divelab/Sys2Bench huggingface dataset:
Question: In a recent election, Ms. Robbins received 8,000 votes cast by independent voters, that is, voters not registered with a specific political party. She also received 20 percent of the votes cast by those voters registered with a political party. If N is the total number of votes cast in the election and 40 percent of the votes cast were cast by independent voters, which of the following represents the number of votes that Ms. Robbins received?
Options:
A)0.06N + 3,200
B)0.1N + 7,200
C)0.4N + 7,200
D)0.12N + 8,000
E)0.06N + 8,000
Rationale: I will go with option D
According to question 40 percent of total votes (N) cas were cast by independent voters. This implies 60 percent of N are voters that belong to political party. And she received 8000 votes from independent voters and 20 percent from registered voters (i.e 0.2 * 0.6 * N = 0.12N). Hence total votes = 8000 + 0.12N ....option D
Answer: D
Question: The ratio of flour to water to sugar in a recipe is 8:4:3. The ratio in a new recipe calls for a doubling of the ratio of flour to water from the original recipe and a halving of the ratio of flour to sugar. If the new recipe calls for 2 cups of water, how much sugar is required?
Options:
A)6
B)5
C)4
D)3
E)2
Rationale: The ratio of flour to water is 16:4=4:1.
The ratio of flour to sugar is 4:3.
The new ratio of flour to water to sugar is 4:1:3
If we need 2 cups of water, then we need 6 cups of sugar.
The answer is A.
Answer: A
Question: It takes 8 high school students, working at identical constant individual rates, 10 hours to paint a certain house. At what time will the house be fully painted if 8 students start painting at 9:00 am and one student, working at the same rate, is added per hour starting at 3:00 pm?
Options:
A)5:40 pm
B)5:50 pm
C)6:00 pm
D)6:10 pm
E)6:20 pm
Rationale: Each student paints at a rate of 1/80 of the house per hour.
In 6 hours, the 8 students can paint 48/80 of the house.
From 3 pm to 4 pm, 9 students paint another 9/80 for a total of 57/80.
From 4 pm to 5 pm, 10 students paint another 10/80 for a total of 67/80.
From 5 pm to 6 pm, 11 students paint another 11/80 for a total of 78/80.
12 students can paint the remaining 2/80 of the house in 2/12 of an hour = 10 minutes.
The house is completed at 6:10 pm.
The answer is D.
Answer: D
Question: If w=1 and (w-b)/c = 1 which of the following is NOT a possible value of b?
Options:
A)-2
B)-1
C)0
D)1
E)2
Rationale: Equation is:
(w-b)/c = 1 where w = 1
so plug in 1 for w and look at it again
(1-b)/c = 1
now C can be anything we want, so if b = -2 we can plug it in and make it work
(1-(-2))/c = 1
3/c = 1
c = 3 and it works
HOWEVER, if we have a 0 in the numerator there isn't a number on earth that makes 0/C = 1
(1-1)/c = 1
0/c = 1
there aren't any matches for C to make this true
B cannot be 1.
Answer is D
Answer: D
Question: Round off the given number to nearest hundreds
8866
Options:
A)8700
B)8800
C)9000
D)8600
E)8900
Rationale: the given number is 8866
its tens digit is 6. so replace each of the tens and ones digit by 0 and increase the hundreds digit by 1 to get the rounded off number to the nearest hundred.
correct answer (E)
Answer: E
Question: A football team lost 5 yards and then gained 11. What is the team's progress?
Options:
A)2
B)4
C)5
D)6
E)8
Rationale: For lost, use negative. For gain, use positive.
Progress = -5 + 11 = 6 yards
D
Answer: D
Question: John throws a coin until a series of six consecutive heads or three consecutive tails appears. What is the probability that the game will end after the seventh throw?
Options:
A)1/64
B)2/16
C)3/16
D)7/16
E)9/16
Rationale: Let's consider the routes that would lead to ending the game on the fourth toss. In order to be a win at that point, tosses #2#3#4 would all have to be the same, either H or T, and in order for the game NOT to end on the third toss, the first toss would have to be different from the other four. Thus, the only two possible sequences are
H-T-T-T-T-T ----> P = (1/2)^7= 1/128
T-H-H-H-H-H ----> P = (1/2)^7= 1/128
Either one of these would satisfy the condition, so we could have one or the other. OR means add in probability.
1/128 + 1/128 = 2/128 = 1/64
Answer(A).
