divelab/Sys2Bench huggingface dataset:
Question: Hali builds a tower using only red, green, and blue toy bricks in a ratio of 4:3:1. She then removes 1/2 of the green bricks and adds 1/3 more blue bricks, reducing the size of the tower by 14 bricks. How many red bricks will she need to add in order to double the total number of bricks used to build the original tower?
Options:
A)82
B)96
C)110
D)120
E)192
Rationale: Hali want to double the original amount of blocks, not just the red blocks
the original tower had 96 bricks, the new tower has 82 bricks and the question is asking how many extra red blocks are needed to build a tower of 192 bricks (double the original: 96*2).
192-82 = 110
so 110 bricks need to be added to the new 82 brick tower to double the original.
They worded the question ashow many red bricks need to be addedbut really it could be any colour just that 110 more bricks need to be there to equal 192=E
Answer: E
Question: What is the sum of the prime factors of 81 and the prime factors of 144?
Options:
A)33
B)45
C)30
D)33
E)36
Rationale: The prime factors of 81 are 3*3*3*3
The prime factors of 144are 12*12
3+3+3+3+12+12 = 36 E is the correct answer
Answer: E
Question: A tradesman by means of his false balance defrauds to the extent of 20%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?
Options:
A)20%
B)45%
C)44%
D)48%
E)50%
Rationale: Explanation:
g% = 20 + 20 + (20*20)/100
= 44%
ANSWER IS C
Answer: C
Question: Which expression is the greatest
Options:
A)3252/3257
B)3456/3461
C)3591/3596
D)3641/3656
E)3453/3458
Rationale: Options can be re-written as (x-5)x => 1-(5/x)
A) 1- (5/3257)
B) 1- (5/3461)
C) 1- (5/3596)
D) 1- (5/3656)
E) 1- (5/3458)
To get the largest among these second half should be the least and so denominator to be largest. Hence 'D'.
Answer: D
Question: In ABC limited, 75% are using Samsung phone at the same time 70% using i phone; If in the same company 85% are using Samsung phone then, what is the percentage of i phone user?
Options:
A)55
B)68
C)38
D)34
E)69
Rationale: Samsung phone user = 75%; i phone user= 80%; Total = 85*100;Percentage of Samsung phone users = 85 - 75 = 10;
Percentage of i phone users = 100 - 80 =20; then total % of i phone users =0.70*20= 14;then total % of i phone users = 20+14 =34. Answer= D
Answer: D
Question: 26% of employees are women with fair hair. 40% of fair-haired employees are women. What percent of employees have fair hair?
Options:
A)25
B)30
C)50
D)55
E)65
Rationale: Think of 100 people total:
From the first fact, 26 of these are women with fair hair.
From the second fact, these 20 women make up 40% of the total fair haired population.
We can then make a ratio of 60:40 fair haired men to fair haired women.
This means that (60/40)*26 equals the number of fair haired men, which is 39 men with fair hair.
Add this 39 to the 26 women and get 65 fair haired men and women out of 100 total men and women.
65%E
Answer: E
Question: The value for D=(0.889 × 55)/9.97 to the nearest tenth is
Options:
A)0.5
B)4.63
C)4.9
D)7.7
E)49.1
Rationale: if we read the Q, we can easily home on to the answer,,
the numerator is clearly between 40 and 50..
denomiator is close to 10..
so D=(0.889 × 55)/9.97 is between 4 and 5..
It may tempt us to solve it since ther are two values between 4 and 5..
but the catch is innearest tenth
4.63 can be called nearest to hundreth and no tenth, so can be eliminated..
4.9 is our answer...
C
Answer: C
Question: All the stocks on the over-the-counter market are designated by either a 1 letter or 2 letter codes that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different stocks that can be designated with these codes?
Options:
A)2(26^5)
B)26(26^4)
C)27(26^1)
D)26(26^5)
E)27(26^5)
Rationale: with 1 letters: 26^1
with 2 letters: 26^2
26^1 + 26^2 = 27*(26^1)
C
Answer: C
Question: What is the area of rectangular field?
