divelab/Sys2Bench huggingface dataset:
Question: |x+1| – |4-x| = |8+x| How many solutions will this equation have?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: You have |x+3| - |4-x| = |8+x|
First, look at the three values independently of their absolute value sign, in other words:
|x+3| - |4-x| = |8+x|
(x+3) - (4-x) = (8+x)
Now, you're looking at x < - 8, so x is a number less than -8. Let's pretend x = -10 here to make things a bit easier to understand.
when x=-10
I.) (x+3)
(-10+3)
(-7)
II.) (4-x)
(4-[-10]) (double negative, so it becomes positive)
(4+10)
(14)
III.) (8+x)
(8+-10)
(-2)
In other words, when x < -8, (x+3) and (8+x) are NEGATIVE. To solve problems like this, we need to check for the sign change.
Here is how I do it step by step.
I.) |x+3| - |4-x| = |8+x|
II.) IGNORE absolute value signs (for now) and find the values of x which make (x+3), (4-x) and (8+x) = to zero as follows:
(x+3)
x=-3
(-3+3) = 0
(4-x)
x=4
(4-4) = 0
(8+x)
x=-8
(8+-8) = 3
D
Answer: D
Question: Speed of a boat in standing water is 14 kmph and the speed of the stream is 1.2 kmph. A man rows to a place at a distance of 4864 km and comes back to the starting point. The total time taken by him is:
Options:
A)200 hours
B)400 hours
C)900 hours
D)700 hours
E)600 hours
Rationale: Speed downstream = (14 + 1.2) = 15.2 kmph
Speed upstream = (14 - 1.2) = 12.8 kmph
Total time taken =4864/15.2+4864/12.8= 320 + 380 = 700 hours
Answer: D
Answer: D
Question: The cost price of an article is 25% of the marked price. Calculate the gain percent after allowing a discount of 50%.
Options:
A)25%
B)50%
C)100%
D)150%
E)none
Rationale: Sol.
Let marked price = Rs. 100. Then, C.P. = Rs. 25. S.P = Rs. 50.
âˆ´ Gain % = [25/25 * 100]% = 100.0%.
Answer C
Answer: C
Question: What is the 23th digit to the right of the decimal point in the decimal form of 36/66?
Options:
A)3
B)4
C)8
D)9
E)6
Rationale: We first have to use some long division. This long division allows us to get 36/66 in decimal form, which is 0.545454… where “54” is repeating.
We can see that the 1st, 3rd, 5th digit to the right of the decimal point is a 5 and that the 2nd, 4th, 6th digit to the right of the decimal point is a 4. In other words, each odd-positioned digit is a 5, and each even-positioned digit is a 4.
Then about the 10 digit to the right of the decimal point and we see that 10 is even, we know that the 10th digit is a 4.
Answer B.
Answer: B
Question: A grocer is storing soap boxes in cartons that measure 25 inches by 42 inches by 60 inches. If the measurement of each soap box is 7 inches by 6 inches by 10 inches, then what is the maximum number of soap boxes that can be placed in each carton?
Options:
A)210
B)252
C)280
D)150
E)420
Rationale: however the process of dividing the volume of box by the volume of a soap seems flawed but it does work in this case due to the numbers
Dimensions of the box =25*42*60
Dimensions of the soap = 10*6*7
we get = 5x6x5 = 150
so the question is why this particular arrangement, in order to maximize number of soaps we need to minimize the space wasted and this is the only config where we dont waste any space so we can expect the maximum number
the answer is (D)
Answer: D
Question: If a-b= 10 and a^2+b^2=150, find the value of ab
Options:
A)10
B)12
C)25
D)18
E)19
Rationale: 2ab = (a^2 + b^2) - (a - b)^2
= 150 - 100 = 50
=> ab = 25
ANSWER: C
Answer: C
Question: In how many years does a sum of Rs. 4500 yield a simple interest of Rs. 16000 at 15% p.a.?
