divelab/Sys2Bench huggingface dataset:
Question: There is a 20% chance that Lions will not win at all during the whole season. There is a 30% chance that Tigers will not play at all in the whole season. What is the greatest possible probability that the Lions will win and Tigers will play during the season?
Options:
A) 55%
B) 60%
C) 70%
D) 72%
E) 80%
Rationale: There is a 20% chance that Lions will not win at all during the whole season
We can infer that there is 80% chance Lions will win .
Similarly There is a 30% chance that Tigers will not play at all in the whole season
We can also infer that there is 70% chance that Tigers will play.
Answer C
Answer: C
Question: If A and B are two events such that P (A) = 1/2, P (B) = 3/4 and P (A n B) = 3/8,
find P (not A and not B).
Options:
A)A)1/7
B)B)1/8
C)C)1/9
D)D)1/10
E)E)2/11
Rationale: P(not A and not B) = 1 - (P(A) + P(B) - P(AB))
which you might find somewhere in your text.
Substituting in our probabilities we get:
P(not A and not B) = 1 - (1/2 + 3/4 - 3/8)
P(not A and not B) = 1 - (7/8)
P(not A and not B) = 1/8.
B
Answer: B
Question: If b= (a-1)(a+2), then what is the least possible value of b?
Options:
A)-9/4
B)3
C)2
D)1
E)0
Rationale: Answer : A
Answer: A
Question: The batting average of a particular batsman is 60 runs in 46 innings. If the difference in his highest and lowest score is 140 runs and his average excluding these two innings is 58 runs, find his highest score.
Options:
A)179
B)367
C)269
D)177
E)174
Rationale: Explanation:
Total runs scored by the batsman = 60*46 = 2760 runs
Now excluding the two innings the runs scored = 58*44 = 2552 runs
Hence the runs scored in the two innings = 2760 â€“ 2552 = 208 runs.
Let the highest score be x, hence the lowest score = x â€“ 140
x + (x - 140) = 208
2x = 348
x = 174 runs
ANSWER: E
Answer: E
Question: There are 8 books in a shelf that consist of 2 paperback books and 6 hardback books. If 3 books are selected at random without replacement, how many different combinations are there that at least one paperback book is selected?
Options:
A)36
B)45
C)50
D)55
E)60
Rationale: 8C3 [Select any four] - 6C3 [Select all hard backs] = 36.
A
Answer: A
Question: If a and y are integers and (15^a + 15^(a+1))/4^y = 15^y what is the value of a?
Options:
A)2
B)3
C)4
D)5
E)Cannot be determined
Rationale: \frac{15^a( 1+ 15)}{4^y} = 15^y
(15^a . 4^2 ) / 4^y = 15^y. 4^0
15^a . 4^(2-y) = 15^y. 4^0
Equating the powers, a = y; 2-y = 0; So a = y = 2=A
Answer: A
Question: 6 points are marked on a straight line and another 7 points are marked on a second straight line with no points in common. How many triangles can be constructed with vertices from among the above points?
Options:
A)9
B)105
C)196
D)21
E)14
Rationale: assuming that the top line can have either 2 points or 1 point...
6! / 1!5! - 6! / 2! 4! yields 9.
A
Answer: A
Question: The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is:
Options:
A)200m
B)225m
C)245m
D)250m
E)260m
Rationale: Speed = 45/18 x	5	m/sec	= 25/2	m/sec.
Time = 30 sec.
Let the length of bridge be x metres.
Then,	130 + x/ 30	=	25/2
2(130 + x) = 750
x = 245 m.
ANSWER IS C
Answer: C
Question: Express 25 mps in kmph?
Options:
A)23
B)88
C)90
D)27
E)21
Rationale: 25 * 18/5 = 90 kmph
Answer:C
Answer: C
Question: Jim rides the bus to and from school each day. A one-way trip is 8.12 kilometers. How many kilometers does he travel in 3 days?
Options:
A)77km
B)56km
C)25.9km
D)48.72km
E)50km
Rationale: 1 day=2 trips,
3 days=2*3=6 trips
6*8.12= 48.72km.
