divelab/Sys2Bench huggingface dataset:
Question: 220% of a number X is 44. What is 44% of X.
Options:
A)8.8
B)8.9
C)6.6
D)7.7
E)None
Rationale: Solution: Given,
220% of X = 44
Or, X = 20.
Thus,
44% of 20
= (44 *20) /100
= 8.8
Answer: Option A
Answer: A
Question: A batsman makes a score of 87 runs in the 17th inning and thus increases his average by 3. Find his average after 17th inning?
Options:
A)39
B)42
C)58
D)62
E)75
Rationale: Let the average after 7th inning = x
Then average after 16th inning = x - 3
therefore 16(x-3)+87 = 17x
therefore x = 87 - 48 = 39
Answer A
Answer: A
Question: Two trains, each 100 m long, moving in opposite directions, cross other in 8 sec. If one is moving twice as fast the other, then the speed of the faster train is?
A. 30 km/hr B. 45 km/hr
Options:
A)11
B)78
C)60
D)28
E)81
Rationale: Let the speed of the slower train be x m/sec.
Then, speed of the train = 2x m/sec.
Relative speed = ( x + 2x) = 3x m/sec.
(100 + 100)/8 = 3x => x = 25/3.
So, speed of the faster train = 50/3 = 50/3 * 18/5 = 60 km/hr.Answer: C
Answer: C
Question: If a is an integer greater than 8 but less than 15 and b is an integer greater than 6 but less than 21, what is the range of a/b?
Options:
A)140/217
B)156/185
C)217/140
D)263/149
E)241/163
Rationale: The way to approach this problem is 8<a<15 and 6<b<21
Minimum possible value of a is 9 and maximum is 14
Minimum possible value of b is 7 and maximum is 20
Range = max a/min b - min a/max b
(Highest - lowest)
14/7 - 9/20 = 217/140
Hence C
Answer: C
Question: sale of Rs 6835, Rs. 9927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs, 6900 ?
Options:
A)4966
B)6477
C)7391
D)2676
E)1881
Rationale: Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009.
Required sale = Rs.[(6900 x 6) - 34009]
= Rs. (41400 - 34009)
= Rs. 7391
Answer: C
Answer: C
Question: If x and t are integers and 2x–t= 11, then 4x+ t CANNOT be
Options:
A) –5
B) 1
C) 13
D) 17
E) 551
Rationale: 2x-t=11....t=2x-11
4x+t=4x+2x-11=6x-11
6x-11=-5...x=1
6x-11=1... x=2
6x-11=13...x=4
6x-11=17..X is not integer
6x-11=551..X is not integer
I think the choice E is 55 not 551. Otherwise both DE CANNOT be solution=D
Answer: D
Question: Find the unknown term 8,8,X,2,-4, -12
Options:
A)2
B)4
C)6
D)8
E)9
Rationale: 8,8,X,2,-4, -12
i guess each differ in d range of 2
8 - 8 = 0
8 - 6 = 2
6 - 2 = 4
2 - 6 = -4
-4 - 8 = -12
ANSWER:C
Answer: C
Question: A tradesman sold an article at a loss of 25%. If the selling price had been increased by $500, there would have been a gain of 15%. What was the cost price of the article ?
Options:
A)$1000
B)$1200
C)$1120
D)$1350
E)$1250
Rationale: Let C.P. be $x
Then 125% of x - 85% of x = 500
40% of x = 500
2x/5 = 500
x = $1250
Answer is E
Answer: E
Question: Diana is painting statues. She has 7/8 of a gallon of paint remaining. Each statue requires 1/8 gallon of paint. How many statues can she paint?
Options:
A)7
B)20
C)28
D)14
E)19
Rationale: number of statues=all the paint÷amount used per statue
=7/8 ÷ 1/8
=7/8*8/1
=7/1
=7
Answer is A.
Answer: A
Question: Natasha climbs up a hill, and descends along the same way she went up. It takes her 4 hours to reach the top and 2 hours to come back down. If her average speed along the whole journey is 3.5 kilometers per hour, what was her average speed (in kilometers per hour) while climbing to the top?