Options:
A)23.7 years
B)24.7 years
C)25.7 years
D)26.7 years
E)27.7 years
Rationale: T = (100 * 16000)/(15 * 4500) = 23.7 years
ANSWER:A
Answer: A
Question: If m is the average (arithmetic mean) of the first 10 positive multiples of 8 and if M is the median of the first 10 positive multiples of 8, what is the value of M – m ?
Options:
A) –5
B) 24
C) 5
D) 25
E) 5
Rationale: The first 10 positive multiples of 8 is an evenly spaced set. One of the most important properties of evenly spaced set (aka arithmetic progression) is:in any evenly spaced set the arithmetic mean (average) is equal to the median.
Hence M=m --> M-m=0.
Answer: E.
Answer: E
Question: For four days of work, a clerk had daily earnings of $190, $180, $190, and $190 respectively. In which of the following intervals does the standard deviation of the daily earnings lie?
Options:
A)Between $10 and $100
B)Between $25and $50
C)Between $0 and $10
D)Between $50 and $100
E)Between $20 and $40
Rationale: The standard deviation is between 0 and 10.
The reason is that none of the numbers in the set is further away from the mean than 10(or rather Abs(180-(190*3+180)/4)). I am not fully sure how to calculate the standard deviation(I simply remember that there were some formula for calculating the average of the squared distances from the mean for all items in the set from statistics classes - variation), but I believe this will suffice for any GMAT question related to standard deviation.
Answer : C
Answer: C
Question: A small college reduced its faculty by approximately 25 percent to 195 professors. What was the original number of faculty members?
Options:
A)182
B)260
C)224
D)254
E)302
Rationale: If x is the original number of faculty members, then after 25% reduction in faculty members number is .75x
but we are given .75x = 195
x = 260
So the original number of faculty members is 260
Correct Answer - B
Answer: B
Question: What is the probability of getting equilateral triangles from the vertices of regular hexagon?
Options:
A)1/10
B)2/10
C)3/10
D)4/10
E)5/10
Rationale: total no. of triangles that can b made with the vetices hexagon= 6C3=20
no. of possible outcomes i.e. no. of equality triangles=2.
.'. probability= 2/20=1/10
ANSWER:A
Answer: A
Question: The simple interest at b% for b years will be $b on a sum of
Options:
A)$ (1000)/b
B)$(100)b^2
C)$ b
D)$ (100)/b
E)$ 100b
Rationale: Principal =$(100*b)/(b*b)=$(100/b).
Answer is D
Answer: D
Question: The two lines y = x and x = -4 intersect on the coordinate plane. If z represents the area of the figure formed by the intersecting lines and the x-axis, what is the side length R of a cube whose surface area is equal to 6z?
Options:
A)R=16
B)R=8√2
C)R=8
D)R=2√2
E)(√2)/3
Rationale: 800 score Official Solution:
The first step to solving this problem is to actually graph the two lines. The lines intersect at the point (-4, -4) and form a right triangle whose base length and height are both equal to 4. As you know, the area of a triangle is equal to one half the product of its base length and height: A = (1/2)bh = (1/2)(4 × 4) = 8; so z = 8.
The next step requires us to find the length of a side of a cube that has a face area equal to 8. As you know the 6 faces of a cube are squares. So, we can reduce the problem to finding the length of the side of a square that has an area of 8. Since the area of a square is equal to s², where s is the length of one of its side, we can write and solve the equation s² = 8. Clearly s = √8 = 2√2 , oranswer choice (D).
Answer: D
Question: A man can row upstream at 12 kmph and downstream at 38 kmph, and then find the speed of the man in still water?
Options:
A)11
B)25
C)30
D)88
E)34
Rationale: US = 12
DS = 38
M = (12 + 38)/2 = 25
Answer:B
Answer: B
Question: Carmen made a sculpture from small pieces of wood. The sculpture is 2 feet 10 inches tall.Carmen places her sculpture on a base that is 10 inches tall. How tall are the sculpture andbase together?
