divelab/Sys2Bench huggingface dataset:
Question: Shreehari has 500 chocolates in his self. He eats 10% of the chocolates per month. How many chocolates will he have after 2 months?
Options:
A)450
B)400
C)405
D)410
E)425
Rationale: Formula :
( After =100 denominator
Ago = 100 numerator)
500 Ã— 90/100 Ã— 90/100 = 405
C
Answer: C
Question: A, B and C started a business with capitals of Rs.6000, Rs.8000, and Rs.10000 respectively. At the end of the year, the profit share of B is Rs1000. The difference between the profit shares of A and C is
Options:
A)Rs. 400
B)Rs. 450
C)Rs. 500
D)Rs. 550
E)Rs. 650
Rationale: Ratio of investments of A,B and C is 6000 : 8000 : 10000 = 3 : 4 : 5.
And also given that, Profit share of ‘B’ is Rs.1000.
Now required difference is 5 – 3 = 2 parts.
Therefore, Required difference = 2/4 (1000) = Rs.500.
ANSWER:C
Answer: C
Question: A shopkeeper labeled the price of his articles so as to earn a profit of 20% on the cost price. He then sold the articles by offering a discount of 5% on the labeled price. What is the actual percent profit earned in the deal?
Options:
A)24%
B)20%
C)17%
D)18%
E)None of these
Rationale: Explanation:
Let the CP of the article = Rs.100.
Then labeled price = Rs.120.
SP = Rs.120- 5% of 120 = Rs.120-6 = Rs.124.
Gain = Rs.124 â€“ Rs.100 = Rs.24
Therefore, gain/profit percent = 24%.
Answer: Option A
Answer: A
Question: A set consist of 2l-1 element. What is the number of subsets of this set which contain at most l-1 elements?
Options:
A)2^(2l-2)
B)2^(2l) - 2
C)2^(2l) -1
D)2^(2l)
E)2^(2l-1)
Rationale: I used l=3, so then we have
5!/2!3! + 5!/4!1! + 5!/0!5!
10 + 5 + 1 = 16
So our target is 16
Now replace in answer choices
A gives us 2^4 = 16
Hence A is the correct option
Read carefully it says at most so keep in mind that picking a small number such as 3 will help you save time since you have to list fewer outcomes
Avoid 2 since you will get 1 arrangement (l-1) and may be risky since 1 is a number with certain unique properties
Answer: A
Question: During the months May through October, Teddy the bear quintuples his weight, and during the months November through April, Teddy loses 100 pounds. If at the beginning of November 1973, Teddy's weight was m pounds, what was Teddy's weight in pounds by the end of April 1976?
Options:
A)25m - 1300
B)25m - 1200
C)5m - 1300
D)5m - 1200
E)5m
Rationale: Nov ' 73 = m
April ' 74 = m - 100
Oct ' 74 = 5m - 300
April' 75 = 5m - 400
Oct' 75 = 25m - 1200
April'76 = 25m - 1300
Hence answer will be (A) 25m - 1300
Answer: A
Question: If X and Y are positive integers, X - 5 is divisible by 4 and Y - 1 is divisible by 4, all of the following could be the value of X - Y Except?
Options:
A)0
B)8
C)4
D)7
E)24
Rationale: X-5 = 4Y
=> P = 4Y + 5 = 5,9,13,17,21,25,29,33,37,41,45
Y-1 = 4X
=> Y = 4X + 1 = 1,5,9,13,17,21,25,29,33,37,41
0=5-5
8=13-5
4=5-1
24=45-21
So , we can see that all the answer choices are possible here except D
Answer: D
Question: A committee of three people is to be chosen from 7 married couples. What is the number of different committees that can be chosen if two people who are married to each other cannot both serve on the committee?