I.	The perimeter of the field is 110 metres.
II.	The length is 5 metres more than the width.
III.	The ratio between length and width is 6 : 5 respectively.
Options:
A)I and II only
B)Any two of the three
C)All I, II and III
D)I, and either II or III only
E)None of these
Rationale: EXPLANATION
I. 2(l + b) = 110 l + b = 55.
II. l = (b + 5) l – b = 5.
III. l/b = 6/5 => 5l – 6b = 0.
These are three equations in l and b. We may solve them pairwise.
Any two of the three will give the answer.
answer is (B).
Answer: B
Question: If 27.5% of the 880 students at a certain college are enrolled in biology classes, how many students at the college are NOT enrolled in a biology class?
Options:
A)638
B)330
C)550
D)430
E)880
Rationale: Students enrolled in biology are 27.5% and therefore not enrolled are 72.5%. so of 880 is 880*.225 = 638
Answer is A 638
Answer: A
Question: Sanoop bought 8 t-shirts at an average price (arithmetic mean) of Rs.526. If Sanoop returned 5 t-shirts to the retailer, and the average price of the remaining t-shirts was Rs.505, then what is the average price, of the three returned t-shirts?
Options:
A)560
B)561
C)562
D)538.6
E)564
Rationale: Total price of 8 t-shirts= 8*526=4208
Total price of 3 t-shirts=5*505=1515
Total price of 5 t-shirts=4208-1515=2693
Average price of 3 t-shirts=2693/5=538.6
Correct option Answer:D
Answer: D
Question: A student scored an average of 80 marks in 3 subjects: Physics, Chemistry and Mathematics. If the average marks in Physics and Mathematics is 90 and that in Physics and Chemistry is 70, what are the marks in Physics?
Options:
A)11
B)66
C)77
D)80
E)71
Rationale: Given M + P + C = 80 * 3 = 240 --- (1)
M + P = 90 * 2 = 180 --- (2)
P + C = 70 * 2 = 140 --- (3)
Where M, P and C are marks obtained by the student in Mathematics, Physics and Chemistry.
P = (2) + (3) - (1) = 180 + 140 - 240 = 80
Answer:D
Answer: D
Question: When p is divided by 9, the remainder is 4. All of the following are possible values of p, except for which of the following?
Options:
A)13
B)31
C)49
D)52
E)67
Rationale: If a number is divisible by 9, the sum of its digits must be divisible by 9. --> If a number leaves a remainder 4 when divided by 9 the sum of its digits must be 4.
52
Answer: D
Answer: D
Question: If the LCM of 2, 5, 6, and a is 210, which of the following could be a?
Options:
A)5
B)6
C)4
D)7
E)12
Rationale: Using elimination method, eliminate the option to arrive at
if a is replaced by 7 and the LCM is calculated you arrive at 210
D
Answer: D
Question: (178% of 1265) ÷ 5.96 = ?
Options:
A)125
B)175
C)225
D)375
E)524
Rationale: Explanation :
? = (178 x 1265/100) ÷ 6 = 2250/600 = 375
Answer : Option D
Answer: D
Question: The C.P of 10 pens is equal to the S.P of 12 pens. Find his gain % or loss%?
Options:
A)16 2/8%
B)16 8/3%
C)16 2/3%
D)16 4/3%
E)16 6/3%
Rationale: 10 CP = 12 SP
12 --- 2 CP loss
100 --- ? => 16 2/3%
Answer:C
Answer: C
Question: If s is an integer greater than 6, which of the following must be divisible by 3?
Options:
A)s (s+3) (s-5)
B)s (s+2) (s-1)
C)s (s+1) (s-4)
D)s (s+4) (s-2)
E)s (s+5) (s-6)
Rationale: anything in the form of (s-1) (s) (s+1) is divisible by 3. in other word, a product of any 3 consecutive intevers is divisible by 3.
s (s+1) (s-4) = s (s+1) ((s-1)-3) is equivalant to (s-1) (s) (s+1)
s (s+2) (s-1) is equivalant to (s+1) missing.
s (s+3) (s-5) is equivalant to (s-1) missing and s repeating.
s (s+4) (s-2) is equivalant to odd/even consqcutive integers
s (s+5) (s-6) is equivalant to (s+1) missing and s repeating.