Options:
A)3.1 feet
B)3.66 feet
C)3.3 feet
D)3.4 feet
E)3.5 feet
Rationale: we know 1 feet =12 inch then
2 feet =24 inch
24+10=34 then
34+10=40
44/12=3.66 feet
ANSWER:B
Answer: B
Question: Each person who attended a company meeting was either a stockholder in the company, an employee of the company, or both. If 62 percent of those who attended the meeting were stockholders and 45 percent were employees, what percent were stockholders who were not employees?
Options:
A) 34%
B) 38%
C) 45%
D) 53%
E) 55%
Rationale: Let M represent the number of meeting attendees. Then, since 62% of M or 0.62M
were stockholders and 47% of M or 0.45M were employees, it follows that 0.62M +
0.45M = 1.07M were either stockholders, employees, or both. Since 1.07M exceeds
M, the excess 1.07M − M = 0.07M must be the number of attendees who were both
stockholders and employees, leaving the rest 0.62M − 0.07M = 0.55M, or 55%, of
the meeting attendees to be stockholders but not employees.
The correct answer is E.
Answer: E
Question: The speed of a boat in upstream is 60 kmph and the speed of the boat downstream is 100 kmph. Find the speed of the boat in still water and the speed of the stream?
Options:
A)70, 10 kmph
B)35, 27 kmph
C)50, 60 kmph
D)80, 20 kmph
E)45, 65 kmph
Rationale: Speed of the boat in still water = (60+100)/2 = 80 kmph. Speed of the stream = (100-60)/2 = 20 kmph
ANSWER:D
Answer: D
Question: Find the value of y from (12)^3 x 6^4 ÷ 432 = y?
Options:
A)2560
B)3400
C)3690
D)4500
E)5184
Rationale: Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184
432 12 x 62
E
Answer: E
Question: There is a number which is greater than the aggregate of its third. tenth and the twelfth parts by 58
Can you find the number?
Options:
A)125
B)153
C)120
D)234
E)116
Rationale: C
120
Answer: C
Question: In order to obtain an income of Rs. 580 from 15% stock at Rs. 100, one must make an investment of
Options:
A)5363
B)6240
C)8700
D)5600
E)2732
Rationale: To obtain Rs. 10, investment
= Rs. 100.
To obtain Rs. 580, investment =
= Rs. 8700.
Answer: C
Answer: C
Question: 6, 11, 21, 36, 56, 81, 111, ?
Options:
A)512
B)146
C)812
D)612
E)912
Rationale: The pattern is + 5, + 10, + 15, + 20, + 25, + 30, + 35, + 40, + 45, + 50,....
Answer : B.
Answer: B
Question: 90, 180, 12, 50, 100, 80, ?, 3, 20, 4, 25, 2, 6, 30, 3
Options:
A)100
B)150
C)180
D)90
E)60
Rationale: 30*3=90
6*30=180
6*2=12
25*2=50
4*25=100
20*4=80
3*20=60 ans is 60
ANSWER:E
Answer: E
Question: If 3 persons can do 3 times of a particular work in 3 days, then, 7 persons can do 7 times of that work in?
Options:
A)2 days
B)3 days
C)4 days
D)5 days
E)6 days
Rationale: That is, 1 person can do one time of the work in 3 days.
Therefore, 7 persons can do 7 times work in the same 3 days itself.
B)
Answer: B
Question: If 30% of a number exceeds 20% of it by 18, then find the number?
Options:
A)120
B)200
C)180
D)150
E)None of these
Rationale: Let the number be x.
30% of x = 30/100 * x = 3x/10
20% of x = 20/100 * x = x/5 = 2x/10.
Given that 3x/10 - 2x/10 = 18 => x = 180.
Required number is 180.
ANSWER:C
Answer: C
Question: A tank with a volume of 20 cubic feet has one inlet pipe and 2 outlet pipes. The inlet pipe fills water into the tank at the rate of 5 cubic inches/min and the 2 outlet pipes empty it out at the rates of 9 cubic inches/min and 8 cubic inches/min respectively. If all 3 pipes are opened when the tank is full, how many minutes does it take to empty the tank? (1 foot = 12 inches)
Options:
A)2110
B)2220
C)2440
D)2660
E)2880
Rationale: The tank is emptied at this rate: 9 + 8 - 5 = 12 cubic inches/min
The tank has a volume of 20*12*12*12 = 34560 cubic inches.
