If there are 56 laborers in a crew, and on a certain day, 30 were present. Calculate the percentage that showed up for work? (round to the nearest tenth).
Options:
A)53.6%
B)52.6%
C)54.6%
D)55.6%
E)59.6%
Rationale: 30/56*100=53.57
53.6%
correct answer A
Answer: A
Question: A, B and C can do a piece of work in 24, 30 and 40 days respectively. They start the work together but C leaves 4 days before the completion of the work. In how many days is the work done?
Options:
A)15 days
B)14 days
C)13 days
D)11 days
E)10 days
Rationale: Explanation:
x/24 + x/30 + x/40 = 1
x = 11 days
Answer: D
Answer: D
Question: Two horses begin running on an oval course at the same time. One runs each lap in 8 minutes; the other takes 12 minutes to run each lap. How Many minutes after the start will the faster horse have a one lap lead?
Options:
A)24
B)12
C)9
D)4
E)3
Rationale: The rate of the faster horse is 1/8 lap/minute;
The rate of the slower horse is 1/12 lap/minute;
Their relative rate is 1/8-1/12=1/24 lap/minute;
The faster horse to gain one full lap will need time=distance/rate=1/(1/24)=24 minutes.
Answer: A.
Answer: A
Question: Stuart bought a sweater on sale for 30% off the original price and another 25% off the discounted price. If the original price of the sweater was $80, what was the final price of the sweater?
Options:
A)$25.75
B)$35.75
C)$15.75
D)$ 45.75
E)$42
Rationale: The price with 30% off
80 - 30% of 80 = 80 - (30 / 100) *80 = 56
The price with another 25% off
56 - 25% of 56 = 56 - (25/100)* 56 = $42
correct answer E
Answer: E
Question: In how many different number of ways 4 boys and 2 girls can sit on a bench?
Options:
A)720
B)740
C)760
D)780
E)800
Rationale: npn = n!
6p6 = 6 × 5 × 4 × 3 × 2 × 1 = 720
A
Answer: A
Question: A, B and C enter into a partnership. They invest Rs. 40,000, Rs. 80,000 and Rs. 1,20,000 respectively. At the end of the first year, B withdraws Rs. 40,000, while at the end of the second year, C withdraws Rs. 80,000. In what ratio will the profit be shared at the end of 3 years ?
Options:
A)3 : 4 : 8
B)3 : 4 : 7
C)3 : 4 : 2
D)3 : 4 : 1
E)3 : 4 : 5
Rationale: A : B : C = (40000 x 36) : (80000 x 12 + 40000 x 24) : (120000 x 24 + 40000 x 12)
= 144 : 192 : 336
= 3 : 4 : 7.
Answer: B
Answer: B
Question: The sum of all the digits of the integers from 18 to 21 inclusive is 24 (1 + 8 + 1 + 9 + 2 + 0 + 2 + 1 = 24). What is the sum R of all the digits of the integers from 0 to 99 inclusive?
Options:
A)450
B)810
C)900
D)1000
E)1100
Rationale: We want the sum of the digits from 0 to 99, so I approximated:
0-9 ->45-> (9+0)*10/2
40-49 ->85(13+4)*10/2
90-99 ->135(18+9)*10/2
We can see at a glance that theweightgoes up as the numbers go up (meaning the difference between 85 and 45 is 40, while 135-85 is 50, this means that the second part of this sequence carries more weight for our result), so we know that the final answer has to be more than 850 (85*10) but close to it, and that's just R=900:the answer is C.
Answer: C
Question: The overall age of X and Y is 18 year greater than the overall age of Y and Z. Z is how many decades younger that X?
Options:
A)11
B)15
C)12
D)17
E)18
Rationale: E
18
(X + Y) â€“ (Y + Z) = 18
X â€“ Z = 18
Answer: E
Question: How many positive factors do 150 and 90 have in common?
Options:
A)8
B)12
C)16
D)18
E)24
Rationale: The number of common factors will be same as number of factors of the Highest Common Factor(HCF)
HCF of 150 and 90 is 30
Number of factors of 30 = 8
Answer :A
Answer: A
Question: Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively . If they cross each other in 23 seconds, what is the ratio of their speeds?
Options:
A)1:3
B)3:1
C)2:3
D)3:2
E)3:4
Rationale: Let the speed of the trains be x and y respectively
length of train1 = 27x
length of train2 = 17y
Relative speed= x+ y
Time taken to cross each other = 23 s
= (27x + 17 y)/(x+y) = 23
= (27x + 17 y)/ = 23(x+y)
= 4x = 6y
=x/y = 6/4 = 3/2 i.e 3:2
Answer :D
Answer: D
Question: John was thrice as old as Tom 6 yrs back. He will be 5/3 times as old as Tom 6 years hence. How old is Tom today?
Options:
A)7
B)8
C)12
D)14
E)16
Rationale: Sol. RMBflSk -6 = 3 (Ravi - 6) ...(j)
and Rupesh + 6 = | (Ravi + 6) ...(ii)
Solving both the equations we get,
Ravi = 12 years.
C
Answer: C
Question: A set of consecutive positive integers beginning with 1 is written on the blackboard. A student came along and erased one number. The average of the remaining numbers is 35 7/17. What was the number erased?
Options:
A)SEVEN 7
B)8
C)9
D)15
E)17
Rationale: 2) The average of the new group of numbers is 35 7/17. The denominator of THAT fraction tells us that the total number of terms in the new list MUST be a multiple of 17:
17, 34, 51, 68, 85, etc.