Answer : C
Answer: C
Question: A rectangular parking space is marked out by painting three of its sides. If the length of the unpainted side is 9 feet, and the sum of the lengths of the painted sides is 37 feet, find out the area of the parking space in square feet?
Options:
A)120
B)122
C)124
D)128
E)126
Rationale: length =9 feet
breadth =37−92=14 feet
Area =9×14=126 square feet
Answer is E.
Answer: E
Question: If four coins are tossed, the probability of getting two heads and two tails is
Options:
A)3/8
B)3/4
C)3/5
D)3/3
E)3/1
Rationale: Since four coins are tossed, sample space = 24
Getting two heads and two tails can happen in six ways.
n(E) = six ways
p(E) = 6/24
= 3/8
Answer:A
Answer: A
Question: If −y ≥ x, and −x < −8, then which of the following must be true?
Options:
A)y = −8
B)y > −8
C)−y > 8
D)y ≤ −8
E)y ≥ −8
Rationale: −y ≥ x, and −x < −8
y <= -x < -8
As '-x' is less than '-8' and Y is less than or equal to '-x'
we have y < -8 which is similar to -y > 8.
C) -y > 8
Answer: C
Question: A rectangular swimming pool is 20 feet by 18 feet. A deck that has uniform width surrounds the pool. The total area of the pool and deck is 624 square feet. What is the width of the deck?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: Let the width =W
Total Area of the pool and deck= (2W+20)(2W+18)
We can Test the answer choices along with unit digit method
A) 2 feet ...........24*22 has unit digit 8..........Eliminate
B) 2.5 feet.........25*23 has unit digit 5..........Eliminate
C) 3 feet............26*24 has unit digit 4...........Hold
D) 4 feet............28*26 has unit digit 8...........Eliminate
E) 5 feet............30*38 has unit digit 0...........Eliminate
Answer: B w=3
Answer: B
Question: If 3 girls can do 3 times of a particular work in 3 days, then, 7 girls can do 7 times of that work in
Options:
A)1 1/5 days
B)2 days
C)2 1/5 days
D)3 days
E)4 days
Rationale: Answer: Option 'D'
That is, 1 girl can do one time of the work in 3 days.
Therefore, 7 girls can do 7 times work in the same 3 days itself.
Answer: D
Question: A dice is rolled 3times & sum of 3 no.'sappearing on the uppermost face is 15. The chance that the first roll was four is?
Options:
A)2/113
B)3/114
C)1/108
D)2/213
E)3/111
Rationale: Sol. Total number of favorable outcomes n(S) . e . 216 Combinations of outcomes for getting sum of 15 on uppermost face = (4, 5, 6) (5, 4, 6) (6, 5, 4) (5, 6, 4), (4, 6, 5), (6, 4, 5), (5, 5, 5), (6, 6, 3), (6, 3, 6) (3, 6, 6) Now outcomes on which first roll was a four, n(E) = (4, 5, 6), (4, 6, 5) P(E) n(E) 2 1 Pt') = n(S) = 216 = 1/108
C
Answer: C
Question: 2056 x 987 = ?
Options:
A)1936372
B)2029272
C)1896172
D)1923472
E)None of them
Rationale: =2056 x 987
=2056 x (1000 - 13)
=2056 x 1000 - 2056 x 13
=2056000 - 26728
=2029272
Answer is B
Answer: B
Question: Which of the following is not a composite number ?
Options:
A)234
B)211
C)525
D)603
E)217
Rationale: Clearly 211 is not a composite number. All others are divisible by 3. Ans : A
Answer: A
Question: By how much does the larger root of the equation 2b^2+5b = 12 exceed the smaller root?