Answer: A
Question: The combined salaries of three brothers is $135,000. Mr. Big earns twice what Mr. Small earns, and Mr. Middle earns 1 1/2 times what Mr. Small earns. What is the smallest salary of the three brothers?
Options:
A) 20,000
B) 22,000
C) 25,000
D) 30,000
E) 40,000
Rationale: Mr. Small = x;
Mr. Middle = 3/2*x;
Mr. Big = 2x.
x + 3/2*x + 2x = 135 --> x=30
Answer: D
Answer: D
Question: Q-1) Of the 84 parents who attended a meeting at a
school, 25 volunteered to supervise children during
the school picnic and 11 volunteered both to supervise
children during the picnic and to bring refreshments to
the picnic. If the number of parents who volunteered
to bring refreshments was 1.5 times the number of
parents who neither volunteered to supervise children
during the picnic nor volunteered to bring
refreshments, how many of the parents volunteered to
bring refreshments?
Options:
A)25
B)36
C)38
D)45
E)42
Rationale: i used the following formula: total = group1 + group2 + neither - both
using the information from the question stem, we have:
84 total people
25 who supervise (group1)
x who neither supervise nor bring refreshments
1.5x people who bring refreshments (group2)
11 who supervise AND bring refreshments (both)
therefore...
84 = 25 + 1.5x + x - 11
solving, we get x = 28
since we want the value of those who bring refreshments AND supervise:
1.5(28) = 42
answer is E
Answer: E
Question: A school has received 50% of the amount it needs for a new building by receiving a donation of $400 each from people already solicited. People already solicited represent 40% of the people from whom the school will solicit donations. How much average contribution is requited from the remaining targeted people to complete the fund raising exercise?
Options:
A)$200
B)$177.78
C)$100
D)$277.78
E)$377.78
Rationale: Let the amount school needs = X
Let total people school plans to solicit = T
School has received 60 % of X => (3/5) X
People already solicited = 40% of T => (2/5) T
Now, as per the information given in the question :
(3/5)X = $400 . (2/5) . T --------------------------- 1
Remaning Amount is 40 % i.e ( 2/5 ) X ------because school has already received 60%
And the remaining people are 60 % i.e (3/5) .T -----because 40% of the people are already solicited
So, average contribution required from the remaining targeted people is
(2/5) X = (Amount required) . (3/5) . T ----------------------------------- 2
Divide eqn 1 by eqn 2
Amount required = $277.78
D
Answer: D
Question: A sum of Rs. 2678 is lent into two parts so that the interest on the first part for 8 years at 3% per annum may be equal to the interest on the second part for 3 years at 5% per annum. Find the second sum?
Options:
A)1629
B)1648
C)2677
D)2986
E)2679
Rationale: (x*8*3)/100 = ((2678 - x)*3*5)/100
24x/100 = 40170/100 - 15x/100
39x = 40170 => x = 1030
Second sum = 2678 â€“ 1030 = 1648
Answer:B
Answer: B
Question: Each of three investments has a 20% of becoming worthless within a year of purchase, independently of what happens to the other two investments. If Simone invests an equal sum in each of these three investments on January 1, the approximate chance that by the end of the year, she loses no more than 1/3 of her original investment is
Options:
A)90%
B)80%
C)70%
D)60%
E)40%
Rationale: Since amount invested is same for all 3 , and probability of investment turning worthless is 20%, the required probability is
80%×80%×80% + 20%×80%×80×\frac{3!}{2!}
=89.6%
Answer A
Answer: A
Question: If xy not equal 0 and x^2*y^2 -xy = 20, which of the following could be y in terms of x?
I. 1/2x
II. -5/x
III. 4/x
Options:
A)II
B)II and III
C)I &II
D)III
E)IV
Rationale: x2y2 - xy = 20
x2y2-xy-20 = 0
(xy-4)(xy+5)=0
xy = 4 or xy=-5
y = 4/x or y = -5/x
II and III only
B
Answer: B
Question: The price of the jewel, passing through three hands, rises on the whole by 74%. If the first and the second sellers 20% and 25% profit respectively find the percentage profit earned by the third seller.
Options:
A)20
B)10
C)16
D)25
E)30
Rationale: Let the original price of the jewel be $ p and let the profit earned by the third seller be x% Then, (100+x)% of 125% of 120% of P =174% Of P ((100+X)/100*125/100*120/100*P)=(174/100*P)
==> (100+X)=(174*100*100)/(125*120)=116=>X=16%
Answer C
Answer: C
Question: Write 230,000,000,000 in scientific notation.
