divelab/Sys2Bench huggingface dataset:
Question: Solve below question 6x - 1 = -13
Options:
A)-8
B)-2
C)-5
D)-4
E)1
Rationale: 1. Subtract 1 from both sides: 6x - 1 + 1 = -13 + 1 2. Simplify both sides: 6x = -12 3. Divide both sides by 6: 4. Simplify both sides: x = -2 B
Answer: B
Question: Cars M and N are approaching each other on the same highway. Car M is moving at 55 mph northbound and Car N is moving at 65 mph southbound. At 2:00 pm, they are approaching each other and 195 miles apart. Eventually they pass each other. At what clock time are they moving away from each other and 45 miles apart?
Options:
A) 4:00 pm
B) 4:07 pm
C) 4:54 pm
D) 5:21 pm
E) 6:00 pm
Rationale: Total distance, which should be covered by both cars is 195+45=240 miles.
Let t be the time so the equation will be 55t+65t=240 thus,
t=2 hours
Answer: A
Answer: A
Question: in a party 65% of women wearing black tshirts 50% of the total people in party wearing black t shirts ,then what is the ratio of male is to female.35% of the man wearing black t shirs. There are 120 people in the party.
Options:
A)1:1
B)1:2
C)1:3
D)1:4
E)1:5
Rationale: suppose male =m,female=f,
so, 65% of f+35% of m=50% (f+m)
solving,
65% of f +35% of m=50% of f +50%of m
15% of f=15% of m
f/m=15%/15% =1:1
ANSWER:A
Answer: A
Question: The sum and the product of two numbers are 25 and 144 respectively, the difference of the number is?
Options:
A)4
B)2
C)5
D)7
E)3
Rationale: x + y = 25
xy = 144
(x- y)2 = (x + y)2 â€“ 4xy
(x- y)2 = 625 â€“ 576 => (x â€“ y) = 7
Answer D
Answer: D
Question: This is how Edward’s Lotteries work. First, 8 different numbers are selected. Tickets with exactly 5 of the 8 numbers randomly selected are printed such that no two tickets have the same set of numbers. Finally, the winning ticket is the one containing the 5 numbers drawn from the 8 randomly. There is exactly one winning ticket in the lottery system. How many tickets can the lottery system print?
Options:
A) 9P6
B) 8P3
C) 9C9
D) 8C6
E) 8C5
Rationale: since we have to select random 5 numbers from 8 and they all are distinct. i think it should be 8C5or E
Answer: E
Question: A garment company declared 15% discount for whole sale buyers. Mr Sachdev bought garments from the company for 25,000 after getting discount. He fixed up the selling price of garments in such a way that he earned a profit of 8% on original company price. What is the approximate total selling price?
Options:
A)28,000
B)29,000
C)32,000
D)28,500
E)29,500
Rationale: Original S.P. of company = 25,000×100/85= 29411.8
∴ Approximate total S.P = 29411.8×108/100 = 32,000
Answer C
Answer: C
Question: One-third of 1206 is what percent of 134 ?
Options:
A)3
B)30
C)300
D)None of these
E)cannot be determined
Rationale: Answer
Let one-third of 1206 is N% of 134.
∵ 1206/3 = (N x 134)/100
∴ N = (402 x 100) / 134 = 300
Correct Option: C
Answer: C
Question: Winson traveled the entire 60 miles trip. If he did the first 10 miles of at a constant rate 20 miles per hour and the remaining trip of at a constant rate 48 miles per hour, what is the his average speed, in miles per hour?
Options:
A)20mph
B)24mph
C)30mph
D)32mph
E)40mph
Rationale: Average speed=sum of distance/sum of time. If he travelled the first 10 miles at 20 miles/hr, it would take 0.5 hr. For the remaining trip, if he went at 48 miles/1hr, it would take 1 hour. Then, the average speed is 60miles/(0.5+1)hrs=40miles/1hr.
Therefore, the answer is E.
Answer: E
Question: If $1000 is invested at x percent simple annual interest for n years, which of the following represents the total amount of interest, in dollars, that will be earned by this investment in the n years?
