divelab/Sys2Bench huggingface dataset:
Question: If x and y are integer, which of the following must also be an integer?
I. xy
II. y
III. y/x
Options:
A)I alone
B)II alone
C)III alone
D)I and III
E)None of the above
Rationale: Let's take X = 4and Y = 3
Then X/Y = 4/3 Not an integer.
Y/X = 3/4 Not an integer.
Y alone is 3 which is an integer.
Hence B.
Answer: B
Question: Without any stoppage, a person travels a certain distance at an average speed of 42 km/h, and with stoppages he covers the same distance at an average speed of 28 km/h. How many minutes per hour does he stop?
Options:
A)30 minutes
B)28 minutes
C)11 minutes
D)17 minutes
E)20 minutes
Rationale: Let the total distance to be covered is 84 kms.
Time taken to cover the distance without stoppage = 84/42 hrs = 2 hrs
Time taken to cover the distance with stoppage = 84/28 = 3 hrs.
Thus, he takes 60 minutes to cover the same distance with stoppage.
Therefore, in 1 hour he stops for 20 minutes.
Answer: E
Answer: E
Question: Present ages of souju and tharak are in the ratio of 6:4 respectively. Three years hence, the ratio of their ages will become 12:9 respectively. What is tharak's present age in years?
Options:
A)2 years 7 months
B)3 years 2 months
C)3 years 5 months
D)3 years 7 months
E)4 years 7 months
Rationale: Ratio of the present age of souju and tharak =6:4
Let present age of Souju =6x
Present age of Tharak =4x
After 3 years, ratio of their ages =12:9
⇒(6x+3):(4x+3)=12:9
⇒9(6x+3)=12(4x+3)
⇒54x+27=44x+36
⇒10x=36−27=9
=>x=9/10=0.9
Tharak's present age =4x=4*0.9=3.6=3 years 7 months
ANSWER:D
Answer: D
Question: What is the smallest positive integer that can be multiplied by 1,008 to make it a perfect square?
Options:
A)2
B)3
C)5
D)7
E)11
Rationale: 1008 = 2^4 x 3^2 x 7.
Therefore the smallest integer to multiplied to 1008 to make it a perfect square is 7.
Answer D.
Answer: D
Question: Of the final grades received by the students in a certain math course, 1/5 are A's, 1/4 are B's, 1/2 are C's, and the remaining 25 grades are D's. What is the number of students in the course?
Options:
A) 80
B) 110
C) 160
D) 500
E) 400
Rationale: We start by creating a variable for the total number of students in the math course. We can say:
T = Total number of students in the math course
Next, we can use variable T in an equation that we translate from the given information. We are given that, of the final grades received by the students in a certain math course, 1/5 are A's, 1/4 are B's, 1/2 are C's, and the remaining 25 grades are D's. Since this represents all the grades in the class, it represents all the students in the class. Thus we know:
#A’s + #B’s + #C’s + #D’s = Total number of students in the class
1/5(T) + ¼(T) + ½(T) + 25 = T
We can multiply the entire equation by 20 to cancel out the denominators of the fractions and we have:
4T + 5T + 10T + 500 = 20T
19T + 500 = 20T
500 = T
There are a total of 500 students in the math class.
Answer is D.
Answer: D
Question: The probability of a lottery ticket being a prized ticket is 0.2. When 4 tickets are purchased, the probability of winning a prize on atleast one ticket is
Options:
A)0.5909
B)0.5904
C)0.59076
D)0.5907
E)0.59012
Rationale: P(winning prize atleast on one ticket)
= 1 - P("Losing on all tickets")
= 1 - (0.8)4 = (1 + (0.8)2)(1 - (0.8)2)
= (1.64)(0.36) = 0.5904
Answer: B
Answer: B
Question: There are 300 female managers in a certain company. Find the total number of female employees in the company, if 2/5 of all the employees are managers and 2/5 of all male employees are managers.