Options:
A)2.3 x 10*11*eleventh
B)2.03 x 10*11*eleventh
C)23 x 10*11*eleventh
D)23.0 x 10*11*eleventh
E)230 x 10*11*eleventh
Rationale: a × 10 n , where a is a real number such that 1 ≤ |a| < 10 and n is an integer.
230,000,000,000 = 2.3 × 100,000,000,000 = 2.3 × 10 *11*
correct answer A)2.3 x 10*11*eleventh
Answer: A
Question: A man bought 40 shares of Rs. 60 at 7 discount, the rate of dividend being 1212%The rate of interest obtained is
Options:
A)13.64%
B)15.5%
C)14%
D)14.15%
E)14.95%
Rationale: Explanation :
Face Value of a share = Rs.60
He bought each share at Rs.60 - Rs.7 = Rs.53
Number of shares = 40
Dividend = 12 1/2%=25/2%
Dividend per share = 60×25/2×100=Rs.7.5
Total dividend = (40 × 7.5)
ie, He got a dividend of (40 × 7.5) for an investment of Rs.(40 × 53)
Interest obtained = 40×7.5×100/40×53=14.15%
Answer : Option D
Answer: D
Question: In a chocolate company, 30 men completed two-fifth of a piece of work in 28 days. How many more men should be employed to finish the rest of the work in 35 more days?
Options:
A)32
B)36
C)6
D)8
E)7
Rationale: Explanation :
Solution: Let the total number of men be x. work done = 2/5, remaining work = (1-2/5) = 3/5.
More work, more men (DP)
More days, less men (IP)
work 2/5 : 3/5
} : : 30 : x
days 35 : 28
.'. (2/5 * 35 * x) = 3/5 * 28 * 30
=> x = 36.
Answer : C
Answer: C
Question: How many digits will be there to the right of the decimal point in the product of 95.75 and .02554 ?
Options:
A)5
B)6
C)7
D)8
E)9
Rationale: EXPLANATION
Sum of decimal places = 7.
Since the last digit to the extreme right will be zero (since 5 x 4 = 20), so there will be 6 significant digits to the right of the decimal point.
Answer B
Answer: B
Question: A retailer bought a shirt at wholesale and marked it up 80% to its initial price of $45. By how many more dollars does he need to increase the price to achieve a 100% markup?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: x is the buy price. x+80%x = 1,8x is the sale price = 45 so x, the buy price becomes 45/1,8=25
%100 mark up means x+100%x=2x so 50. 50-45=5
ANSWER:E
Answer: E
Question: In a group of 80 children and 10 youngsters, each child got sweets that are 15% of the total number of children and each youngster got sweets that are 25% of the total number of children. How many sweets were there?
Options:
A)1160
B)1100
C)1080
D)1210
E)None of these
Rationale: Number of sweets each child got = 15% of 80 = 15/100 * 80 = 12.
Number of sweets 80 children got = 80 * 12 = 960.
Number of sweets each youngster got = 25% of 80 = 25/100 * 80 = 20.
Number of sweets 10 youngsters got = 10 * 20 = 200.
Total number of sweets = 960 + 200 = 1160.
ANSWER:A
Answer: A
Question: If Teena is driving at 55 miles per hour and is currently 7.5 miles behind Yoe, who is driving at 40 miles per hour in the same direction then in how many minutes will Teena be 15 miles ahead of Yoe?
Options:
A)15
B)60
C)75
D)90
E)105
Rationale: This type of questions should be solved without any complex calculations as these questions become imperative in gaining that extra 30-40 seconds for a difficult one.
Teena covers 55 miles in 60 mins.
Yoe covers 40 miles in 60 mins
So teena gains 15 miles every 60 mins
Teena need to cover 7.5 +15 miles.
Teena can cover 7.5 miles in 30 mins
Teena will cover 15 miles in 60 mins
So answer 30+60= 90 mins.D
Answer: D
Question: How many 2x2x2 cubes could fit in a box of 7x9x4?
Options:
A)31
B)32
C)30
D)33
E)29
Rationale: The answer is A) 31. A 2x2x2 cube has an area of 8. A 7x9x4 box has an area of 252. If you divide 252 by 8, you get 31.5. Since that means you can only fit 31 entire cubes in the box, the answer is 31.
Answer: A
Question: A and B’s salaries together amount to Rs. 4,000. A spends 95% of his salary and B spends 85% of his. If now their savings are the same, what is B’s salary?