Options:
A)1000n(x/100)
B)10,000(x/100)^n
C)10,000n(x/100)
D)10,000(1+x/100)^n
E)10,000n(1+x/100)
Rationale: I think answer D is for compound interest (which i assumed)
and answer A is for simple interest because it is not compounding.
Answer: A
Question: Raj invested an amount of Rs.17400 for two years. Find the rate of compound interest that will fetch him an amount of Rs.1783.50 at the end of two years?
Options:
A)4
B)3
C)2
D)5
E)6
Rationale: Let the rate of interest be R% p.a.
17400[1 + R/100]2 = 17400 + 1783.50
[1 + R/100]2 = (17400 + 1783.50)/17400
= 1 + 1025/10000 = 1 + 41/400
= 441/400 = [21/20]2
[1 + R/100] = 21/20
R/100 = 1/20
Therefore R = 5
Answer: D
Answer: D
Question: A lacrosse team plays games only against the other five teams in its league and always in the following order: Smiley, Ranch, Broad, Thomas and Jake. If the team’s final game of the season is against Thomas, which of the following could be the number of games in the team’s schedule?
Options:
A)34
B)72
C)56
D)24
E)81
Rationale: IMO 'D' is the answer.
Matches will be in multiples of 5x+4. The answer that satisfies this condition is D
Answer: D
Question: The profit earned by selling an article for Rs 900 is double the loss incurred when the same article is sold for Rs.490. At what price should the article be sold to make 25% profit?
Options:
A)715
B)469
C)400
D)750
E)560
Rationale: Let C.P be Rs. x900 - x = 2(x - 450)=> x = Rs.600 C.P = 600 gain required is 25% S.P = [(100+25)*600]/100 = Rs.750 Answer : D
Answer: D
Question: R campers fished for 7 hours. If m of the campers caught 2 fish apiece and the rest caught a combined total of n fish, how many fish did the R campers catch per hour?
Options:
A)2m + n(R-m)
B)(2m + n(R-m))/3
C)(2m + n(m-R))/3
D)(2m + n)/7
E)(2m + n)/R
Rationale: m of the campers caught 2 fish apiece in 7 hours --> total fish caught by m campers = 2m;
The rest caught a combined total of n fish.
Total fish caught in 7 hours = 2m+n --> per hour (2m+n)/7.
Answer: D.
Answer: D
Question: The number of multiples of 10 which are less than 1000, which can be written as a sum of four consecutive integers is
Options:
A)22
B)50
C)88
D)76
E)18
Rationale: Answer: Option A
Sol:
We can write 10 = 1 + 2 + 3 + 4. So we have to find how many multiples of 10 can be written in this manner.
Let the first of the four numbers be n. So
n + (n+1) + (n+2) + (n+3) = 10k
4n + 6 = 10k
2n + 3 = 5k
n = 5k−325k−32 = 2k – 1 + k–12k–12
So n is intezer for k = an odd number. So for k = 1, 3, 5, .... 99 we can write a number as a sum of four consecutive intezers.
So there are 50 numbers.
Answer:B
Answer: B
Question: A certain car traveled twice as many miles from Town A to Town B as it did from Town B to Town C. From Town A to Town B, the car averaged 12 miles per gallon, and from Town B to Town C, the car averaged 14 miles per gallon. What is the average miles per gallon that the car achieved on its trip from Town A through Town B to Town C?
Options:
A)13
B)13.5
C)14
D)14.5
E)15
Rationale: Ans is E
Given d_ab = 2*d_bc
let d_ab = d and d_bc = x so d=2x
for average miles per gallon = (d+x)/((d/12)+(x/14)) = 15 (formula avg speed = total distance/ total time)
Answer: E
Question: In how many ways a committee, Consisting of 2 men and 3 women can be formed from 8 men and 10 women?
Options:
A)2660
B)3360
C)11760
D)5040
E)720
Rationale: To choose Required number of ways to form a committee:
Select 2 men out of 8 men and 3 women out of 10 women.