Answer is D.
Answer: D
Question: If the number of 53,n87, where n represents the hundreds digit, is a multiple of 3, then the value of n could be which of the following?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: Then for any number to be a multiple of 3,The sum of its digits should be the multiple of 3.
i.e 5+3+n+8+7 = multiple of three
or, 23 + n = multiple of 3.
If n=1, 23 + n =24,which is a multiple of 3.
Hence answer is B.
Answer: B
Question: A box contains 20 electric bulbs, out of which 4 are defective. Two bulbs are chosen at random from this box. The probability that at least one of these is defective is
Options:
A)7/19
B)6/19
C)5/19
D)4/19
E)None of these
Rationale: Explanation:
Please remember that Maximum portability is 1.
So we can get total probability of non defective bulbs and subtract it form 1 to get total probability of defective bulbs.
So here we go,
Total cases of non defective bulbs
16C2=16∗15/2∗1=120
total cases = 20C2=20∗19/2∗1=190
probability = 120/190=12/19
P of at least one defective = 1−12/19=7/19
Option A
Answer: A
Question: The average monthly income of P and Q is Rs. 5050. The average monthly income of Q and R is Rs. 6250 and the average monthly income of P and R is Rs. 5200. The monthly income of P is?
Options:
A)Rs. 3000
B)Rs. 4000
C)Rs. 5000
D)Rs. 6000
E)Rs. 7000
Rationale: Let P, Q and R represent their respective monthly incomes. Then, we have:
P + Q = (5050 x 2) = 10100 .... (i)
Q + R = (6250 x 2) = 12500 .... (ii)
P + R = (5200 x 2) = 10400 .... (iii)
Adding (i), (ii) and (iii), we get: 2(P + Q + R) = 33000 or P + Q + R = 16500 .... (iv)
Subtracting (ii) from (iv), we get P = 4000.
P's monthly income = Rs. 4000.
B)
Answer: B
Question: The mean of 50 observations is 200. But later he found that there is decrements of 34 from each observations. what is the the updated mean is ?
Options:
A)165
B)166
C)190
D)198
E)199
Rationale: 166
Answer is B
Answer: B
Question: X and Y run a 50 m race,where X beats Y by 5 m. To do a favor to Y, X starts 5 m behind the starting line in a second 50 m race. Both run at the same previous speed. Which of the following is true?
Options:
A)X Beats Y by 2m
B)X Beats Y by 0.5 m
C)Y Beats X by 10m
D)Y Beats X by 11m
E)Y Beats X by 11m
Rationale: Let's suppose that the speed of X is 5m/s and that the speed of Y is 4.5m/s.
So, in the first race, the results are the following:
X crosses the finish line in 10s. In other words, X has run 50 m in 10 s.
In 10s, Y has run 45 meters.
Therefore, there is the difference of 5 meters mentioned in the question.
Now, let's review the second race.
In 11 seconds, X can complete the 50 meters race. We have to remember that X is 5 meters behind the starting line.
But in 11 seconds, Y has covered (45+4.5 ) =49.5 meters. Also, it is important to notice that in 11 seconds Y cannot arrive to the finish line.
So, 50- 49.5 = 0.5 meter
Answer: B
Answer: B
Question: What is the perimeter of a regular polygon with sides of length 15 cm and internal angles measuring 144° each?
Options:
A)96 cm
B)108 cm
C)120 cm
D)132 cm
E)150 cm
Rationale: Sum of all interior angles is given by:
180(n-2) = n is number of sides
180(n-2) = 144*n
from here
n = 10
So perimeter becomes 15*10= 150
answer E
Answer: E
Question: 78, 64, 48, 30 10, (...)
Options:
A)-12 number
B)-14
C)2
D)8
E)6
Rationale: Explanation :
78 - 14 = 64
64 - 16 = 48
48 - 18 = 30
30 - 20 = 10
10 - 22 = -12
Answer : Option A
Answer: A
Question: Working together, John and Jack can type 10 pages in one hour. If they would be able to type 12 pages in one hour if Jack increases his typing speed by 25%, what is the ratio of Jack's normal typing speed to that of John?