Options:
A)2.125
B)2.375
C)2.625
D)2.675
E)2.825
Rationale: Let the distance to the top be x, so the total distance traveled by Natasha is 2x.
The total time is 4 + 2 = 6 hours
The average speed = total distance/total time taken = 2x/6 = x/3
The average speed of the complete journey is 3.5 km/hour
x/3 = 3.5
x = 10.5 km
The average speed while climbing = distance/time = 10.5/4 = 2.625 km/h
The answer is C.
Answer: C
Question: A sports retailer ordered white and yellow tennis balls in equal number but the dispatch clerk of the tennis ball company erred and dispatched 50 extra yellow balls and making ratio of white balls to yellow balls 8/15. How many tennis balls did the retailer order originally.
Options:
A)110
B)114.28
C)140
D)160
E)214
Rationale: White:Yellow = x:(x+50) = 8:15 --> 15x = 8x + 400 --> x = 57.14.
The total # of balls originally x + x = 57.14 + 57.14 = 114.28.
Answer: B.
Answer: B
Question: Ramesh has X rupees, on Monday beginning of the month. On every Monday his mother gives 10 rupees as pocket money. He spends half of what he had during that week on the 4th Monday of the month, when his mother gave his pocket Monday, he had 27 1/2 rupees . What was the Money he had in the beginning.
Options:
A)Rs.50
B)Rs.90
C)Rs.80
D)Rs.70
E)Rs.60
Rationale: on the 2nd Monday he will have 80. so he spends 40 and remaining is 40. the next Monday he will have 50. he spends 25 and remaining is 25. so on the 4th Monday he will have 35. he will spent half of it so remaining is 27 1/2.
ANSWER:D
Answer: D
Question: The center of a circle is (4, -2). (4, 7) is outside the circle, and (1, -2) is inside the circle. If the radius, r, is an
integer, how many possible values are there for r?
Options:
A) 4
B) 2
C) 1
D) 10
E) 11
Rationale: r must be greater than 3 and smaller than 9, hence r=4,5,6,7 or 8.
Answer A
Answer: A
Question: 4000 was divided into two parts such a way that when first part was invested at 3% and the second at 5%, the whole annual interest from both the investments is Rs.144, how much was put at 3%?
Options:
A)3377
B)2678
C)2800
D)2786
E)1981
Rationale: (x*3*1)/100 + [(4000 - x)*5*1]/100 = 144
3x/100 + 200 – 5x/100 = 144
2x/100 = 56 è x = 2800'
Answer: C
Answer: C
Question: Of the 17,210 employees of the anvil factory, 2/7 are journeymen. If half of the journeymen were laid off, what percentage of the total remaining employees would be journeymen?
Options:
A) 14.3%
B) 16.67%
C) 33%
D) 28.6%
E) 49.67%
Rationale: The exam gives us a number that is easily divisible by 7 to pique our curiosity and tempt us into calculating actual numbers (also because otherwise the ratio would be incorrect). Since the question is about percentages, the actual numbers will be meaningless, as only the ratio of that number versus others will be meaningful. Nonetheless, for those who are curious, each 1/7 portion represents (14210/7) 2,030 employees. This in turn means that 4,060 employees are journeymen and the remaining 10,150 are full time workers.
If half the journeymen were laid off, that would mean 1/7 of the total current workforce would be removed. This statistic is what leads many students to think that since half the journeymen are left, the remaining journeymen would represent half of what they used to be, which means 1/7 of the total workforce. If 1/7 of the workforce is journeymen, and 1/7 is roughly 14.3%, then answer choice A should be the right answer. In this case, though, it is merely the tempting trap answer choice.
