divelab/Sys2Bench huggingface dataset:
Question: 90 percent of the members of a study group are women, and 60 percent of those women are lawyers. If one member of the study group is to be selected at random, what is the probability that the member selected is a woman lawyer?
Options:
A)0.34
B)0.44
C)0.54
D)0.64
E)0.74
Rationale: Say there are 100 people in that group, then there would be 0.9*0.60*100=54 women lawyers, which means that the probability that the member selected is a woman lawyer is favorable/total=54/100.
Answer: C
Answer: C
Question: In a group of 5 boys and 5 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be selected?
Options:
A)100
B)110
C)179
D)205
E)219
Rationale: Number of ways to select four children is 10C4 = 210
Number of ways to choose only girls is 5C4 = 5
Number of ways that at least one boy is selected is 210 - 5 = 205
The answer is D.
Answer: D
Question: Ms. Lopez deposits $ 140 in an account that pays 20% interest, compounded semiannually. How much money will there be in the account at the end of one year?
Options:
A)$118.00
B)$120.00
C)$169.40
D)$122.00
E)$140.00
Rationale: Using Formula - A = P(1+r/n)^nt
Given
P=140
n=2
t=1
r=0.2
Substituting value in formula
A = 140(1+0.2/2)^2
A= 169.40$=C
Answer: C
Question: Two vessels P and Q contain 62.5% and 87.5% of alcohol respectively. If 2 litres from vessel P is mixed with 4 litres from vessel Q, the ratio of alcohol and water in the resulting mixture is?
Options:
A)19:1
B)19:4
C)19:8
D)19:5
E)19:2
Rationale: Quantity of alcohol in vessel P = 62.5/100 * 2 = 5/4 litres
Quantity of alcohol in vessel Q = 87.5/100 * 4 = 7/2 litres
Quantity of alcohol in the mixture formed = 5/4 + 7/2 = 19/4 = 4.75 litres
As 6 litres of mixture is formed, ratio of alcohol and water in the mixture formed
= 4.75 : 1.25 = 19:5.
Answer: D
Answer: D
Question: Three candidates contested an election and received 1136, 7636 and 11628 votes respectively. What percentage of the total votes did the winning candidate get?
Options:
A)45%
B)57%
C)34%
D)90%
E)49%
Rationale: B
57%
Total number of votes polled = (1136 + 7636 + 11628) = 20400.
Required percentage = (11628/20400 x 100)% = 57%.
Answer: B
Question: How many numbers between 100 and 630 are divisible by 2, 3, and 7 together?
Options:
A)112
B)77
C)267
D)13
E)99
Rationale: Explanation:
As the division is by 2, 3, 7 together, the numbers are to be divisible by: 2*3*7 = 42
The limits are 100 and 600
The first number divisible is 42*3 = 126
To find out the last number divisible by 42 within 630:
630/42 = 13
Hence, 42*15 = 630 is the last number divisible by 42 within 630
Hence, total numbers divisible by 2, 3, 7 together are (15 â€“ 2) = 13
ANSWER: D
Answer: D
Question: Jack and Jill collect ladybugs. Jack only collects the ones with 2 spots,
and Jill only collects the ones with 7 spots. Jack has 5 more ladybugs
than Jill. The total number of spots found on all of their ladybugs is 100.
How many ladybugs do they have in their combined collection?
Options:
A)17
B)21
C)23
D)25
E)35
Rationale: If x is the number of ladybugs that Jack has and y is the number of ladybugs that Jill has, then
x − y = 5 and 2x + 7y = 100. Multiplying the first of these equations by 5 and the second by 2
and adding gives 9(x + y) = 225. Hence, x + y = 25.
correct answer D
Answer: D
Question: Two persons A and B can complete a piece of work in 30 days and 60 days respectively. If they work together, what part of the work will be completed in 10 days?
Options:
A)1/8
B)1/3
C)1/6
D)1/2
E)5/3
Rationale: A's one day's work = 1/30
B's one day's work = 1/60
(A + B)'s one day's work = 1/30 + 1/60 = 1/20
The part of the work completed in 10 days = 10 (1/20) = 1/2.