That is 8C2 * 10C3.
8C2=8!/2!*6!=28
10C3=10!/3!*7!=120
The Required number of ways=28*120=3360
B
Answer: B
Question: A can give B 100 meters start and C 200 meters start in a kilometer race. How much start can B give C in a kilometer race?
Options:
A)111.12
B)111.18
C)111.15
D)111.13
E)191.18
Rationale: A runs 1000 m while B runs 900 m and C runs 800 m.
The number of meters that C runs when B runs 1000 m,
= (1000 * 800)/900 = 8000/9 = 888.88 m.
B can give C = 1000 - 888.88 = 111.12 m.
Answer: A
Answer: A
Question: Vijay says that his weight is between 75kg and 85 kg. But his younger sister disagrees with Vijay and says that his weight is greater than 70kg but less than 80 kg. Vijay’s mother says that his weight cannot be greater than 78 kg. If all the three predictions are correct, what is the average of different probable weights of Vijay?
Options:
A)76.5
B)92.9
C)82.3
D)28.3
E)28.1
Rationale: Explanation:
Vijay’s opinion: - 75 < Vijay’s age < 85
Sister’s opinion: - 72 < Vijay’s age < 82
Mother’s opinion: - Vijay’s age < 78
As all the above three conditions are true, the values satisfying them are 76 & 77.
Average value = (76 + 77)/ 2 = 76.5
ANSWER: A
Answer: A
Question: In a bank 60 percent employees are men.80%men and 20%women belong to retirement plan.what percent of people belong to retirement plan?
Options:
A)55%
B)57%
C)56%
D)58%
E)59%
Rationale: 60% employees are men thus 40% are women.
80% of 60 % men is 48% and 20% of 40% women is 8%. so total is 48+8=56%.
Thus answer is 56%
ANSWER:C.
Answer: C
Question: A contractor isengaged for 30days on the condition that he receives Rs.25 for eachday he works & fined Rs.7.50 for each day is absent. He gets Rs.425 in all. For how many days was heabsent?
Options:
A)8
B)10
C)15
D)17
E)21
Rationale: 30 * 25 = 750
425
-----------
325
25 + 7.50 = 32.5
325/32.5 =
B
Answer: B
Question: On a dinner date, a couple is sitting around a circular table. Their seating arrangement is considered different only when the position of the couple is different relative to each other. what is the total number of possible seating arrangement for the couple?
Options:
A)a.5
B)b.10
C)c.24
D)d.1
E)e.120
Rationale: for 2 people seating arrangement around a circular table = (2-1)!
= 1!
= 1
OA is D
Answer: D
Question: Evaluate combination
12C4
Options:
A)10000
B)1000
C)10
D)495
E)0
Rationale: Explanation:
nCn=1
nCr=n!/r!(n-r)!
12C4=12!/4!(12-4)!=495
Option D
Answer: D
Question: What is the least number that should be added to 1076, so the sum of the number is divisible by 23?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: (1076 / 23) gives a remainder 18 so we need to add 5.
The answer is E.
Answer: E
Question: A man sells a horse for Rs.800 and loses something, if he had sold it for Rs.980, his gain would have been double the former loss. Find the cost price of the horse?
Options:
A)288
B)277
C)208
D)860
E)281
Rationale: CP = SP + 1CP = SP - g
800 + x = 980 - 2x
3x = 180 => x = 60
CP = 800 + 60 = 860
Answer:D
Answer: D
Question: Dick and Jane each saved $2,500 in 1989. In 1990 Dick saved 9 percent more than in 1989, and together he and Jane saved a total of $5200. Approximately what percent less did Jane save in 1990 than in 1989?
Options:
A)1%
B)4%
C)6%
D)8%
E)9%
Rationale: 1990
Dick saved = $ 2725
Jane saved = $ 2475 (jane saved $25 less than she did the prior year)
Jane saved approximately $25/$2500 (1%) less in 1990
Answer: A
Answer: A
Question: The ratio of the number of boys and girls in a college is 7 : 8. If the percentage increase in the number of boys and girls be 20% and 10% respectively, what will be the new ratio?