Options:
A)650
B)700
C)750
D)800
E)None of these
Rationale: as per question stem 2/5M (Portion of Men employees who are managers) + 200 (Portion of Female employees who are managers) = 2/5T (Portion of Total number of employees who are managers), thus we get that 2/5M+300= 2/5T, or 2/5(T-M)=300, from here we get that T-M=750, that would be total number of female employees and the answer (C)
Answer: C
Question: A car is running at a speed of 90 kmph. What distance will it cover in 15 second?
Options:
A)100 m
B)255 m
C)375 m
D)Cannot be determined
E)None of these
Rationale: Explanation:
Given : Speed = 108 kmph = (90 x (5/18)) m/sec = 25 m/sec
Distance covered in 15 second = (25 x 15) m = 375 m.
ANSWER: C
Answer: C
Question: Two years ago, Claire put $2,000 into a savings account. At the end of the first year, her account had accrued $100 in interest bringing her total balance to $2,100. The next year, her account balance increased by 10%. At the end of the two years, by what percent has Claire's account balance increased from her initial deposit of $2,000 ?
Options:
A)10%
B)12%
C)15.5%
D)17%
E)20%
Rationale: investment 2000 dollars
1 st year total gained = 100
total amount end of first year = 2100
second year account increased by 10 % = 2100*0.1 = 210
therefore total amount by second year end = 2310
so total percentage increase in money = (2310-2000)*100/2000 = 15.5 %
Correct Answer C=15.5%
Answer: C
Question: A train ride from Two P to Town Q costs $6.85 more than does a bus ride from Town P to Town Q. Together, the cost of one train ride and one bus ride is $9.65. What is the cost of a bus ride from Town P to Town Q?
Options:
A)$1.40
B)$2.50
C)$4.10
D)$4.70
E)$8.20
Rationale: Let x be the cost of a bus ride.
x + (x+685) = 965
2x = 280
x = $1.40
The answer is A.
Answer: A
Question: The sum of two numbers is 120. If the greater number is four times the less, what are the numbers?
Options:
A)80
B)84
C)85
D)96
E)None
Rationale: Let x = the less number
4x = the greater number
The sum of two numbers is 120
x+4x=120
5x=120
x=24
4x=96
Option D
Answer: D
Question: Find the length of a rope by which a cow must be tethered in order that it may be able to graze an area of 9856 sq meters.
Options:
A)56
B)28
C)99
D)27
E)19
Rationale: Explanation:
clearly the cow will graze a circular field of area 9856 sq m and
radius equal to the length of the rope.
Let the length of the rope be r mts
{\color{Black} then,\Pi r^{2}=9856\Rightarrow r^{2}=\frac{9856\times 7}{22}=3136\Rightarrow r=56m}
Answer: A) 56m
Answer: A
Question: Which of the following is a parallelogram?
Options:
A)120,50,120,50(angle in deg)
B)120,30,130,20(angle in deg)
C)90,90,90,90(angle in deg)
D)a & c
E)none
Rationale: sum of adjacent angles is 180 degrees.
ANSWER:C
Answer: C
Question: A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man?
Options:
A)5.78
B)5.79
C)5.76
D)5.74
E)5.721
Rationale: M = 6
S = 1.2
DS = 7.2
US = 4.8
x/7.2 + x/4.8 = 1
x = 2.88
D = 2.88 * 2 = 5.76.Answer: C
Answer: C
Question: What percent is 120 of 90?
Options:
A)133 1/3 %
B)134 1/3 %
C)135 1/3 %
D)140 1/3 %
E)143 1/3 %
Rationale: 120/90 = 4/3
4/3 × 100 = 400/3 = 133 1/3 %
A
Answer: A
Question: It takes Avery 2.5 hours to build a brick wall while Tom can do it in 5 hours. If the two start working together and after an hour Avery leaves, how much time will it take Tom to complete the wall on his own?
Options:
A)15 minutes.