Options:
A)3/1
B)1/3
C)4/1
D)1/4
E)5/4
Rationale: Lets say John types x pages an hour and Jack types y pages an hour.
We know that x+y=10
Jack increase speed by 25% means he will type 1.25y pages an hour.
So we get x+1.25y=12
We need to know the ratio of Jack's speed to John's speed. This is going to be proportional to the number of pages each can type in an hour, hence (y/x).
Subtracting both : 0.25y=2 so y=8 ... so x=2
(y/x)=8/2 =4/1
Answer is (C)
Answer: C
Question: 3^x + 9*3^-x = 6 What is the value of x?
Options:
A)-1
B)1
C)0
D)1/2
E)-1/2
Rationale: let 3^x = t
t+9/t =6
t^2 -6t +9 =0
(t-3)^2=0
t-3=0
t=3
3^x=3
x=1
Ans: B
Answer: B
Question: A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets Euro 1000 more than D, what is B's share?
Options:
A)Euro 1000
B)Euro 3000
C)Euro 5000
D)Euro 4000
E)Euro 2000
Rationale: E
Euro 2000
Let the shares of A, B, C and D be Euro 5x, Euro 2x, Euro 4x and Euro 3x respectively.
Then, 4x - 3x = 1000
x = 1000.
B's share = Euro 2x = Euro (2 x 1000) = Euro 2000.
Answer: E
Question: The average age of a husband and his wife was 23 years at the time of their marriage. After five years they have a one-year old child. The average age of the family now is :
Options:
A)25
B)23
C)19
D)18
E)17
Rationale: Explanation:
Sum of the present ages of husband, wife and child = (23 * 2 + 5 * 2) + 1 = 57 years.
Required average = (57/3) = 19 years. Answer: C
Answer: C
Question: The sum of money will be double itself in 10years and simple interest find rate of interest?
Options:
A)10%
B)15%
C)20%
D)25%
E)30%
Rationale: T = 10 years
P= principle amount = x
A = total amount = 2x
SI = simple interest = A-P = 2x-x = x
R = 100SI/PT = 100x/10x =10%
Answer is A
Answer: A
Question: Chocolate bars are sold in packages of four or nine only. If Mark bought 97 chocolate bars exactly, what could be the number of large packs Mark bought?
Options:
A)3
B)4
C)8
D)9
E)13
Rationale: Let number of packs of four = f
let number of packs of nine = n
4f + 9n = 97
Now , we need to test for values of n.
Since sum 97 is odd and 4f will always be even , n can't be even .
Now , we can test for values e = 2 , 4 and 6
4*4 + 9*9 = 16 + 81 = 97
Answer D
Answer: D
Question: For the FIFA world cup, Paul the octopus has been predicting the winner of each match with amazing success. It is rumored that in a match between 2 teams A and B, Paul picks A with the same probability as A's chances of winning. Let's assume such rumors to be true and that in a match between Ghana and Bolivia, Ghana the stronger team has a probability of 2/3 of winning the game. What is the probability that Paul will correctly pick the winner of the Ghana-Bolivia game?
Options:
A)1/9
B)4/9
C)5/9
D)2/3
E)1/3
Rationale: Paul picks A with the same probability as A’schances of winning
So probability of picking a winner = prob picking of ghana * ghana winning + prob picking of bolivia * bollivia winning
= 2/3 * 2/3 + 1/3 * 1/3
= 5/9
ANSWER:C
Answer: C
Question: If Susan takes 8 seconds to run y yards, how many minutes will it take her to run x yards at the same rate?
Options:
A)xy/8
B)8x/(60y)
C)60xy/8
D)xy/480
E)480x/y
Rationale: The answer is B.
She runs x yards in 8x/y seconds =8x/60y minutes.
Answer: B
Question: A, B, C enter into a partnership investing Rs. 35,000, Rs. 45,000 and Rs. 55,000 respectively. The respective shares of A, B, C in annual profit of Rs. 40,500 are?