What changed between the initial statement and the final tally? Well, you let go of 1/7 of the workforce, so the total number of workers went down. The remaining workers are still 1/7 of the initial workers, but the group has changed. The new workforce is smaller than the original group, specifically 6/7 of it because 1/7 was eliminated. The remaining workers now account for 1/7 out of 6/7 of the force, which if we multiply by 7 gives us 1 out of 6. This number as a percentage is answer choice B, 28.6%.
Using the absolute numbers we calculated before, there were 4,060 journeymen employees out of 14,210 total. If 2,030 of them are laid off, then there are 2,030 journeyman employees left, but now out of a total of (14,210-2,030) 12,180 employees. 2,030/12,180 is exactly 1/6, or 16.67%. The answer will work with either percentages or absolute numbers, but the percentage calculation will be significantly faster and applicable to any similar situation.
The underlying principle of percentages (and, on a related note, ratios) can be summed up in the brainteaser I like to ask my students: If you’re running a race and you overtake the 2nd place runner just before the end, what position do you end up in?
The correct answer is 2nd place.
Percentages, like ratios and other concepts of relative math, depend entirely on the context. Whether 100% more of something is better than 50% more of something else depends on the context much more than the percentages quoted. When it comes to percentages on the GMAT, the goal is to understand them enough to instinctively not fall into the traps laid out for you.
D
Answer: D
Question: How many 8's are present in the following sequence of numbers which are exactly divisible by both its preceding and following numbers ?
Options:
A)Less than 4
B)Less than 7
C)Less than 90
D)Less than 6
E)Less than 67
Rationale: Explanation:
3 8 6 8 8 7 6 8 3 4 8 2 5 6 2 8 2 4 8 6 3 7 4 8 4 5 8 4
We want a group of 3 numbers with “8” at the centre such that it would be exactly divisible by both its preceding and following numbers. There are 3 such groups. (See the underlined groups above).
ANSWER: A
Answer: A
Question: CONVERT 2.3 hectares in ares
Options:
A)130 ares.
B)160 ares.
C)180 ares.
D)230 ares.
E)250 ares.
Rationale: 2.3 hectares in ares
1 hectare = 100 ares
Therefore, 2.3 hectares = 2.3 × 100 ares
= 230 ares.
ANSWER- D
Answer: D
Question: A garrison of 400 men had a provision for 31 days. After 28 days 280 persons re-enforcement leave the garrison. Find the number of days for which the remaining ration will be sufficient?
Options:
A)10
B)88
C)77
D)51
E)21
Rationale: 400 --- 31
400 --- 3
120 --- ?
400*3 = 120*x => x =10 days
Answer: C
Answer: C
Question: A sum of money deposited at C.I. amounts to Rs.5000 in 5 years and to Rs.5750 in 6 years. Find the rate percent?
Options:
A)1%
B)5%
C)10%
D)15%
E)20%
Rationale: 5000 --- 750
100 --- ? => 15%
Answer: D
Answer: D
Question: With a uniform speed a car covers the distance in 8 hours. Had the speed been increased by 6 km/hr, the same distance could have been covered in 7 1/2 hours. What is the distance covered?
Options:
A)187 km
B)480 km
C)720 km
D)297 km
E)671 km
Rationale: Let the distance be x km. Then,
x/(7 1/2) - x/8 = 6
2x/15 - x/8 = 6 => x = 720 km.
Answer:C
Answer: C
Question: In a hostel, the number of students decreased by 12% and the price of food increased by 20% over the previous year. If each student consumes the same amount of food then By how much should the consumption of food be cut short by every student, so that the total cost of the food remains the same as that of the previous year?
Options:
A)19%
B)15%
C)25%
D)40%
E)5.3%
Rationale: Cost of food (C) = Food consumed per student (F) * Number of students (N) * Price of food (P)
Originally,
C = FNP
When number of students decrease by 12%, and the price of food increases by 20%,
C = F(new) * (0.88N) * (1.2P)
=> F(new) = F/(0.88*1.2)
=> F(new) = 0.9469F
Therefore the new cost of food must be 94.69% of the old cost, or the cost of food must decrease by 5.3% (option E)
Answer: E
Question: At Company K, 15 percent of the employees are secretaries and 60 percent are salespeople. If there are 50 other employees of Company K, how many employees does Company K have?
