divelab/Sys2Bench huggingface dataset:
Question: Machine M, N, O working simultaneously Machine M can produce x units in 3/4 of the time it takes machine N to produce the same amount of units. Machine N can produce x units in 2/5 the time it takes machine O to produce that amount of units. If all three machines are working simultaneously, what fraction of the total output is produced by machine N?
Options:
A)1/2
B)5/11
C)4/13
D)8/29
E)6/33
Rationale: Now ultimately the speed of every machine is given with respect to Mach O.
So lets assume the speed of O, say 12 hrs to make x units (assuming 6 because we can see we will need to divide by 3 and 4
Mach O makes x units in 12 hrs
So, Mach N = 2/5 of O = 2/5*12 = 4.8 hrs to make x units
and Mach M = 3/4 of N = 3/4*4.8 = 6 hrs to make x units
No they are running simultaneously. Lets see how much each mach makes in 1 hr
Mach O = x/12 units
Mach N = 5x/24 units
Mach M = x/6 units
In 1 hr, together they make - x/12+5x/24+x/6 = 11/24
So what ratio of this has Mach N made?
(5x/24) / (11/24) = 5/11
Ans:B=5/11
Answer: B
Question: How many words can be formed from the letters of the word ‘DIRECTOR’ So that the vowels are always together?
Options:
A)1524
B)7845
C)2160
D)2541
E)5631
Rationale: In the given word, we treat the vowels IEO as one letter.
Thus, we have DRCTR (IEO).
This group has 6 letters of which R occurs 2 times and others are different.
Number of ways of arranging these letters = 6!/2! = 360.
Now 3 vowels can be arranged among themselves in 3! = 6 ways.
Required number of ways = (360x6) = 2160.
Ans: C
Answer: C
Question: A box contains 2 red, 3 black and 4 blue balls. 3 balls are randomly drawn from the box. If two balls are found to be different, what is the probability that the third ball is blue?
Options:
A)8/3
B)9/3
C)5/3
D)2/3
E)1/3
Rationale: there are 6 ways to draw a blue ball at third attempt if first two balls are different. they are
1)RED BLACK BLUE
2)RED BLUE BLUE
3)BLACK RED BLUE
4)BLACK BLUE BLUE
5)BLUE RED BLUE
6)BLUE BLACK BLUE
Probability of 1st way is (2/9)*(3/8)*(4/7)
as at first attempt we got red which are two in number out of 9 and in second we got black which are 3 in number out of 8 (as first ball is removed)and in 3rd attempt we got blue which are 4 in number out of 7 balls left.
similarly probability of other ways is as follows
(2/9)*(4/8)*(3/7)
(3/9)*(2/8)*(4/7)
(3/9) *(4/8)*(3/7)
(4/9)*(2/8)*(3/7)
(4/9)*(3/8)*(3/7)
total probability of getting a blue ball is sum of all above ways so p=(2/9)*(3/8)*(4/7)+(2/9)*(4/8)*(3/7)+(3/9)*(2/8)*(4/7)+(3/9) *(4/8)*(3/7)+(4/9)*(2/8)*(3/7)+(4/9)*(3/8)*(3/7)=1/3
so probability of ball to be blue is 1/3
Answer E
Answer: E
Question: Ramu bought an old car for Rs. 42000. He spent Rs. 13000 on repairs and sold it for Rs. 60900. What is his profit percent?
Options:
A)10.7%
B)19%
C)18%
D)14%
E)16%
Rationale: Total CP = Rs. 42000 + Rs. 13000
= Rs. 55000 and SP
= Rs. 60900
Profit(%) = (60900 - 55000)/55000 * 100
= 10.7%
Answer: A
Answer: A
Question: The length of the bridge, which a train 110 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
Options:
A)255
B)265
C)245
D)277
E)211
Rationale: Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (110 + x)/30 = 25/2 => 2(110 + x) = 750 => x = 265 m.
Answer:B
Answer: B
Question: A shopkeeper loses 15%,if an article is sold for Rs. 102. What should be the selling price of the article to gain 20%?