Answer:D
Answer: D
Question: A discount electronics store normally sells all merchandise at a discount of 10 percent to 30 percent off the suggested retail price. If, during a special sale, an additional 20 percent were to be deducted from the discount price, what would be the lowest possible price of an item costing $200 before any discount?
Options:
A) $112.00
B) $145.60
C) $163.80
D) $182.00
E) $100.00
Rationale: Since the question is essentially just about multiplication, you can do the various mathstepsin a variety of ways (depending on whichever method you find easiest).
We're told that the first discount is 10% to 30%, inclusive. We're told that the next discount is 20% off of the DISCOUNTED price....
We're told to MAXIMIZE the discount (thus, 30% off the original price and then 20% off of the discounted price). Thatmathcan be written in a number of different ways (fractions, decimals, etc.):
30% off = (1 - .3) = (1 - 30/100) = (.7) and the same can be done with the 20% additional discount...
The final price of an item that originally cost $200 would be.....
($200)(.7)(.8) =
($200)(.56)=112
Final Answer:
A
Answer: A
Question: If Sharon's weekly salary increased by 16 percent, she would earn $348 per week. If instead, her weekly salary were to increase by 15 percent, how much would she earn per week?
Options:
A) $374
B) $382
C) $345
D) $392
E) $399
Rationale: (348/116)115 =345
In this case long division does not take much time.
(348/116)=3
3*115=345(300+45)
Answer C
Answer: C
Question: If a * b = a + b/ab , find the value of 5 * (5 * -2) :
Options:
A)-3
B)-10
C)-1.66
D)3/5
E)-12
Rationale: (5 * -2) = (5 x (-2))/(5 + (-2)) = -10/3
So, 5 * (5 * -2) = 5 * (-10/3) = (5 * (-10/3))/(5 + (-10/3))
= (-50/3) * (3/5)
= -10.
ANSWER:B
Answer: B
Question: If x>y>0, which of the following must be true:
I. x^2>y^2
II. x^3 > y^3
III. x<y
Options:
A)I and II
B)II only
C)III only
D)II and III
E)I, II and III
Rationale: Assuming x and y to be integers
X=3,Y=2
X^2=3^2=9
Y^2=2^2=4
So I is true
Now lets look at option III because if option 3 is true E is the answer or else A
As per question X>Y>0 Hence |X| >Y
So OA=A
Answer: A
Question: If a is a positive integer, then 2^a + 2^(a + 1)+ 2^(a + 2)+ 2^(a + 3)+ 2^(a + 4) =
Options:
A)3^(a + 1)
B)2^(a + 1)
C)2a
D)2a^(a + 1)
E)31(2^a)
Rationale: If a is a positive integer, then 2^a + 2^(a + 1)+ 2^(a + 2)+ 2^(a + 3)+ 2^(a + 4) =
2^a(1+2+4+8+16)
2^a(31)
E. 31(2^a)
Answer: E
Question: X and Y can do a piece of work in 20 days and 12 days respectively. X started the work alone and then after 4 days Y joined him till the completion of the work. How long did the work last?
Options:
A)5 days
B)10 days
C)11 days
D)20 days
E)25 days
Rationale: Work done by X in 4 days =1/20	x 4 = 1/5
Remaining work = (1 -1/5) = 4/5
(X + Y)'s 1 day's work = 1/20+1/12 = 8/60 = 2/15
Now,	2/15 work is done by X and Y in 1 day.
So,4/5work will be done by X and Y in	15/2	x 4/5= 6 days.
Hence, total time taken = (6 + 4) days = 10 days.
ANSWER:B
Answer: B
Question: Krishan and Nandan jointly started a business. Krishan invested three times as Nandan did and invested his money for double time as compared to Nandan. Nandan earned Rs. 4000. If the gain is proportional to the money invested and the time for which the money is invested then the total gain was?