Options:
A)Rs. 10,500, Rs. 13,500, Rs. 16,500
B)Rs. 10,600, Rs. 13,500, Rs. 96,500
C)Rs. 10,500, Rs. 73,500, Rs. 16,500
D)Rs. 10,500, Rs. 18,500, Rs. 16,500
E)Rs. 40,500, Rs. 13,500, Rs. 16,500
Rationale: A:B:C = 35000 : 45000 : 55000 = 7:9:11
A's share = 40500 * 7/27 = Rs. 10500
B's share = 40500 * 9/27 = Rs. 13500
C's share = 40500 * 11/27 = Rs. 16500
Answer:A
Answer: A
Question: In a can, there is a mixture of milk and water in the ratio 4 : 5. If it is filled with an additional 8 litres of milk the can would be full and ratio of milk and water would become 6 : 5. Find the capacity of the can?
Options:
A)44
B)73
C)53
D)32
E)62
Rationale: A
44
Let the capacity of the can be T litres.
Quantity of milk in the mixture before adding milk = 4/9 (T - 8)
After adding milk, quantity of milk in the mixture = 6/11 T.
6T/11 - 8 = 4/9(T - 8)
10T = 792 - 352 => T = 44.
Answer: A
Question: Two taps can separately fill a cistern 5 minutes and 10 minutes respectively and when the waste pipe is open, they can together fill it in 15 minutes. The waste pipe can empty the full cistern in?
Options:
A)7
B)8
C)6
D)4.2
E)5
Rationale: 1/5 + 1/10 - 1/x = 1/15
x = 30/7 = 4.2
Answer: D
Answer: D
Question: A plant manager must assign 8 new workers to one of five shifts. She needs a first, second, and third shift, and two alternate shifts. Each of the shifts will receive 2 new workers. How many different ways can she assign the new workers?
Options:
A)243
B)336
C)350
D)486
E)540
Rationale: whatever : my take selecting team of 2 out of 8 to assign to the shifts = 8C2 = 28 ways.
now 2 out of 8 means total of 4 group possible.
so putting them in shifts = counting methode: first, second, third, alt , alt
= 4*3*2*1 = 24
here alt and alt are the same: so 24/2 = 12 ways.
total ways of selecting = (selecting 2 out of 8)*arranging those teams in shifts
= 28*12 = 336
Ans: B
Answer: B
Question: What percent of 250 is 45?
Options:
A)0.25%
B)18%
C)25%
D)40%
E)250%
Rationale: 250*x /100 = 45
x = 45*10/25
x = 18
Ans: B
Answer: B
Question: Six fencers participate in a fencing championship. Assuming all competitors have an equal chance of winning, how many possibilities are there with respect to how a first-place and second-place medal can be awarded?
Options:
A)20
B)24
C)25
D)30
E)36
Rationale: 6*5 = 30
The answer is D.
Answer: D
Question: If x is an integer and (x)(x^2)(x^3)(x^10) is positive, which of the following could be negative?
Options:
A)x^4
B)(x)(x^3)
C)(x)(x)
D)x + x^9
E)3x^2
Rationale: A) X^4 - always positive (or 0).
B) X(X^3) = X^4 - Again always positive (or 0).
C) (x)(x) = X^2 - Again always positive (or 0).
D) x+x^9 - Could be -ve if x is -ve.
E) 3X^2 - again always positive (or 0)
Answer D.
Answer: D
Question: Charlene's annual bonus is calculated in the following manner: Charlene receives 20 percent of her first $11,000 in sales and 40 percent of her sales in excess of $11,000. If Charlene received a bonus of $7,300, what were her annual sales?
Options:
A)$ 10,000
B)$ 12,750
C)$ 24,000
D)$ 26,000
E)$ 28,000
Rationale: Let x be the total sales in $.