Options:
A) 5/2
B) 10/3
C) 7/2
D) 14/3
E) 11/2
Rationale: For 2b^2+5b = 12 Roots are [-5 + sqrt(25 + 96)]/4 OR [-5 - sqrt(25 + 96)]/4
= 1.5 OR -4
Hence larger root 1.5 is 1.5 - (-4) = 5.5 = 11/2 greater than smaller root (-4).
Hence option (E).
Answer: E
Question: The sum of the ages of 4 children born at the intervals of 3 years each is 38 years. What is the age of the youngest child?
Options:
A)2 years
B)3 years
C)4 years
D)5 years
E)6 years
Rationale: Let the ages of the children be x, (x + 3), (x + 6), (x + 9) years.
Then, x + (x + 3) + (x + 6) + (x + 9) = 38
4x = 20 => x = 5.
Age of youngest child = x = 5 years.
ANSWER:D
Answer: D
Question: At a certain stage of a soccer tournament, the score ratio of teams A, B and C was 3:4:5. Eventually, the score ratio of A to B has doubled while the score ratio of A to C has halved. If the final score of team C was 40, what was the final score S of team B?
Options:
A)1)8
B)2)10
C)3)20
D)4)40
E)5)80
Rationale: A to B = 3 : 4
So, on doubling we get 6 : 4
A to C = 3 : 5
So, on halving we get 1.5 : 5 or 3 : 10 or 6 : 20
So final ratio = 6 : 4 : 20.
If 20x = 40
4x = 8
Hence, answer is A
Answer: A
Question: The difference between two positive integers is 3.if the sum of their squares is 369, the the sum of the numbers is:
Options:
A)12
B)29
C)71
D)48
E)23
Rationale: x^2 +(x+3)^2=369
x^2+x^2+9+6x=369
2x^2+6x-360=0
x^2+3x-180=0
(x+15)(x-12)=0
x=12
correct answer A
Answer: A
Question: The length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 972 sq m, then what is the breadth of the rectangular plot?
Options:
A)16
B)17
C)18
D)19
E)14
Rationale: Let the breadth of the plot be b m.
Length of the plot = 3 b m
(3b)(b) = 972
3b2 = 972
b2 = 324
b = 18 m.
Answer: Option C
Answer: C
Question: A, B, C, D and E play a game of cards. A says to B, "If you give me three cards, you will have as many as E has and if I give you three cards, you will have as many as D has." A and B together have 10 cards more than what D and E together have. If B has two cards more than what C has and the total number of cards be 133, how many cards does B have ?
Options:
A)22
B)23
C)25
D)35
E)30
Rationale: Explanation:
Clearly, we have :
B-3 = E ...(i)
B + 3 = D ...(ii)
A+B = D + E+10 ...(iii)
B = C + 2 ...(iv)
A+B + C + D + E= 133 ...(v)
From (i) and (ii), we have : 2 B = D + E ...(vi)
From (iii) and (vi), we have : A = B + 10 ...(vii)
Using (iv), (vi) and (vii) in (v), we get:
(B + 10) + B + (B - 2) + 2B = 133 => 5B = 125=> B = 25.
ANSWER IS C
Answer: C
Question: A discount electronics store normally sells all merchandise at a discount of 5 percent to 25 percent off the suggested retail price. If, during a special sale, an additional 25 percent were to be deducted from the discount price, what would be the lowest possible price of an item costing $300 before any discount?
Options:
A)$130.00
B)$160.75
C)$168.75
D)$182.00
E)$168.00
Rationale: Original price : 300 $
Max first discount = -25%
Thus : 300âˆ—(1âˆ’25/100)=225
Second discount on the discounted price = -25%
Thus : 225âˆ—(1âˆ’25/100)=168.75
Answer C
Answer: C
Question: Alice and Bob race around a running track. Alice runs at a constant rate of one lap every 5 minutes and Bob runs at a constant rate of one lap every 6 minutes. If they both start at the same time, how many minutes will it take for Alice to get exactly one lap ahead of Bob?
Options:
A)30
B)32
C)35
D)36
E)40
Rationale: Let x be the number of minutes it takes for Alice to get one lap ahead.