Options:
A)Rs.148
B)Rs.144
C)Rs.120
D)Rs.129
E)Rs.126
Rationale: Given that SP = Rs. 102 and loss = 15%
CP = [100(SP)]/(100 - l%) = (100 * 102)/85 = 20 * 6 = Rs. 120.
To get 20% profit, New SP = [(100 + p%)CP]/100 = (120 * 120)/100
= Rs.144
Answer:B
Answer: B
Question: 1907 x 1907 = ?
Options:
A)A)3623216
B)B)3624216
C)C)3624316
D)D)3636649
E)E)3625216
Rationale: 1907 x 1907 = (1907)2
= (1900 + 7)2
= (1900)2 + (7)2 + (2 x 1900 x 7)
= 3610000 + 49 + 26600.
= 3636649.
D)
Answer: D
Question: Given f(x) = 3x – 5, for what value of x does 2*[f(x)] – 19 = f(x – 4) ?
Options:
A)2
B)4
C)6
D)8
E)10
Rationale: 2(3x-5)-19 = 3(x-4) - 5
3x = 12
x = 4
The answer is B.
Answer: B
Question: 3 person can fill tank in 25 min, a can fill in 30 min , b can fill in 35 min and c can empty the 5 gallon per min then what is the capacity of tank?
Options:
A)208.26 gallons
B)218.26 gallons
C)228.26 gallons
D)238.26 gallons
E)248.26 gallons
Rationale: A can fill the tank in 30 minutes
B can fill the same tank in 35 minutes
A B C together fill the tank in 25 minutes
Equating we get,
1050/23*5 = 228.26 gallons
ANSWER:C
Answer: C
Question: The edge of three cubes of metal is 3 dm, 4 dm and 5 dm. They are melted and formed into a single cube. Find the edge of the new cube?
Options:
A)1
B)9
C)4
D)6
E)3
Rationale: 33 + 43 + 53 = a3 => a
= 6
Answer: D
Answer: D
Question: A man gains 30% by selling an article for a certain price. If he sells it at double the price, the percentage of profit will be.
Options:
A)130%
B)140%
C)150%
D)260%
E)170%
Rationale: Explanation:
Let the C.P. = x,
Then S.P. = (130/100)x = 13x/10
New S.P. = 2(13x/10) = 26x/10
Profit = 26x/10 - x = 26x/10
Profit% = (Profit/C.P.) * 100
=> (26x/10) * (1/x) * 100 = 260 %
Option D
Answer: D
Question: A doctor prescribed 20 cubic centimeters of a certain drug to a patient whose body weight was 120 pounds. If the typical dosage is 2 cubic centimeters per 15 pounds of the body weight, by what percent was the prescribed dosage greater than the typical dosage?
Options:
A)25%
B)9%
C)11%
D)12.5%
E)14.8%
Rationale: Typical dosage per 15 pound of the body weight = 2 c.c
Typical dosage per 120 pound of the body weight = 2 *(120/15)
= 2 * 8
= 16 c.c
Dosage prescribed by doctor for 120 pound patient = 20 c.c
% prescribed dosage greater than the typical dosage = (20-16/16) *100%
=(2/16) *100%
= 25%
Answer A
Answer: A
Question: The price of lunch for 15 people was $208.00, including a 15 percent gratuity for service. What was the average price per person, EXCLUDING the gratuity?
Options:
A) $11.73
B) $12.60
C) $13.80
D) $14.00
E) $15.87
Rationale: Take the initial price before the gratuity is 100
The gratuity is calculated on the final price, so as we assumed the final bill before adding gratuity is 100 so gratuity is 15% of 100 is 15 so the total price of meals is 115 so the given amount i.e 208 is for 115 then we have to calculate for 100
for 115 208
for 100 x
so by cross multiplication we get 115x=100*208 => x=100*208/110 by simplifying we get x as 189 which is the price of lunch before gratuity so the gratuity is 19 so
as the question ask the average price person excluding gratuity is 189/15=12.6 so our answer is B)
Answer: B
Question: An adventuring party consists of 4 white mages, 6 warriors, and 4 archers. In how many ways can 3 white mages, 2 warriors and 2 archers be selected from the given group?