Options:
A)28,029
B)28,199
C)28,299
D)28,000
E)28,029
Rationale: Explanation:
3:1
2:1
------
6:1
1 ----- 4000
7 ----- ? => Rs.28,000
Answer: D
Answer: D
Question: A reduction in the price of petrol by 10% enables a motorist to buy 5 gallons more for $200. Find the original price of petrol?
Options:
A)$11
B)$5
C)$45
D)$400
E)$4.4
Rationale: Price decreased by 10%, so 9/10 times, which means that original gallons bought increased 10/9 times. Since this increase equals to 5 gallons then 45 gallons were bought originally (45*10/9=50 --> increase 5 gallons). Hence original price was 200/45=$4.4
Answer: E.
Answer: E
Question: What is the units digit of 23^3 * 17^2 * 39^2?
Options:
A)9
B)7
C)5
D)3
E)1
Rationale: The units digit of 23^3 is the units digit of 3*3*3 = 27 which is 7.
The units digit of 17^2 is the units digit of 7*7 = 49 which is 9.
The units digit of 39^2 is the units digit of 9*9 = 81 which is 1.
The units digit of 7*9*1 = 63 is 3.
The answer is D.
Answer: D
Question: Find the odd man out. 362, 482, 551, 263, 344, 284
Options:
A)362
B)482
C)551
D)344
E)284
Rationale: Explanation :
In all numbers except 344, the product of first and third digits is the middle digit.
Answer : Option D
Answer: D
Question: The ratio, by weight, of coffee to sugar to water in a pot of coffee is 3:1:15. The ratio is then altered so that the ratio of coffee to sugar is halved while the ratio of coffee to water is doubled. If the altered pot of coffee contains 12 grams of sugar, how many grams of water does it contain after alteration?
Options:
A)35
B)40
C)45
D)50
E)55
Rationale: The new ratio of coffee to sugar is 1.5:1
The new ratio of coffee to water is 6:15.
The new ratio of coffee to sugar to water is 6:4:15.
If there are 12 grams of sugar, then there are (15/4)*12=45 grams of water.
The answer is C.
Answer: C
Question: In a group of 27 junior high school students, 7 take French, 10 take Spanish, and 4 take both languages. The students taking both French and Spanish are not counted with the 7 taking French or the 10 taking Spanish. How many students are not taking either French or Spanish?
Options:
A)7
B)6
C)9
D)4
E)6
Rationale: A
7
Add 7 + 10 + 4 to get 21.
Then subtract 21 from the total students ⇒ 27 – 21 = 6.
Answer is E
Answer: E
Question: In a certain game of dice, the player’s score is determined as a sum of four throws of a single die. The player with the highest score wins the round. If more than one player has the highest score, the winnings of the round are divided equally among these players. If Jim plays this game against 26 other players, what is the probability of the minimum score that will guarantee Jim some monetary payoff?
Options:
A)41/50
B)1/221
C)1/1296
D)1/84
E)1/42
Rationale: Toguaranteethat Jim will get some monetary payoff he must score the maximum score of 6+6+6+6=24, because if he gets even one less than that so 23, someone can get 24 and Jim will get nothing.
P(24)=1/6^4=1/1296.
Answer: C.
Answer: C
Question: If each side of a square is increased by 25%, find the percentage change in its area?
Options:
A)28.88
B)56.25
C)22.89
D)29.18
E)21.21
Rationale: let each side of the square be a , then area = a x a
As given that The side is increased by 25%, then
New side = =
New area =
increased area=
Increase %= % = 56.25%
Answer: B
Answer: B
Question: A piece of work can be done by 6 men and 5 women in 6 days or 3 men and 4 women in 10 days. It can be done by 9 men and 15 women in how many days ?
Options:
A)3 days
B)4 days
C)5 days
D)6 days
E)7 days
Rationale: Explanation:
To calculate the answer we need to get 1 man per day work and 1 woman per day work.
Let 1 man 1 day work =x
and 1 woman 1 days work = y.