Options:
A)2777
B)1000
C)2789
D)2776
E)2881
Rationale: (5/100) A = (15/100) B
A = 3B
A + B = 1000
4B = 1000 => B = 1000
Answer B
Answer: B
Question: If population of certain city increases at the rate of 2%. If population in 1981 was 138915, then population in 1978 was?
Options:
A)12,0000
B)130000
C)261000
D)130903
E)12690
Rationale: Explanation:
X * (102/100) * (102/100) * (102/100) = 138915
X = 138915/1.061208
X = 130902.70=130903
Answer: Option D
Answer: D
Question: Which of the following fractions is greater than 8/10 and less than 9/10?
1. 8/10 2. 9/10 3. 1/2 4.8/9 5. 1/3 6. 19/10
Options:
A)8/9
B)8/10
C)9/10
D)1/2
E)19/10
Rationale: 8/10 = 0.8, 9/10 = 0.9, 1/2= 0.5, 8/9= 0.88, 1/3= 0.33, 19/10= 1.9.
Clearly, 0.88 lies between 0.80 and 0.90.
Therefore, 8/9 lies between 8/10 and 9/10.
Answer is A.
Answer: A
Question: For her customer feedback score, Jess wants to average at or above an 8.0 rating. For the month of June, she received the following scores: 7, 8, 8, 7, 9, 9, 6, 6, 8 and 7. By what percent did she fall short of her goal?
Options:
A) 4%
B) 5%
C) 8%
D) 3.75%
E) 12%
Rationale: Expected minimum rating = 8
Deviation from the expected minimum rating = (-1 + 0 + 0 - 1 + 1 + 1 - 2 - 2 + 0 - 1)/10 = -3/10 = -0.3
Current rating is 0.3 less than 8.
Percentage = (0.3/8)*100 = 3.75%
Answer: D
Answer: D
Question: What is the length of a bridge (in meters), which a train 140 meters long and travelling at 45 km/h can cross in 30 seconds?
Options:
A)205
B)220
C)235
D)250
E)265
Rationale: speed = 45 km/h = 45000 m / 3600 s = 25/2 m/s
In 30 seconds, the train can travel 25/2 * 30 = 375 meters
375 = length of train + length of bridge
length of bridge = 375 - 140 = 235 meters
The answer is C.
Answer: C
Question: Gwen drove an average speed of 15 miles per hour for the first 40 miles of a tripthen at a average speed of 30 miles/hr for the remaining 40 miles of the trip if she made no stops during the trip what was Gwen's avg speed in miles/hr for the entire trip
Options:
A)35
B)20
C)45
D)50
E)55
Rationale: Avg. speed = total distance / total time
Total distance = 80 miles
Total time = 40 / 15 + 40/30 = 4
Avg. speed = 20.
Answer - B
Answer: B
Question: Mary drove at an average speed of 40 mph for some time and then at an average speed of 60 mph for the rest of the journey. If she made no stops during the trip and her average speed for the entire journey was 50 mph, for what fraction of the total time did she drive at 40 mph?
Options:
A) 1/5
B) 1/3
C) 1/2
D) 2/3
E) 3/5
Rationale: We don't need to get into calculations for solving this question. We can use the concept of weighted averages.
One thing for sure we know that if the average speed for the entire journey is 50 mph, means she drove at 40 mph and 60 mph for an equal duration of time.
10 10
40-----50----60
This shows that you can divide the entire journey into 2 equal parts. Thus, 1/2 parts she drove at 40 mph and 1/2 part she drove at 60 mph.
Answer: C
Answer: C
Question: If Rs. 782 is divided into three parts, proportional to
1/2:2/3:3/4 find the first part.
Options:
A)190
B)204
C)220
D)230
E)None of these
Rationale: Explanation:
1/2:2/3:3/4=6:8:9First part =782∗6/23=204
Option B
Answer: B
Question: Find the average of first 4 multiples of 5?
Options:
A)10
B)12.5
C)22.5
D)31.3
E)40.8
Rationale: average = (5+10+15+20)/4 = 12.5
Answer is B
Answer: B
Question: How many five-digit numbers are there, if the two leftmost digits are even, the other digits are odd and the digit 4 cannot appear more than once in the number.
Options:
A)1875
B)2000
C)2375
D)2500
E)3875
Rationale: Number of combo with 4 as first digit + Number of combos with 4 as second digit = 1*4*5*5*5 + 3*5*5*5 = 2375
ANSWER:C
Answer: C
Question: How many different words beginning with O and ending with E can be formed with the letters of the word ORDINATE, so that the words are beginning with O and ending with E?
Options:
A)8!
B)6!