Then Alice ran x/5 laps and Bob ran x/6 laps.
x/5 = 1+x/6
6x=30+5x
x=30
The answer is A.
Answer: A
Question: What is the next number of the following sequence
125, 25, 175, 35, 245, 49 (...)
Options:
A)282
B)343
C)393
D)434
E)515
Rationale: The series is
125/5=25
25*7=175
175/5=35
35*7=245
245/5=49
49*7=343
ANSWER: B
Answer: B
Question: A train of 24 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 3.5 km long?
Options:
A)4
B)3
C)5
D)7
E)9
Rationale: D = 25 * 60 + 3500 = 5000 m
T = 5000/60 * 18/5 = 300 sec = 5 mins
Answer: C
Answer: C
Question: Difference between the length &breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is?? We have: (l - b) = 23 and 2(l + b) = 206 or (l + b) = 103?
Options:
A)2500 m^2
B)2540 m^2
C)2520 m^2
D)2600 m^2
E)3000 m^2
Rationale: Solving the two equations, we get: l = 63 and b = 40.
Area = (l x b) = (63 x 40) m2 = 2520 m^2
C
Answer: C
Question: If z is a positive integer, which of the following could NOT be the square of z?
Options:
A) 5,008,644
B) 5,004,169
C) 4,999,696
D) 4,995,225
E) 4,990,752
Rationale: A number ending with 2 can never be a perfect square.
Units digit of a perfect square must be:
1,4,9,6,5
Answer E)
9*9=1
1,4,9,6,5
Ans:E
Answer: E
Question: Kamal started a business investing Rs. 9000. After five months, Sameer joined with a capital of Rs. 8000. If at the end of the year, they earn a profit of Rs. 6970, then what will be the share of Sameer in the profit?
Options:
A)2388
B)2380
C)2888
D)2663
E)2922
Rationale: Kamal : Sameer = (9000 * 12) : (8000 * 7)
= 108:56 = 27:14
Sameer's share = 6970 * 14/41 = Rs. 2380.
Answer: B
Answer: B
Question: A, B and C can do a piece of work in 24 days, 30 days and 40 days respectively. They began the work together but C left 10 days before the completion of the work. In how many days was the work completed?
Options:
A)12.5 days
B)16 days
C)18 days
D)11 days
E)38 days
Rationale: One day work of A, B and C = 1/24 + 1/30 + 1/40 = 1/10 Work done by A and B together in the last 10 days = 10*(1/24 + 1/30) = 3/4
Remaining work = 1/4
The number of days required for this initial work = 2.5 days.
The total number of days required = 10 + 2.5 = 12.5 days.
Answer: A
Answer: A
Question: Following the approval of crude oil production cuts by OPEC, the price of crude which has slumped by 28% in the last 3 months is expected to rally and increase by about 5% in the next one month. This will bring the price of crude oil to $60.
Options:
A)79.4
B)75.1
C)80.7
D)68.3
E)89.6
Rationale: -28+5-(28*5)/100=-24.4% net decrease
let initial price be Y
Y(1-24.4/100)=60
Y=60/0.756 = ~79.4
Ans is A)
Answer: A
Question: In a simultaneous throw of pair of dice .find the probability of getting the total more than 7
Options:
A)5/7
B)4/7
C)5/12
D)4/7
E)1/6
Rationale: Here n(S)=(6*6)=36
let E=event of getting a total more than 7
={(2,6),(3,5),(3,6),(4,4),(4,5),(4,6),(5,3),(5,4),(5,5),(5,6),(6,2),(6,3),(6,4),(6,5),(6,6)}
P(E)=n(E)/n(S)=15/36=5/12
Option C
Answer: C
Question: A can do half the work in one day where as B can do it full. B can also do half the work of C in one day. Ratio in their efficiency will be?
Options:
A)3:2:4
B)2:2:4
C)1:2:4
D)4:2:4
E)5:2:4
Rationale: c
1:2:4
WC of A: B = 1:2
B: C = 1:2
---------------------
A: B: C = 1:2:4
Answer: C
Question: If the wheel is 14 cm then the number of revolutions to cover a distance of 1056 cm is?