=> 6x+5y = 1/6
and 3x+4y = 1/10
On solving, we get x = 1/54 and y = 1/90
(9 men + 15 women)'s 1 days work =
(9/54) + (15/90) = 1/3
9 men and 15 women will finish the work in 3 days
Option A
Answer: A
Question: Machine E and machine B are each used to manufacture 660 sprockets. It takes machine E 10 hours longer to produce 660 sprockets than machine B. Machine B produces 10 percent more sprockets per hour than machine E. How many sprockets per hour does machine E produces?
Options:
A)6
B)6.6
C)60
D)100
E)110
Rationale: I think the correct answer is A.
Machine E produces at a speed of E sp/hour and B at a speed of B sp/hour.
so, 660/E=(660/B)+10 and E=1,1 E--->1,1*660=660+11E--->A=6, so answer A is correct
Answer: A
Question: A three-digit code for certain locks uses the digits 0, 1, 2, 3, 4, 5, 6, 7 according to the following constraints. The first digit cannot be 0 or 1, the second digit must be 0 or 1, and the second and third digits cannot both be 0 in the same code. How many different codes are possible?
Options:
A)144
B)152
C)90
D)168
E)176
Rationale: The first digit can be filled in 6 ways
For second digit , it can either be 0 or 1
Case 1 -
If second digit is 1 ,Third digit can take 8 values
number of codes = 6 * 1 * 8 = 48
Case 2 -
If second digit is 0,Third digit can take 7 values ( Third digit can't be zero)
number of codes = 6 * 1 * 7= 42
Total number of codes = 90
Answer C
Answer: C
Question: A basket has 5 apples and 4 oranges. Three fruits are picked at random. The probability that at least 2 apples are picked is -.
Options:
A)25/42
B)9/20
C)10/23
D)41/42
E)1/42
Rationale: Total fruits = 9
Since there must be at least two apples,
(⁵C₂ * ⁴C₁)/⁹C₃ + ⁵C₃/⁹C₃ = 25/42.
ANSWER:A
Answer: A
Question: Bilal and Ahmed play the following game with n sticks on a table. Each must remove 1,2,3,4, or 5 sticks at a time on alternate turns, and no stick that is removed is put back on the table. The one who removes the last stick (or sticks) from the table wins. If Bilal goes first, which of the following is a value of n such that Ahmed can always win no matter how Bilal plays?
Options:
A)7
B)10
C)11
D)12
E)16
Rationale: If the number of sticks on a table is a multiple of 6, then the second player will win in any case (well if the player is smart enough).
Consider n=6, no matter how many stick will be removed by the first player (1, 2, 3 ,4 or 5), the rest (5, 4, 3, 2, or 1) can be removed by the second one.
The same for n=12: no matter how many sticks will be removed by the first player 1, 2, 3 ,4 or 5, the second one can remove 5, 4, 3, 2, or 1 so that to leave 6 sticks on the table and we are back to the case we discussed above.
Answer: D.
Answer: D
Question: There are five different models that are to appear in a fashion show. Two are from Europe, two are from South America, and two are from North America. If all the models from the same continent are to stand next to each other, how many ways can the fashion show organizer arrange the models?
Options:
A)96
B)48
C)64
D)24
E)8
Rationale: Since we have 3 continental pairs (EU, SA, NA), these 3 pairs have 3*2*1 = 6 Combinations. Within each pair, you have however 2 different ways to put them together for each of the pair (2*2*2*2= 16). So we have 6*16 =96.
Please correct me if im wrong.
Answer A.
Answer: A
Question: 81, 64, 27, 16...
Options:
A)12
B)4
C)9
D)3
E)1
Rationale: 81/3 = 27
64/4 = 16
27/3 = 9
ANSWER: C
Answer: C
Question: The Arnolds purchased 550 square feet of Kentucky Gem sod at $1.99 per square foot and 270 square feet of Zelzea Blue sod at $1.38 per square foot. What was the approximate average price per square foot paid for all the sod?