Options:
A)987 ways
B)446 ways
C)360 ways
D)157 ways
E)134 ways
Rationale: The number of ways of selecting three white mages, two warriors and two archers is:
= ⁴C₃ * ⁶C₂ * ⁴C₂
= (4 * 3 * 2)/(3 * 2 * 1) * (6 * 5)/(2 * 1) * (4 * 3)/( 2 * 1)
= 4 * 15 * 6
= 360 ways.
Answer: C
Answer: C
Question: Peter invests a sum of money and gets back an amount of $ 815 in 3 years . David invests an equal amount of money and gets an amount of $850 in 4 years. If both amounts were invested at the same rate (simple interest ) What was the sum of money invested ?
Options:
A)670
B)664
C)698
D)744
E)710
Rationale: Since both Peter and David invested the same amount of money at the same rate, they would earn same interest per year.
David invested for one year more than Peter and hence he got interest amount for one more year.
Interest earned per year = Amount received by David - Amount received by Peter = 850 - 815 = 35
Interest earned for 3 years = 35*3 =105
Amount invested = 815 - 105= 710
Answer: E
Answer: E
Question: If x is equal to the sum of the integers from 60 to 80, inclusive, and y is the number of even integers from 60 to 80, inclusive, what is the value of x + y?
Options:
A)1361
B)1481
C)1601
D)1721
E)1841
Rationale: x = 60 + 61 +...+ 80 = 21(70) = 1470
y = 11
x+y = 1481
The answer is B.
Answer: B
Question: A and B rent a pasture for 10 months. A put in 80 cows for 7 months. How many can B put in for the remaining 3 months, if he pays half as much again as A?
Options:
A)299
B)277
C)281
D)280
E)267
Rationale: 80* 7: x* 3 = 1:1 1/2
560: 3x = 2: 3
x = 280
Answer: D
Answer: D
Question: If 2a – b = 3c, where a, b, and c are non-zero integers, which of the following could be the average (arithmetic mean) of a and b, if the average must itself be an integer?
Options:
A)-2
B)-1
C)1
D)10
E)12
Rationale: Let's say Average of a & b is c
a+b/2=c
a+b= 2c
2a-b=3c
a+b=2c
--------
3a = 5c
a=5c/3
we can plug in all answer choices for average - " c " and see which one gives us an integer as "a" is also an integer.
5(-2)/3 = -10/3
5(-1)/3 = -5/3
5(1)/3 = 5/3
5(10)/3 = 50/3
5(12)/3 = 60/3= 20 ( Hence 12 is the correct answer)
ANSWER:E
Answer: E
Question: A group of n students can be divided into equal groups of 4 with 2 student left over or equal groups of 5 with 2 students left over. What is the sum of the two smallest possible values of n?
Options:
A)33
B)46
C)49
D)64
E)86
Rationale: 4x+2 = 5y+2...........ie: 4x-5y = 0
x,y must be >1 and y is even ie ( 2,4,6,..etc)
if y = 2 thus x is fraction
if y = 4 thus x =5 n =22
if y = 6 thus x = not possible fraction
if y =8 thus x = 10 n =42
n= 22+42= 64
D
Answer: D
Question: What is the number which when multiplied by 13 is increased by 180?
Options:
A)13
B)15
C)23
D)35
E)45
Rationale: 13 × 15 = 195
Answer: B
Answer: B
Question: Over a three-week period, the price of an ounce of gold increased by 10% in the first week, decreased by 20% in the following week, and increased by 10% in the third week. If the price of gold was G dollars per ounce at the beginning of the three weeks, what was the price at the end of the three weeks?
Options:
A)0.968G
B)0.978G
C)0.988G
D)0.998G
E)1.008G
Rationale: After 3 weeks, the price was 1.1*0.8*1.1*G=0.968G
The answer is A.