B)30 minutes.
C)1 hour and 30 minutes.
D)1 hour and 40 minutes
E)2 hours
Rationale: Avery's efficiency is 100/2.5 = 40%
Tom's = 100/5= 20%
they worked together for 1 hour and finished 60 % of the job
remaining = 40 %
Tom will complete 20% in 60 minutes , 40% in 120 minutes
Time taken by Tom to finish the remaining on his own = 120 minutes
ANSWER:E
Answer: E
Question: The dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 7 per square feet if there is one door of dimensions 6 feet * 3 feet and three WINDOWS of dimensions 4 feet * 3 feet each?
Options:
A)4000
B)345
C)5673
D)6342
E)4566
Rationale: Area of the four walls = 2h(l + b)
Since there are doors and WINDOWS, area of the walls = 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3) = 906 sq.ft.
Total cost = 906 * 7 = Rs. 6342
Answer: Option D
Answer: D
Question: Calculate the distance covered by 420 revolutions of a wheel of radius 23.1 cm.
Options:
A)609.84 m
B)409.84 m
C)509.84 m
D)109.84 m
E)709.84 m
Rationale: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 500 resolutions.
= 420 * 2 * 22/7 * 23.1 = 60984 cm = 609.84 m
ANSWER:A
Answer: A
Question: Sawyer is mixing up a salad dressing. Regardless of the number of servings, the recipe requires that 5/8 of the finished dressing mix be peanut oil, 1/4 vinegar, and the remainder an even mixture of salt, pepper and sugar. If Sawyer accidentally doubles the vinegar and forgets the sugar altogether, what proportion of the botched dressing will be peanut oil?
Options:
A)15/29
B)5/8
C)5/16
D)1/2
E)13/27
Rationale: peanut oil = 5/8 = 15/24 --> 15 parts out of 24;
Vinegar = 1/4 = 6/24 --> 6 parts out of 24;
Salt + pepper + sugar = 1-(15/24+6/24)= 3/24, so each = 1/24 --> 1 part out of 24 each;
If vinegar = 12 (instead of 6) and sugar = 0 (instead of 1) then total = 15+12+1+1+0 = 29 parts out of which 15 parts are peanut oil --> proportion = 15/29.
Answer: A.
Answer: A
Question: A bag contains 50black pens and 60 white pens. One ball is drawn at random. What is the probability that the ball drawn is black?
Options:
A)2/3
B)3/14
C)1/7
D)5/11
E)6/13
Rationale: total number of pens = 110
number of black pens = 50
drawing a black pens= 50/110 = 5/11
Answer is D
Answer: D
Question: The ratio of the area of a square to that of the square drawn on its diagonal is?
Options:
A)1:2
B)2:4
C)3:5
D)4:6
E)5:7
Rationale: Explanation:
a^2:(a√2)^2
a^2 : 2a^2=1:2
Answer : A
Answer: A
Question: A committee of three people is to be chosen from 3 married couples. What is the number of different committees that can be chosen if two people who are married to each other cannot both serve on the committee?
Options:
A)12
B)24
C)26
D)30
E)32
Rationale: One of the approaches:
Each couple can send only onerepresentativeto the committee. Let's see in how many ways we can choose 2 couples (as there should be 2 members) out of 3 to send only onerepresentativesto the committee: 3C2=3.
But each of these 3 couples can send two persons (husband or wife): 2*2=2^2=4.
Total # of ways: 3C2*2^2=12.
Answer: A.
Answer: A
Question: A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that atleast one bulb is good.
Options:
A)60/63
B)125/126
C)1/126
D)8/178
E)9/191
Rationale: Explanation:
Required probability = 1 - 1/126 = 125/126
ANSWER B
Answer: B
Question: A circular mat with diameter 20 inches is placed on a square tabletop, each of whose sides is 30 inches long. Which of the following is closest to the fraction of the tabletop covered by the mat?