Options:
A)16
B)39
C)26
D)30
E)49
Rationale: Total no of ways of choosing a committee = 7C3 = 35
No of ways to choose first couple = 7C1 = 7
No of ways to choose 1 person from remaining 12 = 12C1 = 12
Total number of ways of choosing a married couple to be in the same committee = 7*12=84
So, no of ways not choosing a married couple = 84-35 =49
ANS:E. 49
Answer: E
Question: The average price of an antique car increases over the years. If from 1990 to 1996, the price of the car increased by 13% and from 1996 to 2001 it increased by 20%, what is the price of the car in 2001 if the price in 1990 was $11,500?
Options:
A)$15,594.
B)$15,322.
C)$14,786.
D)$14,543.
E)$12,988.
Rationale: Whenever you have a question in which a value is increased by x% and then increased by y% then the overall effective increase = (x + y + xy/100 ) %
The effective increase = 13 + 20 + (13×20/100) = 35.6%
This is a little more 33% or 1/3 the original value.
THE QUICKEST WAY TO SOLVE THIS QUESTION IS TO USE APPROXIMATION.
11500 + 1/ 3 (12000) = 15500
Therefore option A is the answer.
I selected 12000 because it's value is a little more 11500 and it's easier to divide by 3 ( ie to calculate 1/3 or 33%).
Answer: A
Question: Each of seven different locks has a matching key. The keys are randomly reassigned to the locks. What is the probability that exactly two of the keys fit the locks to which they are reassigned?
Options:
A)1/8
B)1/6
C)1/49
D)3/8
E)1/2
Rationale: I was just going over probability questions.
can some one explain me what's wrong in my approach here.
Probability of choosing one right key out of 7 is 1/7.
Probability of choosing another right key is 1/7.
since the question is asking for 2 right keys , probability is multiplication of both = 1/7 * 1/7 = 1/49.
Ans C
Answer: C
Question: Which of the following options represents an approximate value for the question mark (?) in the following equation?
87.542 + 62.511 × 3.2 + ? = 805.925
Options:
A)913.4
B)918.4
C)911.4
D)988.4
E)958.4
Rationale: 87.542 + 62.511 × 3.2 + ? = 805.925
or, ? = 805.925 – 87.542 + 62.511 × 3.2
? = 805.925 – 87.542 + 200.0352
≈ 918.4
Answer B
Answer: B
Question: Which of these must the factor Q of the product of four consecutive even integers:-
1) 48
2) 64
3) 96
4) 192
5) 80
Options:
A)1,2 only
B)Q=2,3 only
C)Q=1,2,3 only
D)Q=1,2,3,4 only
E)All of them
Rationale: Let the four variables be a< b< c< d.
Assume a worst case scenario where the a equal to a prime number (hence odd).
therefore
a = divisible by 1
b = a + 1 (divisible by 2)
c = a + 3 (divisible by 3)
d = a + 4 (divisible by 4)
therefore
each answer choice must be divisible Q by 2 x 3 x 4 = 24
only 80 is not divisible. Therefore answer = D
Answer: D
Question: A five-year promissory note with a face value of $3500, bearing interest at 11% compounded semiannually, was sold 21 months after its issue date to yield the buyer 10% compounded quarterly.What amount was paid for the note
Options:
A)$4336.93
B)4336.99
C)4336.96
D)4336.92
E)4336.91
Rationale: Explanation:
i=j/m
Maturity value = PV (1 + i)^n
Term = 5 years - 21 months= 3.25 years
Price paid = FV(1+ i )^-n
Answer: A) 4336.93
Answer: A
Question: What is the height of a circular cone?
I. The area of that cone is equal to the area of a rectangle whose length is 33 cm.
II. The area of the base of that cone is 154 sq. cm.
Options:
A)I alone sufficient while II alone not sufficient to answer
B)II alone sufficient while I alone not sufficient to answer
C)Either I or II alone sufficient to answer
D)Both I and II are not sufficient to answer
E)Both I and II are necessary to answer
Rationale: EXPLANATION
II gives the value of r.
But, in I, the breadth of rectangle is not given.