3) Since we're removing 1 number from a list of consecutive positive integers, we could quickly limit down the possible number of terms in the ORIGINAL list:
If new = 17, old = 18, but the numbers from 1 to 18 would NOT have an average in the mid-30s (it would be much smaller). ELIMINATE this option.
If new = 34, old = 35, but we run into the same problem. The average won't match here either. ELIMINATE this option.
If new = 51, old = 52, same problem here. ELIMINATE this option.
If new = 68, old = 69....HERE we have a group of numbers that might just be what we're looking for.
In theold group, the average is themiddle term= 35, which is REALLY close to the new average once we remove a number.
Now, we just have to figure out which of the 5 answers was removed (and that changed the new average to 35 7/17). There are a couple of ways to do this math, but I'm going to use the answers to save myself some steps:
Sum of 1 to 69, inclusive = 69(35) = 2415
Remove Answer B....2415 - 8 = 2407
New average = 2407/68 = 35 27/68
Now, we can compare 27/68 to 7/17
27/68 and 28/68
This is REALLY close, but is not the answer. Eliminate B. The answer is either A or C.
Since 28/68 is a BIGGER fraction than 27/68, we need the sum (of the 68 integers) to be BIGGER...which means we need to remove a SMALLER number.
Final Answer:
A
Answer: A
Question: If (x # y) represents the remainder that results when the positive integer x is divided by the positive integer y, what is the sum of all the possible values of y such that (16 # y) = 1?
Options:
A)8
B)9
C)16
D)23
E)24
Rationale: (x # y) represents the remainder that results when the positive integer x is divided by the positive integer y.
Thus (16 # y) = 1 implies that 16=yq+1 --> 15=yq--> y is a factor of 15. The factors of 15 are 1, 3, 5, and 15. Now, y cannot be 1, since 16 divided by 1 yields the remainder of 0 not 1.
Therefore the sum of all the possible values of y is 3+5+15=23.
Answer: D.
Answer: D
Question: The average temperature of Monday, Tuesday, Wednesday and Thursday was 38∘ and that of Tuesday, Wednesday, Thursday and Friday was 40∘. If the temperature on Monday was 33∘, the temperature of Friday was :
Options:
A)41∘
B)39∘
C)38∘
D)30∘
E)None of these
Rationale: Explanation:
M+T+W+Th=(4×38)=152
Monday temperature is 33. So T+W+Th=(152-33)=119
T+W+Th+F=(4×40)=160
F = (160-119)=41∘
Correct Option: A
Answer: A
Question: Three numbers are randomly selected, with replacement, from the set of integers {0, 1, 2, 3, 4, 5, 6}. If the first number selected is w, the second number selected is x, and the third number is y, what is the probability that w < x < y ?
Options:
A)2/7
B)3/7
C)5/49
D)6/49
E)30/343
Rationale: The number of ways to select w, x, and y is: 7*7*7=343
The number of ways to choose three different numbers from the set is 7C3=35.
There are six permutations for each group of three different numbers, but only one permutation satisfies w < x < y.
P(w < x < y) = 35/343 = 5/49
The answer is C.
Answer: C
Question: How many positive integers e less than 30 have no common prime factor with 30?
Options:
A)5
B)6
C)7
D)8
E)9
Rationale: e=30=2*3*5. So, the number must be less than 30 and not have primes 2, 3, or 5.
This means that the number could be: 1, 7, 11, 13, 17, 19, 23, or 29. Total of 8 numbers.
Answer: D.
Answer: D
Question: If A : B = 4 : 7 and B : C = 5 : 9 then A : B : C is :
Options:
A)ratio 20 : 35 : 63
B)35 : 36 : 63
C)30 : 35 : 65
D)25 :34: 68
E)None of these
Rationale: A : B = 4 : 7
B : C = 5 :9 = 5*7/5 : 9 *7/5 = 7 : 63/5
A : B : C = 4 : 7 : 63/5 = 20 : 35 : 63
ANSWER: A
Answer: A
Question: 17 balls are numbered 1 to 17. A ball is drawn and then another ball is drawn without replacement. What is the probability that both balls have even numbers?
Options:
A)1/7
B)3/14
C)5/23
D)7/34
E)9/41
Rationale: P(1st ball is even) = 8/17
P(2nd ball is also even) = 7/16
P(both balls are even) = 8/17 * 7/16 = 7/34
The answer is D.
Answer: D
Question: A train crosses a platform of 140 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train?
Options:
A)190
B)88
C)77
D)62
E)52
Rationale: Length of the train be â€˜Xâ€™
X + 140/15 = X + 250/20
4X + 560 = 3X + 750
X = 190m
Answer: A
Answer: A
Question: Out of 7 consonants and 4 vowels, how many words of 4 consonants and 2 vowels can be formed?
Options:
A)25900
B)151200
C)210
D)120
E)720
Rationale: Required selection = select 4 consonants from 7 and 2 vowels frm 4
= 7C4 * 4C2
= 210
As we have to form 6 letter word the above combination of consonants and vowels can be done in 6! = 720 different ways
Required no. of ways = 210 * 720
= 151200
Ans - B
Answer: B
Question: The function f is defined for all positive integers n by the following rule: f(n) is the product of the distinct prime factors of n. If f(n) < 50 and n is not prime, what is the greatest possible value of f(n)?
Options:
A)48
B)35
C)31
D)32
E)28
Rationale: Since we need the largest value of f (n), we will start with the largest option.
Option A: 48 = 2*2*2*2*3. This is not a product of distinct prime numbers. Hence incorrect
Option B: 35 = 5*7. This is a product of distinct prime numbers.
Rest all the options are smaller that 35.
Correct Option: B
Answer: B