Answer: A
Question: A man can do a piece of work in 5 days, but with the help of his son he can do it in 3 days. In what
time can the son do it alone ?
Options:
A)712days
B)612days
C)512days
D)412days
E)None of these
Rationale: Explanation:
In this type of question, where we have one person work and together work done. Then we can easily
get the other person work just by subtracting them. As
Son's one day work =
(13−15)=(5−315)=215
So son will do whole work in 15/2 days
which is =
712days
Answer: A
Answer: A
Question: Solve the given two equations and find the inequality of X and Y. (a) 2x^2 + 11x + 14 = 0 and (b) 4y^2 + 12y +9 =0
Options:
A)If x>y
B)If x>=y
C)If x<y
D)If x<=y
E)x=y or relationship cannot be established
Rationale: Solution:-
X=-7/2 or -2
Y=-3/2
If x<y
C)
Answer: C
Question: Present ages of Sameer and Anand are in the ratio of 5 : 4 respectively. Eight years hence, the ratio of their ages will become 11 : 9 respectively. What is Anand's present age in years?
Options:
A)Can't be determined
B)40
C)27
D)64
E)None of these
Rationale: Explanation:
Let the present ages of Sameer and Anand be 5x years and 4x years respectively.
Then, (5x+8)/(4x+8)=11/9
⇒ 45x + 72 = 44x + 88⇒ 9(5x + 8) = 11(4x + 8)
⇒ 45x - 44x = 88 - 72
⇒ x = 16.
Anand's present age = 4x = 64 years.
Answer: D
Answer: D
Question: An error 2% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is:
Options:
A)4.00%
B)4.14%
C)4.04%
D)4.26%
E)4.27%
Rationale: 100 cm is read as 102 cm.
A1 = (100 x 100) cm2 and A2 (102 x 102) cm2.
(A2 - A1) = [(102)2 - (100)2]
= (102 + 100) x (102 - 100)
= 404 cm2.
Percentage error = 404	x 100	%	= 4.04%
100 x 100
C
Answer: C
Question: A man can row upstream at 25 kmph and downstream at 35 kmph, and then find the speed of the man in still water?
Options:
A)18 kmph
B)20 kmph
C)30 kmph
D)19 kmph
E)10 kmph
Rationale: US = 25
DS = 35
M = (35 + 25)/2 = 30
Answer:C
Answer: C
Question: The original price of a suit is $200. The price increased 30%, and after this increase, the store published a 30% off coupon for a one-day sale. Given that the consumers who used the coupon on sale day were getting 30% off the increased price, how much did these consumers pay for the suit?
Options:
A)$182
B)$191
C)$200
D)$209
E)$219
Rationale: Given the foregoing discussion, it may be obvious now the trap-mistake answer is (C). Even if you can’t remember the correct thing to do, at the very least, learn to spot the trap!
The multiplier for a 30% increases is 1 + 0.30 = 1.3, and the multiplier for a 30% decrease is 1 – 0.30 = 0.70, so the combined change is 1.3*0.7 = 0.91, 91% percent of the original, or a 9% decreases. Now, multiply $200*0.91 = $182. Answer = (A).
Answer: A
Question: Two trains are running in opposite directions with the same speed. If the length of each train is 240 m and they cross each other in 12 sec, then the speed of each train is?
Options:
A)72
B)89
C)36
D)34
E)23
Rationale: Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (240 + 240)/12 => x = 20
Speed of each train = 20 m/sec.
= 20 * 18/5 =72 km/hr.
Answer: Option A
Answer: A
Question: What is the banker's discount if the true discount on a bill of Rs.540 is Rs.90 ?