Options:
A)17
B)19
C)17
D)12
E)91
Rationale: 2 * 22/7 * 14 * x = 1056 => x
= 12
Answer: D
Answer: D
Question: Excluding stoppages, the speed of a train is 45 kmph and including stoppages it is 36 kmph. Of how many minutes does the train stop per hour?
Options:
A)16
B)17
C)12
D)16
E)16
Rationale: T = 9/45 * 60
12
Answer:C
Answer: C
Question: Machine X and machine B are each used to manufacture 660 sprockets. It takes machine X 10 hours longer to produce 660 sprockets than machine B. Machine B produces 10 percent more sprockets per hour than machine X. How many sprockets per hour does machine X produces?
Options:
A)6
B)6.6
C)60
D)100
E)110
Rationale: I think the correct answer is A.
Machine X produces at a speed of X sp/hour and B at a speed of B sp/hour.
so, 660/X=(660/B)+10 and X=1,1 X--->1,1*660=660+11X--->A=6, so answer A is correct
Answer: A
Question: Sujit incurred a loss of 45% on selling an article for Rs.3960/-. What was the cost price of the article?
Options:
A)Rs.5725/-
B)Rs.5080/-
C)Rs.7200/-
D)Rs.6750/-
E)None of these
Rationale: Explanation:
45% loss means SP of Rs.3960/- is 55% of CP
:. CP = 3960x100/55 = Rs.7200/-
Answer: Option C
Answer: C
Question: 10 men working 12 hours daily finish a work in 24 days. In how many days will they finish 1/4th of the work working 8 hours daily?
Options:
A)9 days
B)10 days
C)11 days
D)12 days
E)18 days
Rationale: The number of days needed to finish 1/4 of the work =1/4*12/8*24 =9 days. Answer : A
Answer: A
Question: What sum of money will produce Rs.75 as simple interest in 4 years at 3 1/2 percent?
Options:
A)337
B)500
C)266
D)288
E)536
Rationale: 75 = (P*4*7/2)/100
P = 536
Answer: E
Answer: E
Question: The present age of a father is 3 years more than three times the age of his son. Three years hence, father's age will be 10 years more than twice the age of the son. Find the present age of the father.
Options:
A)33
B)38
C)29
D)40
E)48
Rationale: if the present age be x years.
father's will be (3x+3)years..
so, (3x+3+3)=2(x+3)+10
or, x=10
so the fathers present age =(3x+3)=(3*10+3)years =33years..
ANSWER : OPTION A
Answer: A
Question: In a function they are distributing noble prize. In how many ways can 3 prizes be distributed among 4 boys when a boy gets any no. of prizes?
Options:
A)34
B)45
C)64
D)76
E)80
Rationale: Ans.(C)
Sol. In this case, repetitions are allowed, so all the three prizes can be given in 4 ways, i.e. (4 x 4 x 4) ways = 43 ways = 64 ways Or nr ways = 43 ways = 64 ways
Answer: C
Question: In an office, totally there are 6400 employees and 65% of the total employees are males. 25% of the males in the office are at-least 50 years old. Find the number of males aged below 50 years?
Options:
A)1040
B)2080
C)3120
D)4160
E)None of these
Rationale: Number of male employees = 6400 * 65/100 = 4160
Required number of male employees who are less than 50 years old = 4160 * (100 - 25)%
= 4160 * 75/100 = 3120.
ANSWER:C
Answer: C
Question: A reduction of 25% in the price of oil enables a house wife to obtain 5kgs more for Rs.800, what is the reduced price for kg?
Options:
A)40
B)60
C)70
D)80
E)20
Rationale: A
800*(25/100) = 200 ---- 5
? ---- 1 => Rs.40
Answer: A
Question: In a school with 5 classes, each class has 2 students less than the previous class. How many students are there in the largest class if the total number of students at school is 140?
Options:
A)28
B)29
C)30
D)31
E)32
Rationale: Let x be the number of students in the largest class.