C)7!
D)7!/2!
E)None
Rationale: Solution
6! ways, O fixed 1st and E fixed in last.
Answer B
Answer: B
Question: (3192 + 6160) / 28
Options:
A)380
B)350
C)334
D)310
E)None of these
Rationale: Explanation:
As per BODMAS rule, first we will solve the equation in bracket then we will go for division
= (9352)/28 = 334
Option C
Answer: C
Question: Of the 250 employees at company X, 80 are full-time, and 100 have worked at company X for at least a year. There are 20 employees at company X who aren’t full-time and haven’t worked at company X for at least a year. How many full-time employees of company X have worked at the company for at least a year?
Options:
A)20
B)30
C)50
D)80
E)100
Rationale: Full time employee who have NOT worked for at least one year = a
Full time employee who have worked for at least one year = b
NON Full time employee who have worked for at least one year = c
NON Full time employee who have NOT worked for at least one year = d
a+b+c+d = 150
a+b = 80
i.e. c+d = 70
b+c = 100
i.e. a+d = 50
d = 20
i.e. c = 70-20 = 50
i.e. b = 100-50 = 50
i.e. a = 80-50 = 30
b = 100
Answer: Option E
Answer: E
Question: The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 125 resolutions?
Options:
A)794 m
B)704 m
C)454 m
D)186 m
E)176 m
Rationale: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 125 resolutions.
= 125 * 2 * 22/7 * 22.4
= 17600 cm
= 176 m
Answer: E
Answer: E
Question: Two cars cover the same distance at the speed of 60 and 64 kmps respectively. Find the distance traveled by them if the slower car takes 1 hour more than the faster car?
Options:
A)287 km
B)960 km
C)187 km
D)173 km
E)266 km
Rationale: 60(x + 1) = 64x
X = 15
60 * 16 = 960 km
Answer: B
Answer: B
Question: How many multiples of 5 are there between 5 to 75?
Options:
A)9
B)18
C)17
D)13
E)Cannot be determined
Rationale: Explanation :
As you know, multiples of 5 are integers having 0 or 5 in the digit to the extreme right (i.e. the units place).
So the numbers are 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70.
Answer : D
Answer: D
Question: What is the value of x in the equation below?
4 + √(1-3x) = 12
Options:
A)21
B)12
C)-21
D)-12
E)4
Rationale: 4 + √(1-3x) = 12
(4-4) + √(1-3x) = 12 - 4 = √(1-3x) = 8
(√(1-3x))^2 = (8)^2 = 1-3x = 64
(1 -1) - 3X = 64 - 1 = -3x = 63
(-3x) / -3 = 63 / -3 = x = -21
Correct option: C) -21
Answer: C
Question: On a Saturday night, each of the rooms at a certain motel was rented for either $40 or $60. If 10 of the rooms that were rented for $60 had instead been rented for $40, then the total rent the motel charged for that night would have been reduced by 20 percent. What was the total rent the motel actually charged for that night ?
Options:
A) $600
B) $800
C) $1,000
D) $1,600
E) $2,400
Rationale: Let total rent the motel charge for all rooms =x
If 10 rooms that were rented for 60 $ had instead been rented for 40 $,
then total difference in prices = 20 $ * 10 = 200 $
Total rent the motel charged would have been reduced by 20 %
.2x = 200
=> x= 1000
Answer C
Answer: C
Question: A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. How far is the place?
Options:
A)2.87
B)2.88
C)2.78
D)2.29
E)2.27
Rationale: M = 6
S = 1.2
DS = 6 + 1.2 = 7.2
US = 6 - 1.2 = 4.8
x/7.2 + x/4.8 = 1
x = 2.88
Answer: B
Answer: B
Question: If x and y are positive integers such that (3x + 7y) is a multiple of 11, then which of the following will be divisible by 11 ?
Options:
A)4x - 9y
B)9x + 4y
C)x + y + 4
D)x + y + 5
E)4x + 6y
Rationale: By hit and trial, we put x = 5 and y = 1 so that (3x + 7y) = (3 x 5 + 7 x 1) = 22, which is divisible by 11.
(4x + 6y) = ( 4 x 5 + 6 x 1) = 26, which is not divisible by 11;
(x + y + 4 ) = (5 + 1 + 4) = 10, which is not divisible by 11;
(9x + 4y) = (9 x 5 + 4 x 1) = 49, which is not divisible by 11;
(4x - 9y) = (4 x 5 - 9 x 1) = 11, which is divisible by 11.