So, we cannot find the surface area of the cone.
Hence, the height of the cone cannot be determined.
Correct answer is (D).
Answer: D
Question: A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that exactly three bulbs are good.
Options:
A)20/69
B)20/63
C)20/61
D)20/66
E)20/63
Rationale: Explanation:
Required probability =
= (10 * 4)/126 = 20/63
Answer: B
Answer: B
Question: If the rectangular screen of a computer monitor is designed to have a length of x inches, a perimeter of P inches and an area of A square inches, which of these equations must be true?
Options:
A)x^2 + Px + A = 0
B)x^2 - Px - 2A = 0
C)2x^2 + Px + 2A = 0
D)2x^2 - Px - 2A = 0
E)2x^2 - Px + 2A = 0
Rationale: Notice that we can discard options A, and C right away. The sum of 3 positive values Cannot be 0.
Now, assume:
Length =x = 1 inchand width = 1 inch;
Perimeter =P = 4 inches;
Area =A = 1 square inches.
Plug the values of x, P, and A into the answer choices: only for E 2x^2 - Px + 2A = 2 - 4 + 2 = 0.
Answer: E.
Answer: E
Question: In a class of 50 students, 20 play Golf, 15 play Cricket and 11 play Football. 7 play both Golf and Cricket, 4 play Cricket and Football and 5 play Golf and football. If 18 students do not play any of these given sports, how many students play exactly two of these sports?
Options:
A)45
B)12
C)35
D)10
E)77
Rationale: Notice that7 play both Golf and Cricket does not mean that out of those 7, some does not play Football too. The same for Cricket/Football and Golf/Football.
[color=#ffff00]{Total}={Golf}+{Cricket}+{Football}-{HC+CH+HF}+{All three}+{Neither}For more checkADVANCED OVERLAPPING SETS PROBLEMS
[/color]
50=20+15+11-(7+4+5)+{All three}+18 --> {All three}=2;
Those who play ONLY Golf and Cricket are 7-2=5;
Those who play ONLY Cricket and Football are 4-2=2;
Those who play ONLY Golf and Football are 5-2=3;
Hence, 5+2+3=10 students play exactly two of these sports.
Answer: D.
Answer: D
Question: A family made a down payment of $75 and borrowed the balance on a set of encyclopedias that cost $500. The balance with interest was paid in 23 monthly payments of $20 each and a final payment of $9. The amount of interest paid was what percent of the amount borrowed?
Options:
A)10.3%
B) 12.5%
C) 13%
D) 11%
E) 10%
Rationale: borrowings = 500-75 = 425
total pmt = 23x20 + 9 = 469
so int = 469 - 425 = 44
interest in terms of borrowing = 44/425 = 10.3%
Answer is A
Answer: A
Question: There were two candidates in an election. Winner candidate received 62% of votes and won the election by 324 votes. Find the number of votes casted to the winning candidate?
Options:
A)456
B)837
C)912
D)1200
E)1400
Rationale: W = 62% L = 38%
62% - 38% = 24%
24% -------- 324
62% -------- ? => 837
ANSWER:B
Answer: B
Question: A family pays $800 per year for an insurance plan that pays 70 percent of the first $1,000 in expenses and 100 percent of all medical expenses thereafter. In any given year, the total amount paid by the family will equal the amount paid by the plan when the family's medical expenses total how much?
Options:
A)$1,000
B)$1,200
C)$1,400
D)$1,800
E)$2,200
Rationale: Assuming the medical expenses are $1000 or more, the family pays $800 + $300 = $1100.
The total amount paid by insurance plan for the first $1000 of expenses is $700.
The insurance will pay another $400 when the medical expenses are $1400.
The answer is C.
Answer: C
Question: When positive integer N is divided by positive integer J, the remainder is 10. If N/J = 134.08, what is value of J?