Options:
A)108
B)120
C)102
D)106
E)105
Rationale: Explanation:
Present Worth, PW = F - TD = 540 - 90 = Rs. 450
Simple Interest on the Present Worth = True Discount
Hence Simple Interest on 450 = 90 ------(Equation 1)
Simple Interest on the face value = Bankers Discount
=> Simple Interest on 540 = Bankers Discount
From Equation 1, Simple Interest on 450 = 90
Hence, Simple Interest on 540 = 90/450×540=540 = Rs. 108
=> Bankers Discount = Rs. 108
Answer: Option A
Answer: A
Question: Each of the integers from 0 to 8, inclusive, is written on a separate slip of blank paper and the ten slips are dropped into hat. If the slips are then drawn one at a time without replacement, how many must be drawn to ensure that the numbers on two of the slips drawn will have a sum of 10?
Options:
A)8
B)9
C)7
D)6
E)5
Rationale: You should consider the worst case scenario: if you pick numbers 0, 1, 2, 3, 4 and 5 then no two numbers out of these 6 add up to 10.
Now, the next, 7th number whatever it'll be (6,7, or 8) will guarantee that two number WILL add up to 10. So, 7 slips must be drawn to ensure that the numbers on two of the slips drawn will have a sum of 10
Answer: C
Answer: C
Question: The average weight of 10 men is increased by 1 ½ kg when one of the men who weighs 48 kg is replaced by a new man. What is the weight of the new man?
Options:
A) 80 kg
B) 63 kg
C) 70 kg
D) 75 kg
E) 85 kg
Rationale: Since the average has increased by 1.5 kg, the weight of the man who stepped in must be equal to 48+10x1.5
48+15=63 Kg
Ans: 'B'
Answer: B
Question: If an article is sold at 19% profit instead of 12% profit, then the profit would be Rs. 105 more. What is the cost price?
Options:
A)Rs. 1505
B)Rs. 1510
C)Rs. 1500
D)Rs. 1490
E)None of these
Rationale: Let the cost price of an article be Rs. x.
(19% of x) - (12% of x) = 105
19x/100 - 12x/100 = 105 => 7x = 105 * 100
=> x = 1500
Cost price = Rs. 1500
ANSWER:C
Answer: C
Question: .005/?= .01
Options:
A).5
B).05
C).005
D).0005
E)None of them
Rationale: Let .005/x = .01;
Then x = .005/.01
= .5/1
= .5
Answer is A
Answer: A
Question: 60% of x is greater than 1/3rd of x by 110.what is x?
Options:
A)100.5
B)200.5
C)300.5
D)350.5
E)412.5
Rationale: 6x/10-x/3=110
4x/15=110
x=412.5
ANSWER:E
Answer: E
Question: The grade point average of one third of the classroom is 69; the grade point average of the rest is 60. What is the grade point average of the whole class?
Options:
A)61.
B)63.
C)65
D)67
E)It depends how many people are there in the class.
Rationale: Let the number of students in class A be = X1 + X2 + ...... + A1 ( where A1 = remaining students )
Now the remaining avg of the students be A1 / T = 60
A1 = 60T ( we are not sure on the number of students , assuming it as T ).
A = X1 + X2 + ...... + A1 ( First set of students + remaining students).
One third of A students avg is 60.
A / 3 = 69
=> A = 207.
Now X1 + X2 + ...... + A1 = 207.
X1 + X2 + ...... = 207 - 60T.
We are not sure about the number of students in the remaining class + whole class and without that we can't solve this.
Answer: E is correct option.
Answer: E
Question: Two trains are running at 40 kmph and 20 kmph respectively in the same direction.Fast train completely passes a man sitting in the slower train in 9 seconds.What is the length of the fast train?
Options:
A)23 m
B)23 2/9 m
C)27m
D)46 m
E)50 m
Rationale: relative speed=20kmph=50/9m/sec
length of the train=50/9*9=50 m
ANSWER:E
Answer: E
Question: The seats in an Engineering college for Computer science, electronics and civil are in the ratio of 5 : 7 :8. There is a proportion to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats ?
Options:
A)2 : 3 : 4
B)6 : 7 : 8
C)6 : 8 : 9
D)6 : 8 : 7
E)none of these
Rationale: Originally, let the number of seats for Computer science, electronics and civil are 5x : 7x : 8x respectively.