For the 1st 11,000 you get 20% ---> 0.2*11000 = 2200$
For the remaining (x-11000) $, you get 40% ---> 0.4*(x-11000)
Thus, 0.4*(x-11000) + 2200 = 7300 ----> x= 12,750 $
B is thus the correct answer.
Answer: B
Question: A security guard at a certain store is instructed to check the receipt of one out of every five customers as they are leaving the store. If, on the guard's shift,
customers leave the store, how many different samples of customers could have been selected to have their receipts checked?
Options:
A)20
B)10
C)59
D)90
E)100
Rationale: to choose the sample of 2 customers from 5. it can be done 5C2 possible ways.
So the answer is B. 10
Answer: B
Question: The revenue from sales items in 1996 increases by x percent, compared in 1995 and the revenue in 1997 decreases by x percent, compared in 1996. If the revenue from sales items in 1997 decreases by 4 percent, compared in 1995, what is the value of x?
Options:
A)10
B)15
C)20
D)30
E)35
Rationale: 1995 - let the value be z
1996 - x% increase - z(1+x/100)
1997 - x% decrease - z(1+x/100)(1-x/100)
from 95 to 97 decrease is 4%
hence, [z-{z(1+x/100)(1-x/100)}]/z = 4/100
solving x = 20%
C is the answer
Answer: C
Question: What is the greatest prime factor of (15!14!) + (15!16!)?
Options:
A)31
B)71
C)181
D)211
E)241
Rationale: 15!14! + 15!16!
= 15!14! (1+15*16)
= 15!14!(241)
The answer is E.
Answer: E
Question: A motorcyclist goes from Bombay to Pune, a distance of 224 kms at an average of 32 kmph speed. Another man starts from Bombay by car 2 ½ hours after the first, and reaches Pune ½ hour earlier. What is the ratio of the speed of the motorcycle and the car?
Options:
A)1:2
B)1:5
C)4:7
D)1:1
E)1:8
Rationale: T = 224/32 = 7 h
T = 7 - 3 = 4
Time Ratio = 7:4
Speed Ratio = 4:7
Answer: C
Answer: C
Question: Three grades of milk are 1 percent, 2 percent and 4 percent fat by volume. If x gallons of the 1 percent grade, y gallons of the 2 percent grade, and z gallons of the 3 percent grade are mixed to give x+y+z gallons of a 1.5 percent grade, what is x in terms of y and z?
Options:
A)y + 4z
B)(y +z) / 4
C)2y + 3z
D)3y + z
E)3y + 4.5z
Rationale: Soln:
The resulting equation is
=> (.01x + .02y + .04z)/(x+y+z) = 1.5/100
=> x + 2y + 4z = 1.5x + 1.5y + 1.5z
taking x to one side and y and z to other side we get
=> x = y + 4z
Ans is a
Answer: A
Question: A total of 30 percent of the geese included in a certain migration study were male. If some of the geese migrated during the study and 30 percent of the migrating geese were male, what was the ratio of the migration rate for the male geese to the migration rate for the female geese? [Migration rate for geese of a certain sex = (number of geese of that sex migrating) / (total number of geese of that sex)]
Options:
A)1/4
B)7/12
C)2/3
D)1
E)8/7
Rationale: Let' take the Number of geese to be 100.
Male = 30. Female = 70.
Now the second part of the Q, Let's take the Number migrated to be 20.
So we have 20 geese that migrated and out of that 20% are male i.e 20/100 *30 = 6 Geese (Males)
And now we know out of the total 20 geese , 6 are male , then 14 have to be female.
Now the ratio part , Male Geese Ratios = 6/30 = 1/5. - A
Female Geese Ratios =14/70=1/5 - B
Cross Multiply Equations A and B and you get =1.
Ans D
Answer: D
Question: If 6th March, 2004 is sunday, what was the day of the week on 6th March, 2005?
Options:
A)monday
B)tuesday
C)friday
D)sunday
E)wednesday
Rationale: The year 2004 is a leap year. So, it has 2 odd days.
But, Feb 2004 not included because we are calculating from March 2004 to March 2005. So it has 1 odd day only.