The time it takes to empty the tank is 34560/12 = 2880 minutes.
The answer is E.
Answer: E
Question: Three Englishmen and three Frenchmen work for the same company. Each of them knows a secret not known to others. They need to exchange these secrets over person-to-person phone calls so that eventually each person knows all six secrets. None of the Frenchmen knows English, and only one Englishman knows French. What is the minimum number of phone calls needed for the above purpose?
Options:
A)5
B)8
C)11
D)15
E)17
Rationale: Explanation :
Let a, b, c be the Englishmen and d, e, f be the Frenchmen.
Let a be the Englishman who knows French. 'a' calls 'b & c' and now knows the secret of both of them. So now 'a' knows 'abc' secrets. 'd' calls 'e & f' and now knows the secret of both of them. So now 'd' knows 'def' secrets. 'a' now calls 'd', and exchange all secrets in French, so now 'a' and 'd' know all the 6 secrets. Now 'a' calls 'b & c' again, and 'd' calls 'e & f' again and tell all the secrets. So, totally 9 calls.
Answer : B
Answer: B
Question: A person is traveling at 25km/hr and reached his destiny in 6hr find the distance?
Options:
A)A)100km
B)B)95km
C)C)135km
D)D)150km
E)E)125km
Rationale: speed = 25km/hr
time = 6hr
distance = 25*6 = 150km
Answer is D
Answer: D
Question: The average age of students in section A of 124 students is 23 years and the average age of students in section B of 159 students is 39 years. Find the average age of students in both sections taken together?
Options:
A)26 years
B)32years
C)15years
D)25years
E)20years
Rationale: The required average = (124*23+159*39)/124+159 = 32 years
Answer is B
Answer: B
Question: The population of a town increased from 1,75,000 to 2,62,500 in a decade. The average percent increase of population per year is
Options:
A)4.37%
B)5%
C)6%
D)8.75%
E)None
Rationale: Solution
Increase in 10 years	= (262500 - 175000)
= 87500.
Increase%	= (87500/175000×100)%
= 50%.
Required average	= (50/10)%
= 5%.
Answer B
Answer: B
Question: At an international conference, “Red” world countries and “Blue” world countries are the only participants. The ratio of “Red” world participants to “Blue” world participants is 10:5. If one-third of “Red” world participants are left-handed and two-thirds of “Blue” world participants are left-handed, then what is the fraction of the participants who are left-handed?
Options:
A)4/10
B)4/9
C)6/5
D)9/2
E)6/4
Rationale: Red: Blue = 10:5
Let Red = 10x and Blue = 5x
1/3 of Red are left handed => 1/3 * 10x = 10x/3 Red left handed
2/3 of Blue are left handed => 2/3 *5x = 10x/3 blue left handed
fraction of participants who are left handed = total left handed/ total participants = (red left handed + blue left handed)/total participants = (10x/3 + 10x/3)/(10x+5x) = 20/45 = 4/9
Answer : B
Answer: B
Question: A car was driving at 66 Km/h for 30 minutes, and then at 100 Km/h for another 45 minutes. What was its average speed?
Options:
A)84.
B)75.
C)70.
D)65.
E)54.
Rationale: driving at 66 Km/h for 30 minutes ,distance covered = 60*1/2=30 km
driving at 100 km/h for 45 minutes ,distance covered = 100*3/4=75 km
average speed = total distance/total time = 105/1.25 = 84 km/h
Answer: A
Answer: A
Question: Simple interest on a certain sum at a certain annual rate of interest is 1/4 of the sum. If the numbers representing rate percent and time in years be equal, then the rate of interest is:
Options:
A)4 %.
B)25/4 %.
C)5 %
D)6 %.
E)3 %.
Rationale: Explanation :
Let sum = x. Then, S.I. = x/4
Let rate = R% and time = R years.