Options:
A)5/12
B)2/5
C)1/2
D)3/4
E)5/6
Rationale: It is a circle inscribed in a square.
Square side=24---> square(table) area=24^2
Circle diameter=20---> Circle area=PiR^2=100Pi (where Pi=~3.14)
covered fraction=100*3.14/9*100=3.14/9 = 0.3489
E
Answer: E
Question: If P(x) = ax^4+bx^3+cx^2+dx+e has roots at x = 1, 2, 3, 4 and P(0) = 48, what is P(5)?
Options:
A)48
B)24
C)0
D)50
E)40
Rationale: Roots are 1,2,3,4
So we can write this
equation As p(x)=
a(x-1)(x-2)(x-3)(x-4).....eq1
Put x=0here we p(0)=48=24a
TheN a=2
Now put a in eq1
And get the answer...
P(5)=a.4.3.2.1=48
ANSWER:A
Answer: A
Question: How many keystrokes are needed to type numbers from 1 to 1000?
Options:
A)3001
B)3001
C)2704
D)2890
E)None of these
Rationale: Explanatory Answer
While typing numbers from 1 to 1000, there are 9 single digit numbers: from 1 to 9.
Each of these numbers requires one keystroke.
That is 9 key strokes.
There are 90 two-digit numbers: from 10 to 99.
Each of these numbers requires 2 keystrokes.
Therefore, 180 keystrokes to type the 2-digit numbers.
There are 900 three-digit numbers: from 100 to 999.
Each of these numbers requires 3 keystrokes.
Therefore, 2700 keystrokes to type the 3-digit numbers.
1000 is a four-digit number which requires 4 keystrokes.
Totally, therefore, one requires 9 + 180 + 2700 + 4 = 2893 keystrokes.
Choice B is the correct answer.
Answer: B
Question: Look at this series: V, VIII, XI, XIV, __, XX, ... What number should fill the blank?
Options:
A)IX
B)XXIII
C)XV
D)XVII
E)None
Rationale: Explanation: This is a simple addition series; each number is 3 more than the previous number.
Answer: Option D
Answer: D
Question: If |x - 9| = 3x, then x=?
Options:
A)1.5
B)3.1
C)4.5
D)-2.25
E)-4.5
Rationale: |x - 9| = 3x ...(given)
x^2 - 18x + 81 = 9x^2
8*x^2 + 18*x - 81 = 0 ....(by solving above eq. we get) , x = -4.5 or 2.25 ===> Ans - E
Answer: E
Question: If two positive numbers are in the ratio 1/8 : 1/7, then by what percent is the second number more than the first?
Options:
A)70%
B)14.28%
C)60%
D)50%
E)65%
Rationale: Given ratio = 1/8 : 1/3 = 3 : 8
Let first number be 7x and the second number be 8x.
The second number is more than first number by 1x.
Required percentage = 1x/7x * 100 = 14.28%.
Answer:B
Answer: B
Question: A man saves 20% of his monthly salary. If an account of dearness of things he is to increase his monthly expenses by 20%, he is only able to save Rs. 200 per month. What is his monthly salary?
Options:
A)Rs.5000
B)Rs.4672
C)Rs.8262
D)Rs.2618
E)Rs.5267
Rationale: Income = Rs. 100
Expenditure = Rs. 80
Savings = Rs. 20
Present Expenditure 80*(20/100) = Rs. 96
Present Savings = 100 – 96 =Rs. 4
100 ------ 4
? --------- 200 => 5000
Answer:a
Answer: A
Question: How many different pairs of numbers (s, t) such that s = 3t can be obtained if s and t are selected from the set of number {3, 4, 5, 6, 7, 8, 9}
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: Given s=3t
t can take 3
and so s = 9
1 such pairs can be formed.
answer A
Answer: A
Question: A warehouse is labeling computer inventory with 3-digit codes. Each code is to consist of four digits between the numbers 0 and 8. The manager is debating whether to allow any 3-digit codes to have leading zero's before a non-zero number is used. If not allowed, then numbers like0025cannot be used.