The day on 6th March, 2005 will be 1 day beyond the day on 6th March, 2004.
Given that, 6th March, 2004 is Sunday
6th March, 2005 is Monday.
Answer: A) Monday
Answer: A
Question: 3 no.'s A, B & C are in the ratio of 12:15:25. If sum of these no.'s is 312, find the ratio between the difference of B & A & the difference of C & B.
Options:
A)1 : 5
B)3 : 10
C)4 : 7
D)4 : 11
E)5 : 9
Rationale: We have, a = 12, b = 15, c = 25 and x = 312.
ax_ 12 X 312
a+b+c 12+15+25
— 72,
bx _ 15 X 312 B — — 90 a +b+c 12 + 15+ 25 cx 25 X 312 And, C =
a+b+c 12 + 15+ 25
...B-A=18 andC-B=60
- 150
Thus, their ratio = 18 : 60 or 3 : 10
B
Answer: B
Question: On a trip covering 450 km, a bicyclist travels the first 300 km at 20 km per hour and the remainder of the distance at 15 km per hour. What is the average speed, in km per hour, for the entire trip?
Options:
A)16.5
B)17.0
C)17.5
D)18.0
E)18.5
Rationale: time 1 = 300 / 20 = 15 hours
time 2 = 150 / 15 = 10 hours
total time = 25 hours
average speed = 450 / 25 = 18 km/hr
The answer is D.
Answer: D
Question: A speaks truth in 75% of cases and B in 80% of cases. In what percentage of cases are they likely to contradict each other, narrating the same incident
Options:
A)30%
B)35%
C)40%
D)45%
E)50%
Rationale: Explanation:
Let A = Event that A speaks the truth
B = Event that B speaks the truth
Then P(A) = 75/100 = 3/4
P(B) = 80/100 = 4/5
P(A-lie) = 1-3/4 = 1/4
P(B-lie) = 1-4/5 = 1/5
Now
A and B contradict each other =
[A lies and B true] or [B true and B lies]
= P(A).P(B-lie) + P(A-lie).P(B)
[Please note that we are adding at the place of OR]
= (3/5*1/5) + (1/4*4/5) = 7/20
= (7/20 * 100) % = 35%
Answer: Option B
Answer: B
Question: In a certain mathematical activity, we have five cards with five different prime numbers on them. We will distribute these five cards among three envelope: all could go in any envelope, or they could be broken up in any way among the envelopes. Then in each envelop, we find the product of all the cards in that envelope: that is the “number” of the envelope. An envelope containing no cards has the number 1. We then put the three envelope numbers in order, from lowest to highest, and that is our set. How many different T sets can be produced by this process?
Options:
A) 41
B) 89
C) 125
D) 243
E) 512
Rationale: Case 1: 1 used envelope => 1 way
Case 2: 2 used envelopes
- 4-1-0: Choose 4 from 5 cards: 5 ways
- 3-2-0: Choose 3 from 5 cards: 10 ways
Case 3: All envelopes used
- 3-1-1: Choose 3 from 5 andno need to choose 1 from 2: 10 ways
- 2-2-1: Choose 2 from 5 and choose 2 from 3, but two groups are the same => (10X3):2 = 15
Total T: 1+5+10+10+15=41 => Answer: A
Answer: A
Question: A set of football matches is to be organized in a "round-robin" fashion, i.e., every
participating team plays a match against every other team once and only once. If 10
matches are totally played, how many teams participated?
Options:
A)4
B)5
C)10
D)7
E)8
Rationale: 2 ways to solve this problem..
summation(x)=n(n-1)/2
n(n-1)/2=10;
n^2-n-20=0
Ans : 5
ANSWER:B
Answer: B
Question: Which one of the following numbers is exactly divisible by 11?
Options:
A)415624
B)415358
C)415647
D)425624
E)415836
Rationale: A
415624 is exactly divisible by 11.
Answer: A
Question: A woman has four blouses of different colors, three skirts of different colors, and two different pairs of shoes. She refuses to wear her pink blouse with her green skirt. How many different blouseskirt-shoe combinations could she wear?