Options:
A)125
B)56
C)78
D)112
E)175
Rationale: When a number is divided by another number, we can represent it as : Dividend = Quotient * Divisor + Remainder
So, Dividend/Divisor = Quotient + Remainder/Divisor
Given that N/J = 134.08
Here 134 is the quotient.
Given that Remainder = 10
So, 134.08 = 134 + 10/J
So, J = 125 ANS A
Answer: A
Question: A young girl counted in the following way on the fingers of her left hand. She started collang the thumb 1, the index finger 2, the middle finger 3, the ring finger 4, the little finger 5, then reversed direction calling the ring finger 6, the the middle finger 7, the index finger 8, the thumb 9 then back to the index finger for 10, the middel finger for 11, and so on. She counted up to 1995. She ended on her
Options:
A)a) thumb
B)b) the index finger
C)c) the middle finger
D)d) the ring finger
E)e) the little finger
Rationale: Notice the pattern. The thumb lansd up at numbers 1,9,17,25,33,... so every 8th number
By this patter the thumb is also at number 1993 (multiple of 8 + 1)
Hence 1995 has to be the middle finger
Answer is (C)
Answer: C
Question: if samaira wallet have 10rs. note,50 rs. note,2000 rs.note.if 10rs. is 3/5 part of his money and 50rs. is 1/5 part of his money.if he has 8000 money consist of 2000 rs.calculate total money in samaira wallet?
Options:
A)18000
B)32000
C)30000
D)40000
E)35000
Rationale: if samaira have total money is x.
part of money in 2000 rs.=(1-(3/5+1/5))=1-4/5=1/5
x*1/5=8000,x=40,000rs.
answer D
Answer: D
Question: A vessel contains 20 liters of a mixture of milk and water in the ratio 3:2. 10 liters of the mixture are removed and replaced with an equal quantity of pure milk. If the process is repeated once more, find the ratio of milk and water in the final mixture obtained?
Options:
A)9:1
B)9:6
C)9:2
D)9:9
E)9:3
Rationale: Milk = 3/5 * 20 = 12 liters, water = 8 liters
If 10 liters of mixture are removed, amount of milk removed = 6 liters and amount of water removed = 4 liters.
Remaining milk = 12 - 6 = 6 liters
Remaining water = 8 - 4 = 4 liters
10 liters of pure milk are added, therefore total milk = (6 + 10) = 16 liters.
The ratio of milk and water in the new mixture = 16:4 = 4:1
If the process is repeated one more time and 10 liters of the mixture are removed, then amount of milk removed = 4/5 * 10 = 8 liters.
Amount of water removed = 2 liters.
Remaining milk = (16 - 8) = 8 liters.
Remaining water = (4 -2) = 2 liters.
The required ratio of milk and water in the final mixture obtained
= (8 + 10):2 = 18:2 = 9:1.
Answer: A
Answer: A
Question: A five-digit number divisible by 3 is to be formed using numerical 0, 1, 2, 3, 4 and 5 without repetition. The total number Q of ways this can be done is:
Options:
A)122
B)210
C)216
D)217
E)225
Rationale: We should determine which 5 digits from given 6, would form the 5 digit number divisible by 3.
We have six digits: 0, 1, 2, 3, 4, 5. Their sum=15.
For a number to be divisible by 3 the sum of the digits must be divisible by 3. As the sum of the six given numbers is 15 (divisible by 3) only 5 digits good to form our 5 digit number would be 15-0={1, 2, 3, 4, 5} and 15-3={0, 1, 2, 4, 5}. Meaning that no other 5 from given six will total the number divisible by 3.
Second step:
We have two set of numbers:
1, 2, 3, 4, 5 and 0, 1, 2, 4, 5. How many 5 digit numbers can be formed using these two sets:
1, 2, 3, 4, 5 --> 5! as any combination of these digits would give us 5 digit number divisible by 3. 5!=120.
0, 1, 2, 4, 5 --> here we can not use 0 as the first digit, otherwise number won't be any more 5 digit and become 4 digit. So, desired # would be total combinations 5!, minus combinations with 0 as the first digit (combination of 4) 4! --> 5!-4!=4!(5-1)=4!*4=96
120+96=216=Q
Answer: C.