Options:
A)8 : 9
B)17 : 18
C)21 : 22
D)25 : 22
E)Cannot be determined
Rationale: Explanation:
Originally, let the number of boys and girls in the college be 7x and 8x respectively.
Their increased number is (120% of 7x) and (110% of 8x).
=>(120/100 X 7X) and (110/100 x 8x)
The required ratio =(42x/5 :44x /5)=21:22.
ANSWER IS C
Answer: C
Question: A number Y is chosen at random from the numbers 1, -3, -1, 0, 1, 2, 3. What is the probability that |X|<3?
Options:
A)1/3
B)2/3
C)3/7
D)3/11
E)None
Rationale: |X||X| can take 7 values.
To get |X|<2|X|<2 ( i.e., −2<x<+2−2<x
⇒ P(|X|<2)= Favourable CasesTotal CasesP(|X|<2)= Favourable CasesTotal Cases
= 3/7
C
Answer: C
Question: A certain sum amounts to Rs.2250 in 5 years and Rs.2550 in 7 years. Find the rate % per annum?
Options:
A)10%
B)11%
C)9%
D)8%
E)7%
Rationale: 5 --- 2250
7 --- 2550
--------------
2 --- 300
N = 1 I = 150 R = ?
P = 2250 - 750= 1500
150 = (1500*1*R)/100
R = 10%
Answer: A
Answer: A
Question: Among 200 students, 56% study sociology, 44% study mathematics and 40% study biology. If 30% of students study both mathematics and sociology, what is the largest possible number of students who study biology but do not study either mathematics or sociology?
Options:
A)60
B)90
C)120
D)172
E)188
Rationale: I would just like to add a bit of explanation after the step where you calculate that the number of students studying both M and S = 60
Using your analysis:
We see that the total number of students who study either Maths or Sociology = 88 + 112 - 60 = 140
So, in the image we know that the number of students in the zone with the black boundary = 140
Let's assume the number of students who studyonlybiology to beb(this is the number that we have to maximize)
And, let's assume the number of students who study none of the three subjects, that is the number of students in the white space =w
Since the total number of students = 200, we can write:
140 +b+w= 200
Or,b+w= 200 - 140 = 60
That is,b= 60 -w
So, the maximum value ofbwill happen forw= 0
This is how we get, the maximum value ofb= 60
A
Answer: A
Question: In a sequence of 40 numbers, each term, except for the first one, is 7 less than the previous term. If the greatest term in the sequence is 282, what is the smallest term in the sequence?
Options:
A)2
B)-2
C)0
D)8
E)9
Rationale: Which term is the greatest? The first or the last? It is given to you that every term is 7 less than the previous term. Hence as you go on, your terms keep becoming smaller and smaller. The first term is the greatest term.
An = 282 + (40 - 1)*(-7)
An = 282 - 273 = 9
E
Answer: E
Question: power windows: 60%
anti-lock brakes: 25%
CD player: 55%
The table above shows the number of vehicles at Bill's car dealership that have certain features. No vehicle has all three features, but 10% have power windows and anti-lock brakes, 15% have anti-lock brakes and a CD player, and 22% have power windows and a CD player. What percent of the vehicles at Bill's car dealership have a CD player but no power windows or anti-lock brakes?
Options:
A)25
B)18
C)11
D)3
E)0
Rationale: Answer:B
Were looking for the number of cars with a CD player but no other features. We know that 40% of the cars have a CD player, 15% have a CD player and anti-lock brakes, while 22% have a CD player and power windows. Since no car has all three features, those account for all of the possibilities except for what were looking for.
If a car has a CD player, it must either have anti-lock brakes, power windows, or no other features. Since the total of cars with a CD player is 55%, we can set up the following equation:
55=15+22+x
x=18, choiceB.
Answer: B
Question: A student multiplied a number by 3/5 instead of 5/3. What is the percentage error in the calculation?
Options:
A)34%
B)44%
C)54%
D)64%
E)None of these
Rationale: Explanation :
Let, the number be x.