The manager wants to measure the magnitude of the number of 3-digit code possibilities that are lost if he disallows the use of leading zero's. How many such codes would be lost?
Options:
A)981
B)1000
C)1011
D)1101
E)200
Rationale: The number of codes possible if leading zero is allowed = 10*10*10=10^3
The number of codes possible if leading zero is NOT allowed = 8*10*10=9*10^2
The difference = 10^3 - 8*10^2 = 10^2(10-8) = 2*10^2.
Answer: E.
Similar questions to practice:
Hope it helps.
Answer: E
Question: find two integers, neither of which ends in a zero, and whose product is exactly 1,00,000
Options:
A)64 and 15,625
B)32 and 3,125
C)64 and 15,620
D)64 and 15,635
E)64 and 16,625
Rationale: 1,00,000=10^5
=10x10x10x10x10
=(2x5)x(2x5)x(2x5)x(2x5)x(2x5)
=(2^5)x(5^5)
= 32x3125
so the numbers are 32 and 3,125
ANSWER:B
Answer: B
Question: Calculate how many ways a woman who has 2 bags and 4 books can put the books in her bag?
Options:
A)12
B)15
C)19
D)17
E)16
Rationale: First paper can be put in 2 ways, similarly second, third and forth books also can be put in 2 ways.
So total number of ways = 2 x 2 x 2 x 2 = 16
E
Answer: E
Question: How many points (x, y) lie on the line segment between (22, 12 2/3) and (16, 17 2/3) such that x and y are both integers?
Options:
A)1
B)5
C)7
D)8
E)9
Rationale: slope = (17 2/3 - 12 2/3) / (16 - 22) = -5/6
y = mx + b => 12 2/3 = -22*5/6 + b => b = 31
y = -5x/6 + 31
Only integer values work, and the only multiples of 6 between 16 and 22 for x values is 18, thus 1 point.
A
Answer: A
Question: When 12 is divided by the positive integer k, the remainder is 7, for how many different values of k is this true?
Options:
A)2
B)3
C)4
D)7
E)8
Rationale: When 20 is divided by k, remainder is 2 i.e. there are 2 balls leftover after grouping. so k must be greater than 2.
It also means that 18 is completely divisible by k.
Factors of 18 are 1, 2, 3, 6, 9, 18
Out of these, k can be 3, 6, 9 and 18.
Answer (C)
Answer: C
Question: On Sunday, Bill ran 4 more miles than he ran on Saturday. Julia did not run on Saturday, but she ran twice the number of miles on Sunday that Bill ran on Sunday. If Bill and Julia ran a total of 20 miles on Saturday and Sunday, how many miles did Bill run on Sunday?
Options:
A)5
B)6
C)7
D)8
E)9
Rationale: Let Bill run x on saturday, so he will run x+4 on sunday..
Julia will run 2*(x+4) on sunday..
totai= x+x+4+2x+8=20..
4x+12=20..
x=2..
ans =x+4=2+4=6
Answer B
Answer: B
Question: A worm is at the bottom of a forty foot hole. It can crawl upwards at the rate of four feet in one day, but at night, it slips back three feet. At this rate, how long will it take the worm to crawl out of the hole?
Options:
A)33
B)87
C)37
D)28
E)921
Rationale: Explanation:
For each day worm climb only 4 - 3 = 1feet.
After 36 days worm reach the 36 foot.
Exactly the 37th day worm reach 40 foot and won't slips back.
Answer: C
Answer: C
Question: A dishonest dealer professes to sell his goods at Cost Price but still gets 20% profit by using a false weight. What weight does he substitute for a kilogram?
Options:
A)833 1/7
B)833 1/3
C)833 1/2
D)833 1/9
E)833 1/5
Rationale: If the cost price is Rs.100, then to get a profit of 20%, the selling price should be Rs.120.