Answer: C
Question: A corporation paid $7 million in federal taxes on its first $50 million of gross profits and then $30 million in federal taxes on the next $150 million in gross profits. By approximately what percent did the ratio of federal taxes to gross profits increase from the first $50 million in profits to the next $150 million in profits?
Options:
A)6%
B)14%
C)20%
D)23%
E)43%
Rationale: Initial ratio of federal taxes to gross profits : 7/50 = 0.14
Final ratio : 30/150 = 0.2
Thus, the percentage change : (0.2-0.14)/0.14*100 = 6/14*100 = 3/7*100 = Just less than 50 % .
ANSWER:E
Answer: E
Question: Two airplanes, one from Atlanta to New York and the other from New York to Atlanta, start simultaneously. After they meet, the airplanes reach their destinations after 16 hours and 4 hours respectively The ratio of their speeds is
Options:
A)2 : 3
B)4 : 3
C)4 : 2
D)1 : 2
E)None
Rationale: Solution
Let us name the planes
as A and B.	= (A'S speed) : (B's speed)
=âˆšb : âˆša
= âˆš16 : âˆš4
= 4 : 2
Answer C
Answer: C
Question: If the roots of a quadratic equation are 20 and -7, then find the equation?
Options:
A)x2 - x - 15 = 0
B)x2 - 12x - 50 = 0
C)x2 - 13x - 140 = 0
D)x2 - 4x - 40 = 0
E)x2 - 23x - 150 = 0
Rationale: Explanation:
Any quadratic equation is of the form
x2 - (sum of the roots)x + (product of the roots) = 0 ---- (1)
where x is a real variable. As sum of the roots is 13 and product of the roots is -140, the quadratic equation with roots as 20 and -7 is: x2 - 13x - 140 = 0.
Answer C
Answer: C
Question: Rectangle A has sides a and b, and rectangle B has sides c and d. If a/c=b/d=3/5, what is the ratio of rectangle A’s area to rectangle B’s area?
Options:
A)5/3
B)9/5
C)9/25
D)3/5
E)25/9
Rationale: The area of rectangle A is ab.
c=5a/3 and d=5b/3.
The area of rectangle B is cd=25ab/9.
The ratio of rectangle A's area to rectangle B's area is ab / (25ab/9) = 9/25.
The answer is C.
Answer: C
Question: The third proportional to 3 and 6 is?
Options:
A)8
B)7
C)12
D)5
E)3
Rationale: (6*6)/3 = 12
Answer:C
Answer: C
Question: At what rate percent of simple interest will a sum of money double itself in 12 years?
Options:
A)8 1/8
B)8 1/3
C)8 1/0
D)8 1/2
E)8 1/1
Rationale: Let sum = x. Then, S.I. = x.
Rate = (100 * S.I.) / (P * T) = (100 * x) / (x * 12)
= 25/3 = 8 1/3 %
Answer: B
Answer: B
Question: Let A be the event that a randomly selected two digit number is divisible by 10 and let B be the event that a randomly selected two digit number is divisible by 5. What is P(A and B)?
Options:
A)1/50
B)1/30
C)1/15
D)1/10
E)1/5
Rationale: P(A and B) = 1/10*1/5 = 1/50
The answer is A.
Answer: A
Question: Mr. John invested in Fund A and Fund B. The total amount he invested, in both funds combined, was $100,000. In one year, Fund A paid 23% and Fund B paid 17%. The interest earned in Fund B was exactly $200 greater than the interest earned in Fund A. How much did Mr. John invest in Fund A?