According to the question, the error is :-
=>(5x/3)−(3x/5).
=>16x/5.
Hence, the percentage error is :-
=>16x/15 /5x/3∗100.
=>64%.
Answer : D
Answer: D
Question: If a certain coin is flipped, the probability that the coin will land heads is 1/2. If the coin is flipped 6 times, what is the probability that it will land heads up on the first 4 flips but not on the last 2 flips?
Options:
A)1/8
B)1/16
C)1/32
D)1/64
E)1/128
Rationale: P(HHHHTT) = 1/2*1/2*1/2*1/2*1/2*1/2 = 1/64
The answer is D.
Answer: D
Question: What is the least number of digits (including repetitions) needed to express 10^200 in decimal notation?
Options:
A)a) 201
B)b) 100
C)c) 101
D)d) 1000
E)e) 1001
Rationale: 10^n is a decimal number with a 1 followed by n zeros.
So 10^200 will include 200 0's + 1 digit for 1 = 201
So the answer is A
Answer: A
Question: 00
a3
+4b
___
96
If a and b represent positive single digits in the correctly worked computation above, what is the value of the two digit integer ab?
Options:
A)43
B)35
C)45
D)43
E)46
Rationale: 0+3+b=6
b=3
0+a+4=8
a=4
ab=43
ans=A
Answer: A
Question: Father is aged three times more than his son Ronit. After 8 years, he would be two and a half times of Ronit's age. After further 8 years, how many times would he be of Ronit's age?
Options:
A)2 times
B)2 1/2 times
C)2 3/4 times
D)3 times
E)4 times
Rationale: Let Ronit's present age be x years. Then, father's present age =(x + 3x) years = 4x years.
(4x + 8) = 5/2(x + 8)
8x + 16 = 5x + 40
3x = 24
x = 8.
Hence, required ratio = (4x + 16)/(x + 16)	= 48/24 = 2.
ANSWER:A
Answer: A
Question: A is twice as good a workman as B and they took 7 days together to do the work B alone can do it in.
Options:
A)22
B)77
C)21
D)77
E)88
Rationale: WC = 2:1
2x + x = 1/7
x = 1/21 => 21 days
Answer: C
Answer: C
Question: A die is thrown three times. Events X and Y are defined as below:
X : 4 on the third throw
Y : 6 on the first and 5 on the second throw
What is the probability of X given that Y has already occurred.
Options:
A)1/6
B)1/7
C)1/8
D)2/7
E)2/11
Rationale: The sample space has 216 outcomes.
Now X =
(1,1,4) (1,2,4) ... (1,6,4) (2,1,4) (2,2,4) ... (2,6,4)
(3,1,4) (3,2,4) ... (3,6,4) (4,1,4) (4,2,4) ...(4,6,4)
(5,1,4) (5,2,4) ... (5,6,4) (6,1,4) (6,2,4) ...(6,5,4) (6,6,4)
Y = {(6,5,1), (6,5,2), (6,5,3), (6,5,4), (6,5,5), (6,5,6)}
and X n Y = {(6,5,4)}.
Now P(Y) = 6/216
and P (X n Y) = 1/216
Then P(X|Y) = (1/216)/(6/216) = 1/6.
A
Answer: A
Question: If A:B = 1/6: 1/3 B:C = 1/2:1/3 then A:B:C?
Options:
A)9:6:6
B)9:6:8
C)9:18:12
D)9:6:4
E)9:6:1
Rationale: A:B = 1/6:1/3 = 3:6
B:C = 1/2:1/3 = 3:2
--------------------
A:B:C = 9:18:12
Answer:C
Answer: C
Question: Yesterday it took Robert 6 hours to drive from City A to City B. Today it took Robert 4.5 hours to drive back from City В to City A along the same route. If he had saved 30 minutes in both trips, the speed for the round trip would be 90 miles per hour. What is the distance between city A and city B?