If 120kg are to be sold, and the dealer gives only 100kg, to get a profit of 20%.
How many grams he has to give instead of one kilogram(1000 gm).
120 gm ------ 100 gm
1000 gm ------ ?
(1000 * 100)/120 = 2500/3 = 833 1/3 grams.
Answer: B
Answer: B
Question: You buy a piece of land with an area of √900, how long is one side of the land plot?
Options:
A)28
B)29
C)30
D)31
E)32
Rationale: Try filling the numbers into the answer y x y =
Find the closest to 900.
Answer C
Answer: C
Question: By selling 12 pencils for a rupee a man loses 20%. How many for a rupee should he sell in order to gain 20%?
Options:
A)8
B)9
C)7
D)66
E)2
Rationale: 80% --- 12
120% --- ?
80/120 * 12 = 8
Answer:A
Answer: A
Question: Of the 14 members of a dancing group,10 can perform modern dancing, 8 can perform traditional dancing, and 4 can perform both type of dancing. If one member is chosen at random, what is the probability that the member chosen will be someone who can not perform neither type of dancing?
Options:
A)a) 1/5
B)b) 1/10
C)c) 1/7
D)d) 1/4
E)e) 0
Rationale: You know how to solve for Total number of people who can perform at least one type of dancing:
Total = n(A) + n(B) - n(A and B)
Total people who can use at least one machine = 10 + 8 - 4 = 14
So all 14 people know how to perform at least one type of dancing. Hence, if you pick anyone, the probability is 0 that he/she wouldn't know how to perform any type of dancing
Answer (E)
Answer: E
Question: A 20 litre mixture of milk and water contains milk and water in the ratio 3 : 2. 10 litres of the mixture is removed and replaced with pure milk and the operation is repeated once more. At the end of the two removal and replacement, what is the ratio R of milk and water in the resultant mixture?
Options:
A)17 : 3
B)9 : 1
C)3 : 17
D)5 : 3
E)11: 2
Rationale: he 20 litre mixture contains milk and water in the ratio of 3 : 2. Therefore, there will be 12 litres of milk in the mixture and 8 litres of water in the mixture.
Step 1.
When 10 litres of the mixture is removed, 6 litres of milk is removed and 4 litres of water is removed. Therefore, there will be 6 litres of milk and 4 litres of water left in the container. It is then replaced with pure milk of 10 litres. Now the container will have 16 litres of milk and 4 litres of water.
Step 2.
When 10 litres of the new mixture is removed, 8 litres of milk and 2 litres of water is removed. The container will have 8 litres of milk and 2 litres of water in it. Now 10 litres of pure milk is added. Therefore, the container will have 18 litres of milk and 2 litres of water in it at the end of the second step. Therefore, the ratio of milk and water is 18 : 2 or 9 : 1.
Shortcut.
We are essentially replacing water in the mixture with pure milk.
Let W_o be the amount of water in the mixture originally = 8 litres.
Let W_r be the amount of water in the mixture after the replacements have taken place.
Then,{W_r}/{W_o}= (1-R/M)^n
where R is the amount of the mixture replaced by milk in each of the steps, M is the total volume of the mixture and n is the number of times the cycle is repeated.
Hence, {W_r}/{W_o} =(1/2)^2  =1/4
Therefore R,W_r ={W_o}/4= 8/4 = 2 litres.B
Answer: B
Question: The price of 3 pens and 6 pencils is Rs. 1500. With the same money one can buy 1 pen and 12 pencils. If one wants to buy 23 pencils, how much shall he have to pay ?
Options:
A)2400
B)2300
C)2200
D)2100
E)2000
Rationale: Let the price of a pen and a pencil be Rs. x and Rs. y respectively.
Then, 3x + 6y = 1500 .... (i)
and x + 12y = 1500 .... (ii)
Divide equation (i) by 3, we get the below equation.