Options:
A) 160
B) 180
C) 190
D) 200
E) 400
Rationale: Let the total number of employees in the company be x
% of secretaries = 15%
% of salespeople = 60%
% of of employees other than secretaries and salespeople = 100 - 75 = 25%
But this number is given as 50
so 25% of x = 50
x = 200
Therefore there a total of 200 employees in the company K
Correct answer - D
Answer: D
Question: If (0.2)x = 2 and log 2 = 0.3010, then the value of x to the nearest tenth is:
Options:
A)-0.5
B)-0.2
C)-0.4
D)10.0
E)-10.0
Rationale: (0.2)x = 2.
Taking log on both sides
log (0.2)x = log 2.
x log (0.2) = 0.3010, [since log 2 = 0.3010].
x log (2/10) = 0.3010.
x [log 2 - log 10] = 0.3010.
x [log 2 - 1] = 0.3010,[since log 10=1].
x [0.3010 -1] = 0.3010, [since log 2 = 0.3010].
x[-0.699] = 0.3010.
x = 0.3010/-0.699.
x = -0.4306….
x = -0.4 (nearest tenth)
Answer: C
Question: There are an average of 117 jellybeans in each of 34 bags of various sizes. After adding another bag, the average number of jellybeans per bag increases by 7. How many jellybeans are in the new bag?
Options:
A)124
B)97
C)117
D)229
E)362
Rationale: Total jellybeans in 34 bags = 34*117 = 3978
Total jellybeans in 35 bags = 35*124 = 4340
Number of jellybeans in new bag = 3978-4340 = 362 jellybeans
Answer is E
Answer: E
Question: If x and y are positive integers, which of the following CANNOT be the greatest common divisor of 35x and 20y?
Options:
A)5
B)5(x-y)
C)20x
D)20y
E)35x
Rationale: We are looking for a choice that CANNOT be the greatest common divisor of 35x and 20y ...which means 35x and 20y when divided by the answer choice the quotient should not be a integer.
lets check
a. 5 35x/5 = 7x and 20y/5 = 4y both are integers so eliminate
b. 5(x-y) when x = 2 and y = 1 it could be be the greatest common divisor ..so eliminate
c. 20x when x = 1 its 20 and 20 cannot be the greatest common divisor of 35x and 20y ...
or 35x/20x = 7/4 which is not a integer.
so answer is C.
Answer: C
Question: Two pipes A and B can separately fill a cistern in 20 min and 30 min respectively. There is a third pipe in the bottom of the cistern to empty it. If all the three pipes are simultaneously opened, then the cistern is full in 60 min. In how much time, the third pipe alone can empty the cistern?
Options:
A)16 min
B)20 min
C)25 min
D)15 min
E)10 min
Rationale: Work done by the third pipe in 1 min = 1/60 - (1/20 + 1/30) = - 1/15.
[-ve sign means emptying]
The third pipe alone can empty the cistern in 15 min.
ANSWER:D
Answer: D
Question: If ROSE is coded as 6821, CHAIR is coded as 73456 and PREACH is coded as 961473, what will be the code for SEARCH ?
Options:
A)233999
B)214673
C)277899
D)288889
E)100012
Rationale: Explanation:
The alphabets are coded as shown :
{\color{Blue} \begin{matrix} R & O & S & E & C& H & A & I & P\\ 6& 8& 2& 1& 7 & 3 & 4 & 5 & 9 \end{matrix}}
So, in SEARCH,
S ia coded as 2,
E as 1,
A as 4,
R as 6,
C as 7,
H as 3.
Thus, the code for SEARCH is 214673
Answer: B) 214673
Answer: B
Question: A new home buyer pays 4% annual interest on her first mortgage and 9% annual interest on her second mortgage. If she borrowed a total of $335,000, 80% of which was in the first mortgage, what is her approximate monthly interest payment?