Options:
A) $32,000
B) $36,000
C) $40,000
D) $41,000
E) $42,000
Rationale: A+B=100,000
0.17B=0.23A+200
Take away decimals first: 17B=23A+20,000
Isolate first equation to solve for A (your goal): B=100,000-A
Plug in for B:
17(100,000-A)=23A+20,000
1,700,000-17A=23A+20,000
1,680,000=40A
1,680,000/40=A
A=42,000=Answer Choice E
Answer: E
Question: Out of 15 students in a class, 9 are wearing blue shirts, 3 are wearing green shirts, and 3 are wearing red shirts. Four students are to be selected at random. What is the probability that at least one is wearing a green shirt?
Options:
A)28/61
B)38/71
C)48/81
D)58/91
E)68/101
Rationale: Total possible ways to choose 4 students out of 15 = 15C4 = 1365
The number of ways to choose 4 students with no green shirts = 12C4 = 495
P(no green shirts) = 495/1365 = 33/91
P(at least 1 green shirt) = 1 - 33/91 = 58/91
The answer is D.
Answer: D
Question: Find the simple interest on Rs. 68,000 at 16 2/3% per annum for 9 months.
Options:
A)Rs.8500
B)Rs.8000
C)Rs.7500
D)Rs.7000
E)Rs.6500
Rationale: P = Rs.68000,R = 50/3% p.a and T = 9/12 years = 3/4years.
S.I. = (P*R*T)/100 = Rs.(68,000*(50/3)*(3/4)*(1/100))
= Rs.8500
Answer is A.
Answer: A
Question: Which of the following numbers is divisible by 8?
Options:
A)10021
B)17511
C)26778
D)18520
E)26711
Rationale: 18520. This is the only option with last two digits divisible by 8
Answer:D
Answer: D
Question: At Didymus Corporation, there are just two classes of employees: silver and gold. The average salary of gold employees is $60,000 higher than that of silver employees. If there are 120 silver employees and 160 gold employees, then the average salary for the company is how much higher than the average salary for the silver employees?
Options:
A)$24,000
B)$28,000
C)$32,000
D)$36,000
E)$40,000
Rationale: The answer should be -> D. $36,000
Answer: D
Question: Mike took a bus from home to market, that travels at 30 kmph. While walking back at 6 kmph,
halfway through, he suddenly realized he was getting late and he cycled back the remaining distance in 20 kmph. Find the average speed.
Options:
A)21.2 kmph
B)12.1 kmph
C)23.4 kmph
D)20.4 kmph
E)none of these
Rationale: Let the distance be 2x(one way)
Time taken by bus = 2x/30, by walking =x/6, by cycling = x/20 hours
:. Average speed = Total Distance/Total time
= 6x / x/15 + x/6 + x/20
= 6 *60 / 4+10+3
= 21.2
ANSWER:A
Answer: A
Question: If the speed of X meters per hour is equivalent to the speed of Y kilometers per hour, what is Y in terms of X? (1 kilometer=1000 meters)
Options:
A)0.1X
B)0.01X
C)0.001X
D)0.0001X
E)0.005X
Rationale: X meters per hour -->
--> 1X meters per hour(as there are 3,600 seconds in one hour);
--> X/1,000=0.001X kilometers per hour (as there are 1,000 meters in one kilometer).
Answer: C.
Answer: C
Question: A certain car increased its average speed by 5 miles per hour in each successive 5-minute interval after the first interval. If in the first 5-minute interval its average speed was 2 miles per hour, how many miles did the car travel in the third 5-minute interval?
Options:
A)1.0
B)1.5
C)2.0
D)2.5
E)3.0
Rationale: In the third time interval the average speed of the car was 2+5+5=12 miles per hour;
In 5 minutes (1/12 hour) at that speed car would travel 12*1/12=1 miles.
Answer: A.
Answer: A
Question: 150 ml of 30% sulphuric acid was added to approximate 400 ml of 12% sulphuric acid solution. Find the approximate concentration W of the acid in the mixture?