[x * R * R / 100] = x / 4? R^2 = 100/4=25
R = 5
Hence, rate of interest = 5 %.
Answer : C
Answer: C
Question: A group of 5 friends—Archie, Betty, Jerry, Moose, and Veronica—arrived at the movie theater to see a movie. Because they arrived late, their only seating option consists of 3 middle seats in the front row, an aisle seat in the front row, and an adjoining seat in the third row. If Archie, Jerry, or Moose must sit in the aisle seat while Betty and Veronica refuse to sit next to each other, how many possible seating arrangements are there?
Options:
A)32
B)36
C)48
D)72
E)120
Rationale: First, place one person in the isle seat - 3 possibilities.
Second, place the two girls Betty and Veronica (more specifically separate them) and then place the remaining two persons - the girls can sit either in the middle seats, one seat apart, or one girl in the third row and then the other girl with the remaining two guys in the middle seats - which is 2*2! + 2*3! = 16.
Total number of possibilities 3*16 = 48.
Answer C
Answer: C
Question: Mr. Peterson deposits $ 200 in an account that pays 20% interest, compounded semiannually. How much money will there be in the account at the end of one year?
Options:
A)$118.00
B)$120.00
C)$242.00
D)$122.00
E)$140.00
Rationale: Using Formula - A = P(1+r/n)^nt
Given
P=200
n=2
t=1
r=0.2
Substituting value in formula
A = 200(1+0.2/2)^2
A= 242.00$=C
Answer: C
Question: Vijay sells a cupboard at 14% below cost price. Had he got Rs.2086 more, he would have made a profit of 14%. What is the cost price of the cupboard?
Options:
A)7458
B)7456
C)7450
D)7454
E)7453
Rationale: Explanation:
Cost price = 2086/(0.14 + 0.14) = 2086/0.28
= Rs.7450
ANSWER: C
Answer: C
Question: An amount of money is to be divided between P, Q and R in the ratio of 3:7:12. If the difference between the shares of P and Q is Rs.2400, what will be the difference between Q and R's share?
Options:
A)1266
B)3000
C)2866
D)2999
E)2678
Rationale: 4 --- 2000
5 --- ? => 3000
Answer: B:
Answer: B
Question: In a kilometer race, A beats B by 100 meters or 10 seconds. What time does A take to complete the race?
Options:
A)90 sec
B)190 sec
C)290 sec
D)490 sec
E)390 sec
Rationale: Time taken by B run 1000 meters = (1000 * 10)/100
= 100 sec.
Time taken by A = 100 - 10
= 90 sec.
Answer:A
Answer: A
Question: A and B are positive two-digit integers such that the tens digit in A is the same as the units digit in B, and the units digit in A is the same as the tens digit in B. Which of the following could be the difference of A and B ?
Options:
A)72
B)46
C)33
D)24
E)92
Rationale: A and B are positive two-digit integers such that the tens digit in A is the same as the units digit in B, and the units digit in A is the same as the tens digit in B:
A = 10x + y
B = 10y + x
A - B = (10x + y) - (10y + x) = 9(x - y). As you can see the difference must be a multiple of 9. Only option A is a multiple of 9.
Answer: A.
Answer: A
Question: Find the average of first 4 multiples of 8?
Options:
A)20
B)12.6
C)22.5
D)31.3
E)40.8
Rationale: average = (8+16+24+32)/4 = 20
Answer is A
Answer: A
Question: A store has 10 bottles of juice, including 6 bottles of apple juice. In the evening, 6 bottles of juice are sold one by one. What is the probability of selling 3 bottles of apple juice among the 6 bottles? Assume that every bottle has an equal chance of being bought.
Options:
A)2/11
B)4/15
C)6/17
D)8/21
E)10/25
Rationale: The total number of ways to sell 6 bottles from 10 is 10C6 = 210.
The number of ways to sell 3 bottles of apple juice is 6C3*4C3 = 20*4 = 80
P(selling 3 bottles of apple juice) = 80/210 = 8/21
The answer is D.