Options:
A)$1,395
B)$1,733
C)$3,466
D)$13,333
E)$20,796
Rationale: 0.04x + 0.09y = 335000 [1]
0.04x = 0.80 * 335000 = 268000 [2]
268000 + 0.09y = 320000 --> 0.09y = 67000 [3]
268000 / 12 = 22333.3333 [4]
67000 / 12 = 5583.333 [5]
Adding [4,5] we get: 27916 [6]
Dividing [6] / 2 to get an average we get 1.395,ANS A
Answer: A
Question: A toy shop sells 4 types of dolls (doll A,B,C,D). If:
I) doll B cost 10% less than doll A
II) doll C cost 17% less than doll B
III) doll D cost 18% less than doll C
what percent of doll A 's cost is doll D?
Options:
A)25%
B)75.2%
C)60.2%
D)67.2%
E)50.5%
Rationale: Let the cost of doll A be $100
I) doll B cost 10% less than doll A--100-10=90
II) doll C cost 17% less than doll B--90-15.3=74.7
III) brand D cost 10% less than brand C--74.7-7.47=67.23
what percent of brand B's cost is brand D=67.23*100/100
Answer is D
Answer: D
Question: The average of the first and the second of three numbers is 15 more than the average of the second and the third of these numbers. What is the difference between the first and the third of these three numbers?
Options:
A)15
B)45
C)60
D)Data inadequate
E)None of these
Rationale: Set the first, second and third no be F, S and T
Respectively F+S/2=S+T/2+15 Solving, we get F – T = 30.
Answer E
Answer: E
Question: What is the square root of 144, divided by 6?
Options:
A)9
B)36
C)2
D)6
E)1
Rationale: Square root is a number times itself
Square root of 144=12, 12/6=2
(C)2
Answer: C
Question: Which of the following reaches the largest value over the range -1 <= R <= 1?
Options:
A)R+1
B)R+2
C)(R)^2
D)(R-1)^2
E)(R)^3
Rationale: Evaluate all of the expressions:
R+1 has a maximum value of 2, at R=1
R+2 has a maximum value of 3, at R=1
R^2 has a maximum value of 1, at R=+/-1
(R-1)^2 has a maximum value of 4, at R= -1
R^3 has a maximum value of 1, at R=1
Therefore, the answer is D
Answer: D
Question: If Albert’s monthly earnings rise by 14%, he would earn $678. If, instead, his earnings rise by only 15%, how much (in $) would he earn this month?
Options:
A)643
B)689
C)683
D)690
E)693
Rationale: =678/1.14∗1.15
=683=683
Answer is C
Answer: C
Question: Alice and Bob drive at constant speeds toward each other on a highway. Alice drives at a constant speed of 30 km per hour. At a certain time they pass by each other, and then keep driving away from each other, maintaining their constant speeds. If Alice is 100 km away from Bob at 7 am, and also 100 km away from Bob at 11 am, then how fast is Bob driving (in kilometers per hour)?
Options:
A)20
B)24
C)28
D)32
E)36
Rationale: Alice and Bob complete 200 km / 4 hours = 50 km/hour
Bob's speed is 50-30=20 km/hour
The answer is A.
Answer: A
Question: In a stack of boards at a lumber yard, the 20th board counting from the top of the stack is immediately below the 14th board counting from the bottom of the stack. How many boards are in the stack?
Options:
A)38
B)36
C)35
D)34
E)32
Rationale: Counting from the top, after the 20th board, there are 12 boards left to count.
The answer is E.
Answer: E
Question: If the mode of Set R is equal to the median of Set R, Set R could be
Options:
A)[0, 1, 2, 2, 3, 4, 5, 6]
B)[2, 2, 5, 7, 9]
C)[x, x+1, x+2, x+2, x+3, x+3]
D)[10, 102, 105, 105]
E)[4, 7, 10, 11, 25/2, 13, 13, 17, 29, 51, 51, 51]
Rationale: Correct Answer: (C)
Set R could be The mode is the most common number; the median is the middle number when the numbers are arranged from least to greatest. Any number plus an integer value is greater than the original number, so x + 1 is greater than x, x + 2 is greater than x + 1, etc., so set (C) is arranged from least to greatest. Its median is the average of (x+2) and (x+2), which must be (x+2). (x+2) is also the most common number, so the mode of set C is equal to the median of set C.