Options:
A)1/2
B)1/3
C)1/4
D)1/6
E)1/5
Rationale: Do not need any computation
30%-----------21%---------12%
if volume of both sol. were equal the concentration W would be 21%=1/5, but 12% is more than 3 times
only possibility is 1/6
D
Answer: D
Question: The slant height of a right circular cone is 10 m and its height is 8 m. Find the area of its curved surface.
Options:
A)30 m2
B)40 m2
C)50 m2
D)60 m2
E)80 m2
Rationale: l = 10 m,
h = 8 m.
So, r = l2 - h2 = (10)2 - 82 = 6 m.
Curved surface area = rl = ( x 6 x 10) m2 = 60 m2.
Answer: Option D
Answer: D
Question: David obtained 76, 65, 82, 67 and 85 marks (out in 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks?
Options:
A)65
B)69
C)72
D)75
E)None of these
Rationale: Solution
Average =
(76+65+82+67+85 / 5)	=(375 / 5)
= 75.
Answer D
Answer: D
Question: x and y are positive integers of V. If 1/x + 1/y < 2, which of the following must be true?
Options:
A) x + y > 4
B) xy>1
C) x/y + y/x < 1
D) (x - y)^2 > 0
E) None of the above
Rationale: Answer is B:
1/X + 1/Y < 2
The maximum value of 1/X is 1 because if X equals any other number greater than one it will be a fraction. The same is true with 1/Y.
So 1/X and 1/Y will always be less than 2 as long as both X and Y are not both equal to one at the same time.
Another way of putting it is:
X*Y>1.B
Answer: B
Question: What is the sum of 100 consecutive integers from -49 inclusive, in a increasing order?
Options:
A)-29
B)50
C)-30
D)30
E)60
Rationale: From -49 to -1 --> 49 nos.
zero --> 1 number
from +1 to +49 --> 49 nos.
When we add up nos. from -49 to + 49 sum will be zero. Total 99 nos will be added.
100th number will be 50.
Sum of these 100 nos. = 50.
B is the answer.
Answer: B
Question: We bought 85 hats at the store. Blue hats cost $6 and green hats cost $7. The total price was $550. How many green hats did we buy?
Options:
A)A)36
B)B)40
C)C)41
D)D)42
E)E)44
Rationale: Let B be the number of blue hats and let G be the number of green hats.
B+G=85.
B=85-G.
6B+7G=550.
6(85-G)+7G=550.
510-6G+7G=550.
G=550-510=40.
The answer is B.
Answer: B
Question: A vessel is filled with liquid, 3 parts of which are water and 5 parts of syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?
Options:
A)1 / 3
B)1 / 4
C)1 / 5
D)1 / 7
E)None
Rationale: Suppose the vessel initially contains 8 litres of liquid. Let x littres of this liquid be replaced with water.
Quantity of water in new mixture = (3 - 3x/8 + x) litres.
Quantity of syrup in new mixture = (5 - 5x/8) litres.
(3 - 3x/8 + x) = (5 - 5x/8) = 5x + 24 = 40 - 5x
=› 10x = 16 =› x = 8/5
So, part of the mixture replaced = (8/5 x 1/8) = 1/5.
Answer C
Answer: C
Question: A fruit seller had some apples. He sells 40% apples and still has 420 apples. Originally, he had:
Options:
A)700
B)680
C)720
D)760
E)660
Rationale: Apples Sold = 40%
So Remaining Apples = 60%
60% = 420
Full (100%) = (100/60) X 420
= 700
answer :A
Answer: A
Question: Suppose you want to buy three loaves of bread that cost $0.75 each
and a jar of peanut butter that costs $7. A jar of jelly is $2.75, but you
donâ€™t need any jelly. You have $17. How much money will you have left
over?
Options:
A)$7.75
B)$7.50
C)$3.50
D)$4.50
E)$5.50
Rationale: The jelly is extra information. 17.00 â€“ 3 x 0.75 â€“ 7.00 =
17.00 â€“ 2.25 â€“ 7.00 = 7.75.
You have $7.75 left.
correct answer A
Answer: A