Options:
A) 90
B) 120
C) 150
D) 440
E) 430
Rationale: 2d/90 = 9.5 ( because time = 6 + 4.5 - 1 hrs)
=> d = 430
Answer - E
Answer: E
Question: What annual installment will discharge a debt of Rs. 1092 due in 3 years at 12% simple interest?
Options:
A)315
B)345
C)325
D)335
E)None of them
Rationale: Let each Installment be Rs. x
Then, ( x+ ((x*12*1)/100)) + (x+ ((x*12*2)/100) ) + x = 1092
=((28x/25) + (31x/25) + x) = 1092  (28x+31x+25x)=(1092*25)
x= (1092*25)/84 = Rs.325.
Therefore,	Each installment = Rs. 325.
Answer is C.
Answer: C
Question: Suzie’s Discount Footwear sells all pairs of shoes for one price and all pairs of boots for another price. On Monday the store sold 22 pairs of shoes and 16 pairs of boots for $580. On Tuesday the store sold 8 pairs of shoes and 32 pairs of boots for $800. How much more do pairs of boots cost than pairs of shoes at Suzie’s Discount Footwear?
Options:
A)$10.50
B)$12.50
C)$11.50
D)$16.50
E)$9.50
Rationale: Let X be pair of shoes and Y be pair of boots.
22x+16y = 580 ... eq1
8x +32y = 800....eq 2.
Now multiply eq 1 by 2 and sub eq 2.
44x = 1160
8x = 800.
36x = 360 => x = 10.
Sub x in eq 2.... we get 80 + 32y = 800... then we get 32y = 720 then y = 22.50
Differenece between X and Y is 12.50
Answer : B
Answer: B
Question: 20% of a number is added to 120, the result is the same number. Find the number?
Options:
A)300
B)288
C)270
D)129
E)150
Rationale: (20/100) * X + 120 = X
x+600 = 5x
4x= 600
x= 150
Answer : E
Answer: E
Question: P has $32 more than what Q and R together would have had if both B and C had 1/6 of what P has. How much does P have?
Options:
A)$44
B)$48
C)$52
D)$56
E)$60
Rationale: P = (2/6)*P+32
(4/6)*P=32
P=48
The answer is B.
Answer: B
Question: What is the difference between the place value and face value of 3 in the numeral 1375?
Options:
A)280
B)290
C)297
D)333
E)340
Rationale: place value of 3 = 3 * 100 = 300
face value of 3 = 3
300 - 3 = 297
C)
Answer: C
Question: The sum of two numbers is 12 and the product of the numbers is 35. Find sum of the squares of that numbers.
Options:
A)84
B)87
C)96
D)79
E)74
Rationale: Let a and b be the two numbers(a+b)^2=a^2+2ab+b^2Given (a+b)=12ab=35So, 12^2=a^2+b^2+2*35144=a^2+b^2+70a^2+b^2=74Ans E
Answer: E
Question: What least number must be subtracted from 3832 so that the remaining number is divisible by 5?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: On dividing 3832 by 5, we get remainder = 2.
Required number be subtracted = 2
ANSWER:B
Answer: B
Question: Rajan borrowed Rs.4000 at 5% p.a compound interest. After 2 years, he repaid Rs.2210 and after 2 more year, the balance with interest. What was the total amount that he paid as interest?
Options:
A)635.5
B)635.57
C)635.512
D)635.51
E)635.53
Rationale: 4000
200 ---- I
200
10 ---- II
---------------
4410
2210
--------
2000
110 ---- III
110
5.50 ---- IV
-----------
2425.50
2210
-----------
4635.50
4000
----------
635.50
Answer: A
Answer: A
Question: A trader mixes 26 kg of rice at Rs. 20 per kg with 30 kg of rice of other variety at Rs. 36 per kg and sells the mixture at Rs. 30 per kg. His profit percent is:
Options:
A)No profit, no loss
B)5%
C)8%
D)10%
E)14%
Rationale: C.P. of 56 kg rice=Rs.(26x20 + 30x36)= Rs.(520 + 1080)=Rs. 1600.
S.P. of 56 kg rice = Rs. (56 x 30) = Rs. 1680.