Number of increased seats are (140% of 5x), (150% of 7x) and (175% of 8x)
7x : 21x/2 : 14x = 14x : 21x : 28x = 2 : 3 : 4.
ANSWER:A
Answer: A
Question: The average weight of 4 persons increases by 1.5 kg. If a person weighing 65 kg is replaced by a new person, what could be the weight of the new person?
Options:
A)71 kg
B)77 kg
C)76.5 kg
D)Data inadequate
E)None of these
Rationale: total weight increases = 4 × 1.5 = 6 kg
so the weight of new person = 65 + 6 = 71 kg
Answer A
Answer: A
Question: The numerator of a certain fraction is 8 less than the denominator. If 3 is added to the numerator and 3 is subtracted from the denominator, the fraction becomes 3/4. Find the original fraction?
Options:
A)3/11
B)4/11
C)5/11
D)6/13
E)7/13
Rationale: Explanation:
The denominator be P, the numerator will be (P - 8).
The fraction will be (P - 8)/P.
Adding 3 to the numerator and subtracting 3 from the denominator, (P - 8 + 3)/(P - 3) = 3/4.
(P - 5)/(P - 3) = 3/4
P = 20 - 9 => P = 11.
The fraction is: 3/11.
A)
Answer: A
Question: Which of the following leads to the correct mathematical solution for the number of ways that the letters of the word RADAR could be arranged to create a five-letter code?
Options:
A)5!/(2! x 2!)
B)6! − (3! + 2!)
C)6! − (3! × 2!)
D)6!/(3! + 2!)
E)6!/(3! × 2!)
Rationale: Number of letters in word 'RADAR' = 5.
The letters 'A' and 'R' appear 2 times and 2 times respectively in the word 'RADAR'.
Therefore the mathematical solution for number of ways that the letters of the word RADAR can be arranged to create five-letter code
= 5!/(2!*2!)
Answer:A
Answer: A
Question: The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 2 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?
Options:
A)23 years
B)22 years
C)25 years
D)26 years
E)27 years
Rationale: EXPLANATION
Let the average age of the whole team by x years.
11x â€“ (26 + 28) = 9(x -1)
11x â€“ 9x = 45
2x = 45
x = 22.
So, average age of the team is 22 years.
Answer B
Answer: B
Question: In covering a distance of 30 km, A takes 2 hours more than B. If A doubles his speed, then he would take 1 hour less than B. A's speed is:
Options:
A)5 km/hr.
B)3 km/hr.
C)1 km/hr.
D)7 km/hr.
E)9 km/hr.
Rationale: C
5 km/hr.
Let A's speed be X km/hr.
Then, 30/x - 30/2x = 3
6x = 30
x = 5 km/hr.
Answer: A
Question: One half of a two digit number exceeds its one third by 8. What is the sum of the digits of the number?
Options:
A)A)3
B)B)5
C)C)12
D)D)9
E)E)11
Rationale: x/2 – x/3 = 8 => x =48
4 + 8 = 12
ANSWER:C
Answer: C
Question: The ages of two persons differ by 16 years. If 5 years ago, the elder one be 5 times as old as the younger one, their present ages (in years) are respectively
Options:
A)20,20
B)20,10
C)25,9
D)30,10
E)None of these
Rationale: Explanation:
Let their ages be x and (x + 16) years.
5 (x - 5) = (x + 16 - 5) or 4x = 36 or x = 9.
Their present ages are 25 years and 9 years
Option C
Answer: C
Question: Patrick purchased 90 pencils and sold them at a loss equal to the selling price of 40 pencils. The cost of 90 pencils is how many times the selling price of 90 pencils?
Options:
A) 0.75
B) 0.8
C) 1
D) 1.2
E) 1.44
Rationale: Say the cost price of 90 pencils was $90 ($1 per pencil) and the selling price of 1 pencil was p.
Selling at a loss: 90 - 90p = 40p --> p = 9/13.
(cost price)/(selling price) = 1/(9/13) = 13/9 = 1.44.