Options:
A)$1.63
B)$1.64
C)$1.68
D)$1.72
E)$1.79
Rationale: Average price = (550*1.99)+(270*1.38)/550+270=1.79 (Approx)
Answer E
Answer: E
Question: A jogger running at 9 km/hr along side a railway track is 240 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?
Options:
A)2 sec
B)12 sec
C)24 sec
D)50 sec
E)36 sec
Rationale: Explanation:
Speed of train relative to jogger = 45 - 9 = 36 km/hr.
= 36 * 5/18 = 10 m/sec.
Distance to be covered = 240 + 120 = 360 m.
Time taken = 360/10 = 36 sec.
Answer:E
Answer: E
Question: Marginal cost is the cost of increasing the quantity produced (or purchased) by one unit. If the fixed cost for n products is $12,000 and the marginal cost is $200, and the total cost is $16,000, what is the value of n?
Options:
A) 20
B) 50
C) 60
D) 80
E) 100
Rationale: Total cost for n products = fixed cost for n products + n*marginal cost --> $16,000 = $12,000 + n * $200 --> n = 20.
Answer: A.
Answer: A
Question: A train 125 m long passes a man, running at 8 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is?
Options:
A)53
B)50
C)60
D)79
E)80
Rationale: Speed of the train relative to man = 125/10 = 25/2 m/sec.
= 25/2 * 18/5 = 45 km/hr
Let the speed of the train be x km/hr. Then, relative speed = (x - 8) km/hr.
x - 8 = 45 => x = 53 km/hr.
Answer: Option A
Answer: A
Question: A shop owner sells 110 eraser and gains SP of 22 metres. Find the gain %?
Options:
A)25%
B)35%
C)27%
D)23%
E)32%
Rationale: Gain=22 orangesTotal 110 orangesCP 110-22=88(22/88)*100=25%Ans A
Answer: A
Question: What number is 75 more than three-fourth of itself?
Options:
A)138
B)225
C)300
D)324
E)336
Rationale: 3/4x+75= x
That means 75=1/4x
x= 75*4= 300
C is the answer
Answer: C
Question: The cash difference between the selling prices of an article at a profit of 4% and 6% is Rs 3. The ratio of two selling prices is
Options:
A)51:52
B)52:53
C)53:54
D)54:55
E)None of these
Rationale: Explanation:
Let the Cost price of article is Rs. x
Required ratio =
104% of x/ 106% of x
=104/106=52/53=52:53
Option B
Answer: B
Question: If c and d are both negative and cd < d^2, which of the following must be true?
Options:
A)c < d < c^2 < d^2
B)c < d < d^2 < c^2
C)d < c < c^2 < d^2
D)c^2 < d^2 < d < c
E)d^2 < c^2 < d < c
Rationale: Because cd <d^2 and both are negative, I thought c < d. So I crossed off answers c), d), and e).
And because c < d , c^2 < d^2
ans C
Answer: C
Question: The ages of Ashley and Mary are in the ratio 4:7. The sum of their ages is 22. Find the age of Mary.
Options:
A)11yrs
B)12yrs
C)13yrs
D)14yrs
E)15yrs
Rationale: a:m=4:7
let the ages of a & m be x &22-x
x/22-x=4/7
x=8
a=8yrs
m=14yrs
ANSWER:D
Answer: D
Question: How much time will take for an amount of Rs. 400 to yield Rs. 81 as interest at 4.5% per annum of simple interest?
Options:
A)4 1/2 years
B)6 1/2years
C)7 1/2years
D)12 1/2years
E)15 1/2years
Rationale: Time = (100 * 81) / (400 * 4.5) = 4 1/2years
ANSWER:A
Answer: A
Question: After replacing an old member by a new member, it was found that the average age of five numbers of a club is the same as it was 3 years ago. What is the difference between the ages of the replaced and the new member?
Options:
A)2 years
B)4 years
C)8 years
D)15 years
E)NOne
Rationale: Sol.