= x + 2y = 500. --- (iii)
Now subtract (iii) from (ii)
x + 12y = 1500 (-)
x + 2y = 500
----------------
10y = 1000
----------------
y = 100
cost of 23 pencils = 23*100 = 2300
Answer : B
Answer: B
Question: The letters in the word "PLACES" are permuted in all possible ways and arranged in the alphabetical order.Find the word at 48 position.
Options:
A)AESPCL
B)ALCEPS
C)ALSCEP
D)AESPLC
E)AESPLD
Rationale: for words AC**** possible ways for arranging * will be 4!=24
now next seq in alphabatical order will be AE**** so....
same way for AE**** possible ways for arranging * will be 4!=24
..
..
Thus, 48th element will be last element in AE**** that means AE followd by reverse alphabatical order! which is AESPLC
ANSWER:D
Answer: D
Question: In some quantity of alcohol, 50% of pure alcohol and 30% of is water. If 20liters of pure alcohol is added, then the strength of alcohol solution becomes 20%. The original quantity was?
Options:
A)1.42liters
B)2.5liters
C)3liters
D)5.6liters
E)7liters
Rationale: Let the original quantity be x liters
alcohol solution in x liters = 30/100 *x = 3x/10 kg
(3x/10)/(x+20) = 20/100
3x = x/5 + 4
14x = 20
x = 1.42liters
Answer is A
Answer: A
Question: Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?
Options:
A)24000
B)25100
C)25150
D)25200
E)25400
Rationale: Explanation:
Number of ways of selecting 3 consonants from 7
= 7C3
Number of ways of selecting 2 vowels from 4
= 4C2
Number of ways of selecting 3 consonants from 7 and 2 vowels from 4
= 7C3 × 4C2
=
(
7
×
6
×
5
3
×
2
×
1
)
×
(
4
×
3
2
×
1
)
=
210
=(7×6×53×2×1)×(4×32×1)=210
It means we can have 210 groups where each group contains total 5 letters (3 consonants and 2 vowels).
Number of ways of arranging 5 letters among themselves
=
5
!
=
5
×
4
×
3
×
2
×
1
=
120
=5!=5×4×3×2×1=120
Hence, required number of ways
=
210
×
120
=
25200
D)
Answer: D
Question: f(x) is defined as the largest integer n such that x is divisible by 2^n. Which of the following numbers is the biggest?
Options:
A)f(24)
B)f(42)
C)f(62)
D)f(76)
E)f(84)
Rationale: So, we have an integer x. It has some power of 2 in its prime factorization (2^n) and f(x) is the value of that n. Basically f(x) is the power of 2 in prime factorization of x.
For example, if x is say 40, then f(x)=3. Why? Because the largest integer n such that 40 is divisible by 2^n is 3: 40/2^3=5, or 40=2^3*5 --> the power of 2 in prime factorization of 40 is 3.
Hence all we need to do to answer the question is to factorize all options and see which one has 2 in highest power.
A. f(24) --> 24 = 2^3*3
B. f(42) --> 42 = 2*21
C. f(62) --> 62 = 2*31
D. f(76) --> 76 = 2^2*19
E. f(84) --> 84 = 2^2*21
Answer: A.
Answer: A
Question: In a certain series, each term is m greater than the previous term. If the 16th term is 660 and the 13th term is 600, what is the first term?
Options:
A)120
B)180
C)360
D)300
E)360
Rationale: a + 15m = 660 (16th term)
a + 12m = 600 (13th term)
You get a = 360 and m = 20
Answer:C
Answer: C
Question: 0.40 represents what percent of 0.008?
Options:
A)0.05%
B)0.5%
C)5%
D)500%
E)5000%
Rationale: One more method
0.40 represents what percent of 0.008?
Adjusting the decimal
400 represents what percent of 8?
Divide by 8
50 represents what percent of 1?
Answer = 50*100 = 5000% = E
Answer: E