Options:
A)8
B)12
C)22
D)17
E)18
Rationale: total ways = 4*3*2=24..
now its better to find the ways in which the pink blouse and green skirt are together and subtract from total to get the answer..
the ways in which the pink blouse and green skirt are together=1*1*2=2..
total ways =24-2=22..
ANSWER:C
Answer: C
Question: The area of a parallelogram is 128sq m and its altitude is twice the corresponding base. Then the length of the base is?
Options:
A)8
B)9
C)7
D)6
E)1
Rationale: 2x * x = 128
=> x= 8
Answer: A
Answer: A
Question: Sam wrote 7 letters on Tuesday and 3 letters on Wednesday. How many letters did he write on average per day?
Options:
A)10
B)4
C)21
D)3
E)5
Rationale: (7 + 3)/2 = 5
The correct answer is E
Answer: E
Question: If the radius of a circle that centers at the origin is 5, how many W points on the circle have integer coordinates?
Options:
A) 4
B) 8
C) 12
D) 15
E) 20
Rationale: I understand this might not be required but I used the equation of a circle.
Since the origin is at 0, x^2+y^2=5^2.
X,Y could be +/- (0,5 or 5,0) - 4 possibilities.
X,Y could be +/- (3,4 or 4,3) - 8 possibilities.
Ans: W=C
Answer: C
Question: Raman mixed 27 kg of butter at Rs. 150 per kg with 36 kg butter at the rate of Rs. 125 per kg. At what price per kg should he sell the mixture to make a profit of 40% in the transaction?
Options:
A)129
B)287
C)190
D)188
E)112
Rationale: Explanation:
CP per kg of mixture = [27(150) + 36(125)]/(27 + 36) = Rs. 135.71
SP = CP[(100 + profit%)/100]
= 135.71 * [(100 + 40)/100] = Rs. 190.
Answer:C
Answer: C
Question: If 15 and 20 are the lengths of two sides of a triangular region, which of the following can be the length of the third side?
I. 10
II. 20
III. 40
Options:
A)I only
B)II only
C)I and II only
D)II and III only
E)I, II, and III
Rationale: The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.
Let x be the length of the third side.
20-15 < x < 20+15
5 < x < 35
The answer is C.
Answer: C
Question: A train of 35 carriages, each of 60 meters length, when an engine also of 60 meters length is running at a speed of 60 kmph. In what time will the train cross a bridge 1.5 km long?
Options:
A)6
B)3
C)4
D)9
E)3.6
Rationale: D = 35 * 60 + 1500 = 3600 m
T = 3600/60 * 18/5 = 216 sec = 3.6 mins
Answer:E
Answer: E
Question: A car traveling with 5/7 of its actual speed covers 42 km in 1 hr 40 min 48 sec. What is the actual speed of the car?
Options:
A)20
B)25
C)27
D)30
E)35
Rationale: Time = 1 hr 40 min 48 sec = 1hr +40/60hr+48/3600hr=1+2/3+1/75=126/75hr
distance = 42 km
speed=distance/time
=42/(126/75)=42×75/126
⇒57 of the actual speed = 42×75/126
⇒actual speed = 42×75/126×7/5=42×15/18=7×15/3=7×5=35 km/hr
Answer is E.
Answer: E
Question: A bag marked at $125 is sold for $120. The rate of discount is?
Options:
A)10%
B)25%
C)20%
D)50%
E)4%
Rationale: Rate of discount = 5/125 * 100 = 4%
Answer is E
Answer: E
Question: There are r red marbles, b blue marbles and w white marbles in a bag. Write the ratio of the number of blue marbles to the total number of marbles in terms of r, b and w.
Options:
A)r/ (r + b + w)
B)b/ (r + b + w)
C)w / (r + b + w)
D)r / (r + b )
E)r / ( b + w)
Rationale: Solution
The total number of marbles is
r + b + w
The total ratio of blue marbles to the total number of marbles is
r / (r + b + w)
ANSWER IS A
Answer: A