Age decrease = (5 × 3) years = 15 years.
So, the required difference = 15 years.
Answer D
Answer: D
Question: Tough and Tricky questions: Functions. Let a be a positive integer. Let n#a equal n^(2a) if a is odd and n^(3a) if a is even. Then (2#3) + (2#3) – (3#3) is equal to
Options:
A)64
B)82
C)128
D)729
E)1522
Rationale: Answer:
3^6 + 3^6 - 3^6 = 3^6 = 729
ANs D
Answer: D
Question: What is the area of a square field whose diagonal of length 20 m?
Options:
A)300 sq m
B)250 sq m
C)200 sq m
D)400 sq m
E)800 sq m
Rationale: d2/2 = (20 * 20)/2 = 200
ANSWER:C
Answer: C
Question: In an election only two candidates contested. A candidate secured 70% of the valid votes and won by a majority of 172 votes. Find the total number of valid votes?
Options:
A)430
B)570
C)480
D)520
E)550
Rationale: Let the total number of valid votes be x.
70% of x = 70/100 * x = 7x/10
Number of votes secured by the other candidate = x - 7x/100 = 3x/10
Given, 7x/10 - 3x/10 = 172 => 4x/10 = 172
=> 4x = 1720 => x = 430.
ANSWER:A
Answer: A
Question: If a * b * c =(√(a + 2)(b + 3)) / (c + 1), find the value of 6 * 15 * 1.
Options:
A)8
B)5
C)2
D)3
E)4
Rationale: 6 * 15 * 1 = (√(6 + 2)(15 + 3) )/ (1 + 1)
= (√8 * 18) / 2
= (√144) / 2
= 12 / 6 = 2
Answer is C.
Answer: C
Question: A certain school implemented a reading program for its students, with the goal of getting each student to read 6 books per month year-round. If the school has c classes made up of s students in each class, how many books will the entire student body read in one year?
Options:
A)20cs
B)cs/2
C)72cs
D)(2cs)/12
E)(24c)/s
Rationale: Ans: C
Solution: simple multiplication s students , c classes , 6 books/ month= 72 books a year
total number of books = 72cs
Answer: C
Question: Circular gears L and R start to rotate at the same time at the same rate. Gear L makes 20 complete revolutions per minute and gear R makes 40 revolutions per minute. How many seconds after the gears start to rotate will gear R have made exactly 6 more revolutions than gear L?
Options:
A)a) 6
B)b) 8
C)c) 10
D)d) 12
E)e) 15
Rationale: Gear L -- 20 rotations per 60 seconds -- 2 rotation per 6 seconds.
Gear R -- 40 rotations per 60 seconds -- 4 rotations per 6 seconds.
First 6 seconds -- Gear L makes 1 rotation. -- Gear R makes 4 rotations -- Net difference -- 2 rotations
Hence every 6 seconds the difference between the number of rotations of R and L gear is 2 units.
Required net difference should be 6 rotations => 3 (6 seconds later) ==> 18 seconds.
Answer: A
Answer: A
Question: In one hour, a boat goes 11 km along the stream and 3 km against the stream. the sped of the boat in still water (in km/hr) is :
Options:
A)3
B)5
C)7
D)9
E)10
Rationale: Solution
Speed in still water= 1/2(11+3) km/hr= 7kmph. Answer C
Answer: C
Question: Given that X and Y are events such that
Z(X)= 0.02
Z(Y)=0.10
Z(XnY)=0.10
Z(X|Y)=
find Z (X|Y) and Z(X|Y)
Options:
A)1/5
B)1/6
C)1/6
D)1/4
E)1/2
Rationale: Here, X and Y are events
Z(X|Y) = Z(XnY)/Z(Y) = 0.10/0.10= 1
Q(G|H) = Z(XnY)/Z(X) = 0.4/0.02 = 1/5
Answer is A
Answer: A
Question: Patrick purchased 80 pencils and sold them at a loss equal to the selling price of 16 pencils. The cost of 80 pencils is how many times the selling price of 80 pencils?