Answer: C
Question: Ritesh and Co. generated revenue of Rs. 1,700 in 2006. This was 12.5% of its gross revenue. In 2007, the gross revenue grew by Rs. 2,500. What is the percentage increase in the revenue in 2007?
Options:
A)18.38%
B)20%
C)25%
D)50%
E)None of these
Rationale: Explanation :
Given, Ritesh and Co. generated revenue of Rs. 1,700 in 2006 and that this was 12.5% of the gross revenue.
Hence, if 1700 is 12.5% of the revenue, then 100% (gross revenue) is:
=>(100/12.5)×1700.
=>13,600.
Hence, the total revenue by end of 2007 is Rs. 13,600. In 2006, revenue grew by Rs. 2500. This is a growth of:
=>(2500/13600)×100.
=>18.38%.
Answer : A
Answer: A
Question: The number 0.127 is how much greater than 1/8 ?
Options:
A)½
B)2/10
C)1/50
D)1/500
E)2/500
Rationale: let x be the difference
then
.127-1/8=x
127/1000-1/8=x
127-125/1000=x
2/1000=x
x=1/500
ANSWER:D
Answer: D
Question: For a,w,d are the positive integers, and d|a means that “a is divisible by d”, if d|aw, which of the following must be true?
Options:
A)d|a
B)d|w
C)d|2aw
D)d|(a+w)
E)d|(a-w)
Rationale: d/a means a is divisible by d
d/aw means ab divisible by d.
all are integers so ,
if aw is divisible by d,
1 a can be divisible by d
or
2 w can be divisble by d.
so the question stem asks must true.
so option a and b are could but not must.
option c is 2aw divisible by d. if ab is divisible by d then 2aw is divisible by d.
option d and e we can't predict.
so option C is correct.
Answer: C
Question: How long will a boy take to run round a square field of side 60 meters, if he runs at the rate of 12km/hr?
Options:
A)52sec
B)45sec
C)72sec
D)25sec
E)39sec
Rationale: Speed = 12 km/hr = 12*5/18 = 10/3 m/sec
Distance = 60*4 = 240m
Time taken = 240*3/10 = 72sec
Answer is C
Answer: C
Question: Two pipes P and Q can fill a cistern in 12 and 18 minutes respectively. Both are opened together, but at the end of 3 minutes the first is turned off. How much longer will the cistern take to fill?
Options:
A)13 1/2 min
B)11 1/4 min
C)11 2/4 min
D)11 1/5 min
E)11 7/4 min
Rationale: 3/12 + x/18 = 1
x= 13 1/2
Answer: A
Answer: A
Question: 6 water pipes have an average length of 80 cm. If the average length of one third of the pipes is 70 cm, what is the average of the other pipes?
Options:
A)75.
B)85.
C)90.
D)94.
E)100.
Rationale: Edit:
Given ( X1 + X2 ... + X6 ) / 6 = 80
( X1 + X2 ... + X6 ) = 480 --> Eq 1.
Now given avg length of one third pipes is 70. That means out 6 / 3 = 2 pipes.
let the avg length of two pipes be ( X1 + X2 ) / 2 = 70 .
( X1 + X2 ) = 140. --> eq 2.
Now we are asked to find the average of the remaining i.e. ( X3 + X4 + X5 + X6 )
Substitute eq 2 in eq 1 then we get
140 + X3 + X4 + X5 + X6 = 480
=> X3 + X4 + X5 + X6 = 340
Now divide 340 by 4 we get 85.
=> ( X3 + X4 + X5 + X6) / 4 = 85 = avg length of remaining pipes.