Gain =(80/1600)	x 100	% = 5%.
answer :B
Answer: B
Question: A pipe can fill a cistern in 20 minutes whereas the cistern when fill can be emptied by a leak in 28 minutes. When both pipes are opened, find when the cistern will be full?
Options:
A)76 minutes
B)29 minutes
C)70 minutes
D)17 minutes
E)98 minutes
Rationale: 1/20 - 1/28 = 1/70
70 minutes
Answer: C
Answer: C
Question: Every year Taylor goes to the same carnival, and he attempts to shoot a basketball into a small hoop, hoping that he will win a ten-foot tall teddy bear. If the probability that Taylor does not make a basket is 2/5, what is the probability that Taylor makes exactly one basket in three tries?
Options:
A)36/125
B)36/120
C)30/125
D)30/140
E)36/140
Rationale: Probability of basket = 3/5
Probability of no basket = 2/5
Required probability=3* 3/5*2/5*2/5
=36/125
A is the answer .
Answer: A
Question: If the operation € is defined for all x and y by the equation x € y = 2*x*y, then 9 € (4 € 5) =
Options:
A)80
B)720
C)760
D)840
E)860
Rationale: working inside out,
(4 € 5) = 2*4*5 = 40
9 € 40 = 2*9*40 = 720
Hence, answer is B
Answer: B
Question: A shopkeeper sells his goods at cost price but uses a faulty meter that weighs 800 grams. Find the profit percent.
Options:
A)100/17%
B)100/23%
C)100/19%
D)100/4%
E)None of these
Rationale: Explanation:
(100 + g) / (100 + x) = True measure / Faulty measure
x = 0
true measure = 1000
faulty measure = 800
100 + g / 100 + 0 = 1000 / 800
100+g = 5/4*100
g = 100/4 %
ANSWER: D
Answer: D
Question: An advertising agency finds that, of its 150 clients, 115 use Television, 110 use Radio and 130 use Magazines. Also, 85 use Television and Magazines, 75 use Television and Radio, 95 use Radio and Magazines. How many use all the three?
Options:
A)56
B)70
C)50
D)98
E)95
Rationale: Total=150
Television=115
Radio=110
Magazine=130
All the three =150-115-110-130+85+75+95=50
ANSWER C
Answer: C
Question: An even and an odd integer are multiplied together. Which of the following numbers could not be the square of their product?
Options:
A)196
B)400
C)441
D)484
E)900
Rationale: 441 = 3^2*7^2 so it can not be the square of an even number multiplied by an odd number.
The answer is C.
Answer: C
Question: For 6-digit integer 46x,y12, when x and y are drawn at random from {3,5,8}, what is the probability W that the integer drawn is divisible by 8?
* A solution will be posted in two days.
Options:
A)1/6
B)1/3
C)1/2
D)2/3
E)5/6
Rationale: In general, the remainder divided by integer n is the same as the remainder that up to tens of n is divided by 8.
Thus, in order for 46,x,y12 to be divided by 8, y12 should be divided by 8.
Amongst 3,5,8, 3 and 5 can be divided by 8.
Therefore,W= two out of three can be divided and the answer is D.
Answer: D
Question: 31 of the scientists that attended a certain workshop were Wolf Prize laureates, and 16 of these 31 were also Nobel Prize laureates. Of the scientists that attended that workshop and had not received the Wolf prize, the number of scientists that had received the Nobel Prize was 3 greater than the number of scientists that had not received the Nobel Prize. If 50 of the scientists attended that workshop, how many of them were Nobel Prize laureates?
Options:
A)A)11
B)B)18
C)C)24
D)D)27
E)D)36
Rationale: lets solve by creating equation..
W = 31..
Total = 50..
Not W = 50 -31= 19..
Now let people who were neither be x, so out of 19 who won Nobel = x+3..
so x+x+3=19 or x=8..
so who won Nobel but not Wolf = x+3 = 11..
But people who won BOTH W and N = 13..
so total who won N = 11+16 = 27..
D
Answer: D