Options:
A) 0.75
B) 1.2
C) 1.8
D) 2.4
E) 4.25
Rationale: Say the cost price of 80 pencils was $80 ($1 per pencil) and the selling price of 1 pencil was p.
Selling at a loss: 80 - 80p = 16p --> p = 5/6.
(cost price)/(selling price) = 1/(5/6) = 6/5 = 1.2.
Answer: B.
Answer: B
Question: Each of the cucumbers in 100 pounds of cucumbers is composed of 99% water, by weight. After some of the water evaporates, the cucumbers are now 97% water by weight. What is the new weight of the cucumbers, in pounds?
Options:
A)2
B)33
C)92
D)96
E)98
Rationale: Out of 100 pounds 99% or 99 pounds is water and 1 pound is non-water. After somewaterevaporates the cucumbers become 97% water and 3% of non-water, so now 1 pound of non-water composes 3% of cucucmbers, which means that the new weight of cucumbers is 1/0.03=34 pounds.
Answer: B.
Answer: B
Question: Half of 3 percent written as decimal is
Options:
A)5
B)0.5
C)0.015
D)0.005
E)None of these
Rationale: Explanation:
It will be 1/2(3%) = 1/2(3/100) = 3/200 = 0.015
Option C
Answer: C
Question: Out of 40 applicants to a law school, 15 majored in political science, 20 had a grade point average higher than 3.0, and 10 did not major in political science and had a GPA equal to or lower than 3.0. How many E applicants majored in political science and had a GPA higher than 3.0?
Options:
A)5
B)10
C)15
D)25
E)35
Rationale: Total applicants = 40
Political science = 15 and Non political science = 40 - 15 = 25
GPA > 3.0 = 20 and GPA <= 3.0 = 20
10 Non political science students had GPA <= 3.0 --> 15 Non political science students had GPA > 3.0
GPA > 3.0 in political science = Total - (GPA > 3.0 in non political science) E= 20 - 15 = 5
Answer: A
Answer: A
Question: One night a certain hotel rented 2/5 of its rooms, including 2/3 of their air conditioned rooms. If 3/5 of its rooms were air conditioned, what percent of the rooms that were not rented were air conditioned?
Options:
A)20%
B)25%
C)33%
D)36%
E)40%
Rationale: The rooms which were not rented is 3/5
The AC rooms which were not rented is (1/3)*(3/5) = 1/5
The percentage of unrented rooms which were AC rooms is (1/5) / (3/5) = 1/3 = 33%
The answer is C.
Answer: C
Question: A can do a job in 30 days and B can do it in 30 days. A and B working together will finish twice the amount of work in ------- days?
Options:
A)14 days
B)26 days
C)30 days
D)31 days
E)39 days
Rationale: C
1/30 + 1/30 = 1/15
15*2 = 30 days
Answer: C
Question: Find k if 64 ÷ k = 4.
Options:
A)8
B)12
C)16
D)25
E)32
Rationale: Since 64 ÷ k = 4 and 64 ÷ 16 = 4, then
k = 16
correct answer is C)16
Answer: C
Question: If [x] is the greatest integer less than or equal to x, what is the value of [-5.6]+[3.4]+[12.7]?
Options:
A) 3
B) 5
C) 7
D) 9
E) 10
Rationale: You are asked what the closest lesser integer value to [x] is.
[-5.6] = -6.0
[3.4] = 3.0
[12.7] = 12.0
Therefore , answer is: -6.0 + 3.0 + 12.0 = 9.0
Option D.
Answer: A
Question: In how many different number of ways the letters of the word 'ENGINEERING' can be arranged
Options:
A)276800
B)277000
C)277200
D)277400
E)278400
Rationale: 11!/(3! × 3! × 2! × 2! × 1!)
= (11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1)/(3 × 2 × 3 × 2 × 2 × 2 × 1)
= 11 × 10 × 8 × 7 × 5 × 3
= 277200
C)
Answer: C