Answer: E.
Answer: E
Question: Mandy drove from point A to point B at 60 Km/h. On her way back she drove at 80 Km/h and therefore her way back lasted one hour less. What is the distance (in Km) between A and B?
Options:
A)140.
B)200.
C)240.
D)300.
E)600.
Rationale: distance=speed*time
d1=s1t1
d2=s2t2
The distance from point A to point B is the same for each trip so,
d1=d2 and
t2=t1-1
thus,
s1t1=s2(t1-1)
60t1=80(t1-1)
t1=4
60*4= 240
Answer: C
Answer: C
Question: S is the infinite sequence S1 = 2, S2 = 22, S3 = 222,...Sk = Sk–1 + 2(10k–1). If p is the sum of the first 30 terms of S, what is the eighth digit of p, counting right to left from the units digit?
Options:
A)1
B)2
C)4
D)6
E)9
Rationale: C
Sum of unit digits of first 30 terms = 60
Sum of tens digits of first 30 terms = 58
Sum of thousands digits of first 30 terms = 56
and so on..
p1 = 0
p2 = (6+58) = 4
p3 = (6+56) = 2
p4 = (6+54) = 0
p5 = (6+52) = 8
p6 = (5+50) = 5
p7 = (5+48) = 3
p8 = (5+46) = 1
ANSWER : A
Answer: A
Question: In a certain apartment building, there are one-bedroom and two-bedroom apartments. The rental prices of the apartment depend on a number of factors, but on average, two-bedroom apartments have higher rental prices than do one-bedroom apartments. Let M be the average rental price for all apartments in the building. If M is $1,000 higher than the average rental price for all one-bedroom apartments, and if the average rental price for all two-bedroom apartments is $9,000 higher that M, then what percentage of apartments in the building are two-bedroom apartments?
Options:
A)50%
B)40%
C)20%
D)30%
E)10%
Rationale: Ratio of 2 Bedroom Apartment: 1 Bedroom Apartment = 1000 : 9000 -----> 1 : 9
Let total number of Apartments be X
No. of 2 Bedroom Apartment = (1 / 10) * X
percentage of apartments in the building are two-bedroom apartments ---->
(1/10) * 100 ---> 10%
Answer : E
Answer: E
Question: Find the number of square tiles to cover the floor of a room measuring 10 m * 12 m leaving 0.25 m space around the room. A side of square tile is given to be 50 cms?
Options:
A)277
B)476
C)437
D)257
E)212
Rationale: 9 1/2 * 11 1/2 = 1/2 * 1/2 * x => x = 437
Answer:C
Answer: C
Question: Find the value for x from below equation: x/3=-2?
Options:
A)-6
B)-4
C)4
D)5
E)-5
Rationale: 1. Multiply both sides by 3:
x*3/3= -2/3
2. Simplify both sides:
x = -6
A
Answer: A
Question: If m=9^(x−1), then in terms of m, 3^(4x−5) must be which of the following?
Options:
A)m/3
B)9m
C)9m^2
D)m^2/3
E)m^2/9
Rationale: m = 9 ^ (X-1)
m = 3 ^ (2x-2)
m^2 = 3 ^ (4x-4)
m^2/3 = 3 ^ (4x-5)
Answer D
Answer: D
Question: In the first half of the 20th century, the population of a particular country increased by 200 percent. In the second half of the century, the population increased by 300 percent. What was the percent increase for the 20th century as a whole?
Options:
A) 500%
B) 600%
C) 800%
D) 1100%
E) 1200%
Rationale: Say initially population was 100.
What is 200% of 100? It is 200/100 * 100 = 200.
An increase of 200% means the new population became 100 + 200 = 300
What is 300% of 300? It is 300/100 * 300 = 900
An increase of 300% means the new population now is 300 + 900 = 1200
So from 100, the population increased to 1200 i.e. an increase of 1100.
1100 is what percent of 100?
1100 = x/100 * 100
i.e. it is 1100% D
Answer: D