Then x + (x-2) + (x-4) + (x-6) + (x-8) = 140
5x -20 = 140
5x = 160
x = 32
The answer is E.
Answer: E
Question: At a tanning salon, customers are charged $10 for their first visit in a calendar month and $8 for each visit after that in the same calendar month. In the last calendar month, 100 customers visited the salon, of which 30 made a second visit, and 10 made a third visit. All other customers made only one visit. If those visits were the only source of revenue for the salon, what was the revenue for the last calendar month at the salon?
Options:
A)$1220
B)$1240
C)$1300
D)$1340
E)$1880
Rationale: I get B. This question seems too straightforward for 600+. Am I missing something?
100 first-time visits --> 100(10) = $1000
30 + 10 = 40 subsequent visits --> 40(8) = $320
Total revenue: 1000+ 320 = $1320
The answer is B.
Answer: B
Question: A small company employs 3 men and 5 women. If a team of 4 employees is to be randomly selected to organize the company retreat, what is the probability R that the team will have exactly 2 women?
Options:
A)1/14
B)1/7
C)2/7
D)3/7
E)1/2
Rationale: 5C2 * 3C2 -> it gives combination of exactly 2 women and 2 men.
8C4 -> gives total possibilities of 4 people from 5 women and 3 men.
Probability = 5C2*3C2 / 8C4 = 3/7
SECOND METHOD:
Probability of two women -> 5/8 * 4/7.
probability of two men -> 3/6 * 2/5.
Probability: (5/8 * 4/7) * (3/6 * 2/5) = 1/14.
Answer: D
Question: What number is 70 more than one-fourth of itself?
Options:
A)93
B)225
C)288
D)324
E)336
Rationale: 1/4x+70= x
That means 70=3/4x
x= (70*4)/3= 280/3=93
A is the answer.
Answer: A
Question: 387 x 387 + 114 x 114 + 2 x 387 x 114 = ?
Options:
A)250001
B)251001
C)260101
D)261001
E)None of these
Rationale: Answer
Given expression = a2+b2+2ab = (a+b)2
where a = 387 and b = 114
= (387 + 114 )2
= (501)2
=(500 +1 )2
=(500)2 + (1)2+ 2 x 500 x 1
= 250000 + 1 +1000 = 251001.
Option: B
Answer: B
Question: A man misses a bus by 40 minutes if he travels at 30 kmph. If he travels at 40 kmph, then also he misses the bus by 10 minutes. What is the minimum speed required to catch the bus on time?
Options:
A)22
B)45
C)66
D)88
E)12
Rationale: Let the distance to be travelled to catch the bus be x km
x/30 - x/40 = 30/60 => (4x - 3x)/120 = 1/2 => x = 60 km
By traavelling 30 kmph time taken = 60/30 = 2 hours
By taking 2 hours, he is late by 40 min. So, he has to cover 60 km in at most speed = 60/(4/3) = 45 kmph.
Answer: B
Answer: B
Question: If m and n are positive integers of T such that m is a factor of n, how many positive multiples of m are less than or equal to 2n ?
Options:
A)2m/n + 1
B)2n/m + 1
C)2n/(m+1)
D)2m/n
E)2n/m
Rationale: Lets say N=10, M=5
2N=20. so the answer should be 4 (20/5)
lets try to plug in the answers:
A-not an integer
B-not an integer
C-not an integer
D-1 (not the answer)
E-4 - the answer. (the only one).
I would choose E.
Method 2
N=M*A (A is an integer)
So - A=N/M
therefore in 2N A will be 2N/M
Again - Answer is E.
Answer: E
Question: If the seventh day of a month is three days earlier than Friday, What day will it be on the nineteenth
day of the month?
Options:
A)Saturday
B)Monday
C)Sunday
D)Wednesday
E)None of these
Rationale: Explanation :
Given that seventh day of a month is three days earlier than Friday
=> Seventh day is Tuesday
=> 14th is Tuesday
=> 19th is Sunday
Answer : Option C
Answer: C