Answer is A
Answer: A
Question: If b/x = 7/4 and b/y =7/ 5, then (y -x) =
Options:
A)b/2
B)b/7
C)2b
D)3b/7
E)b
Rationale: Ratio 1:
4b = 7x
Ratio 2:
5b = 7y
y -x = b/7
Answer is B
Answer: B
Question: A train 880 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?
Options:
A)510
B)540
C)500
D)420
E)589
Rationale: Speed = 78 * 5/18 = 65/3 m/sec.
Time = 1 min = 60 sec.
Let the length of the train be x meters.
Then, (880 + x)/60 = 65/3
x = 420 m.
Answer: Option D
Answer: D
Question: A and B can do a piece of work in 12 days and 16 days respectively. Both work for 3 days and then A goes away. Find how long will B take to complete the remaining work?
Options:
A)7 days
B)8 days
C)5 days
D)9 days
E)3 days
Rationale: 3/12 + (3 + x)/16 = 1
x = 9 days
Answer: D
Answer: D
Question: Find the next term
8,8,6,2,..?
Options:
A)-2
B)-4
C)-6
D)-8
E)-9
Rationale: 8 , 8, 6, 2, x
i guess each differ in d range of 2
8 - 8 = 0
8 - 6 = 2
6 - 2 = 4
2 - x should be "6"
2 - x = 6
x = -4
ANSWER:B
Answer: B
Question: If a: b = 7: 5, b: c = 9: 11, find a: b: c?
Options:
A)63: 45: 58
B)63: 45: 55
C)63: 45: 56
D)63: 45: 50
E)63: 45: 51
Rationale: a: b = 7: 5
b: c = 9: 11
a: b: c = 63: 45: 55
Answer: B
Answer: B
Question: A boy has seven trousers and 8 shirts. In how many different ways can he select a trouser and a shirt?
Options:
A)56 ways
B)57 ways
C)58 ways
D)108 ways
E)59 ways
Rationale: The boy can select one trouser in seven ways.
The boy can select one shirt in 8 ways.
The number of ways in which he can select one trouser and one shirt is 7 * 8 = 56 ways.
Answer:A
Answer: A
Question: The cost of registration at a professional association meeting was $50 per person; a lunch for registrants only was available for an additional $22 per person. If the number of registrants who paid for lunch was 10 more than the number who did not, and if receipts for registration and lunch totaled $61720, how many people paid just for registration at the meeting?
Options:
A)700
B)800
C)1,300
D)500
E)1,800
Rationale: Hope this might be useful to you.
Let the number of people who have opted only to register = x
Now since the registration cost is 50$ per person, the total amount sums to = 50x $
As per the information given in the question, the number of registrants who paid for lunch was 10 more than the number who did not. That means, total number of people who registered and paid for lunch = 10 + x.
For the people who registered for lunch the cost is 50 $ (for the event registration) + 22 $ (for lunch) = 72 $.
Total amount in this case sums to = 72(10 + x) = 720 + 72x
Now, total amount received was 61,720.
Thus, from the above data,
50x + 720 + 72x = 61720
122x = 61720 - 720
122x = 61000
x = 500.
Hence the correct Ans is D
Answer: D
Question: A bowl of nuts is prepared for a party. Brand P mixed nuts are 20% almonds and Brand Q's Deluxe nuts are 25% almonds. If a bowl contains a total of 68 ounces of nuts, representing a mixture of both brands, and 15 ounces of the mixture are almonds, how many ounces of Brand Q's Deluxe mixed nuts are used?
Options:
A) 16
B) 28
C) 32
D) 44
E) 48
Rationale: lets say x ounces of P is mixed with Q.
=> 68-x ounces of Q is present in the mixture (as the total = 68 ounces)
given total almond weight = 15 ounces
(20x/100)+(25/100)(68-x) = 15
=> x = 40
=> 68-40 = 28 ounces of Q is present in the mixture.
Answer is B.
Answer: B
Question: Bill has d animals, 12 of which were sold at a profit of 10% each while the rest were sold at a loss of 20% each. Overall, Bill made neither a profit nor a loss. Which of the following is equal to d?
Options:
A)6
B)12
C)18
D)24
E)36
Rationale: Total d animals, suppose each has price of x - total price = dx
now 12 were sold at profit of 10%, making equation - - 12*1.1x
now d-12 were sold at loss of 20%, making eqn --- (d-12)*0.8x
Now he made no profit or loss so,
dx = 12*1.1x + (d-12)*0.8x
solving for d, we get d=18
Ans C
Answer: C