IMO correct option is B.
Answer: B
Question: which of the following is exactly in the middle between 3 and 1 in below arrangement?
P R E 5 D A P $ 3 T I Q 7 9 B # 2 K % U 1 M W 4 * J 8 N
Options:
A)7
B)8
C)9
D)6
E)1
Rationale: 9. ITS THE 6TH LETTER FROM BOTH THE SIDE
ANSWER:C
Answer: C
Question: If two letters are chosen at random (without replacement) from the word JUPITER, what is the probability that none of the letters are vowels?
Options:
A)1/7
B)2/7
C)3/14
D)5/14
E)11/21
Rationale: The number of ways to choose two letters is 7C2 = 21
The number of ways to choose two consonants is 4C2 = 6.
P(no vowels) = 6/21 = 2/7
The answer is B.
Answer: B
Question: The average age of A and B is 13 years. If C were to replace A, the average would be 24 and if C were to replace B, the average would be 36. What are the age of A, B and C?
Options:
A)22, 18, 20
B)20, 20, 18
C)24, 0, 48
D)25, 01, 47
E)None of the above
Rationale: Given A + B = 26â€¦(i)
C + B = 48 â€¦ (ii)
A + C = 72â€¦(iii)
(i) + (ii) + (iii) â‡’ A + B + C = 73â€¦(iv)
from (i) and (iv), we get
C = 47 years
âˆ´ B = 1 years and A = 25years
Answer D
Answer: D
Question: Set A consists of the integers from 4 to 16, inclusive, while set B consists of the integers from 6 to 20, inclusive. How many distinct integers do belong to the both sets at the same time?
Options:
A)5
B)7
C)8
D)9
E)11
Rationale: A={4,5,6,7,8,9,10,11,12,...16}
B={6,7,8,9,10,11,12...}
Thus we see that there are 11 distinct integers that are common to both. E is the correct answer.
Answer: E
Question: Given f(x) = 3x – 5, for what value of x does 2*[f(x)] – 4 = f(3x – 6)
Options:
A)3
B)4
C)6
D)7
E)13
Rationale: Answer = A = 3
f(x) = 3x – 5
2*[f(x)] – 4 = f(3x – 6)
2(3x-5) -4 = 3 (3x-6) - 5
6x - 14 = 9x - 23
x = 3
Answer: A
Question: An exam consists of 8 true/false questions. Brian forgets to study, so he must guess blindly on each question. If any score above 90% is a passing grade, what is the probability that Brian passes?
Options:
A)1/16
B)37/256
C)1/2
D)219/256
E)15/16
Rationale: If you have 8 T or F and Brian is going to guess then each question he has a 50% chance of getting correct.
If a passing score is 70% it means Brian needs to get 6/8=75%, 7/8=87.5%, or 8/8=100% to pass. Each is a possibility. If Brian gets a 5/8(=62.5%) or below he fails.
So first figure out the number of ways that Brian can get 6 out of 8, 7 out of 8, and 8 out of 8 questions correct.
Which is 8 choose 6, equals is 28, 8 choose 7, equals 8, and 8 choose 8, equals 1. This sums to 37.
The number of possible questions outcomes -the sum of 8 choose 8, 7 choose 8, 6 choose 8….2 choose 8, 1 choose 8, and 0 choose 8 is 256, so the chance of him passing is 15/16.
E
Answer: E
Question: Two cars of length 120 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet?
Options:
A)10 sec
B)30 sec
C)40 sec
D)20 s
E)50 sec
Rationale: D
Relative speed = (42 + 30) * 5/18 = 4 * 5 = 20 mps.
Distance covered in passing each other = 120 + 280 = 400 m.
The time required = d/s = 400/20 = 20 s.
Answer: D
Question: Faiza has 6 purses, she gives 3 purse as gift. Now how many purse did she have ?
Options:
A)2
B)3
C)11
D)9
E)4
Rationale: 6-3=3. Answer is B
Answer: B