Answer: D
Question: You collect coins. Suppose you start out with 11. Since you're nice, you give Sharon 3 coins. Since you're nice, you give Steven 5 coins. How many coins do you have at the end?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: Solution
Start with 11 coins.
Sharon takes 3 coins from you: 11 - 3 = 8 coins.
Steven takes 5 coins from you: 8 - 5 = 3 coins.
So you have 3 at the end.
Correct answer : B
Answer: B
Question: A shopkeeper bought 600 oranges and 400 bananas. He found 15% of oranges and 8% of bananas were rotten. Find the percentage of fruits in good condition?
Options:
A)92.5%
B)87.8%
C)85.2%
D)96.8%
E)78.9%
Rationale: Total number of fruits shopkeeper bought = 600 + 400 = 1000
Number of rotten oranges = 15% of 600
= 15/100 × 600
= 9000/100
= 90
Number of rotten bananas = 8% of 400
= 8/100 × 400
= 3200/100
= 32
Therefore, total number of rotten fruits = 90 + 32 = 122
Therefore Number of fruits in good condition = 1000 - 122 = 878
Therefore Percentage of fruits in good condition = (878/1000 × 100)%
= (87800/1000)%
= 87.8%
Answer:B
Answer: B
Question: A trader bought a car at 20% discount on its original price. He sold it at a 30% increase on the price he bought it. What percent of profit did he make on the original price?
Options:
A)A)4%
B)B)12%
C)C)14%
D)D)20%
E)E)22%
Rationale: Original price = 100
CP = 80
S = 80*(130/100) = 104
100 - 104 = 4%
A)
Answer: A
Question: A package contains 8 black and 12 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?
Options:
A)5/9
B)3/5
C)6/8
D)7/9
E)1/3
Rationale: Let number of balls = (8+12) = 20.
Number of white balls = 12.
P (drawing a white ball) =	12/20=3/5
B
Answer: B
Question: In an acoustics class, 120 students are male and 100 students are female. 25% of the male students and 20% of the female students are engineering students. 20% of the male engineering students and 25% of the female engineering students passed the final exam. What percentage of engineering students passed the exam?
Options:
A)5%
B)10%
C)16%
D)22%
E)None of these
Rationale: Explanation :
The number of female engineering students in the class is (20/100)×100=20.
Now, 25% of the female engineering students passed the final exam: 25.
Hence, the number of female engineering students who passed is 5.
There are 120 male students in the class. And 25% of them are engineering students.
Hence, the number of male engineering students is (1/4)×120=30.
Now, 20% of the male engineering students passed the final exam :- 20.
Hence, the number of male engineering students who passed is 6.
Hence, the total number of engineering students who passed is:
(Female Engineering students who passed)+ (Male Engineering students who passed)
=>5+6=11.
The total number of engineering students in the class is:
(Number of female engineering students)+ (Number of male engineering students)=
=>30+20=50
Hence, the percentage of engineering students who passed is :-
=>(Total number of engineering students passed/ Total number of engineering students) ×100.
=>(11/50)×100.
=> 22%.
Answer : D
Answer: D
Question: The edge of a cube is 3a cm. Find its surface?
Options:
A)24a8
B)24a4
C)24a1
D)54a2
E)24a7
Rationale: 6a2 = 6 * 3a * 3a = 54a2
Answer:D
Answer: D
Question: If f is the square of a positive integer, which of the following must be equal to the square of the next positive integer?
Options:
A)√n + 1
B)n + 1
C)n^2 + 1
D)f + 2√f + 1
E)n^2 + 2n + 1
Rationale: If f is the square of a positive integer, which of the following must be equal to the square of the next positive integer?
f = (x)^2 where x is a positive integer
To calculate -
(x+1)^2 = x^2 + 2x + 1
root(f) = x
Ans - f + 2 root(f) + 1
This should beD
Answer: D
Question: x+(1/x) = 3 find x^2 + (1/x^2)
Options:
A)2.25
B)7
C)4.25
D)5.25
E)6.25
Rationale: squaring on both sides (x+1/x)^2=3^2
x^2+1/X^2=9-2
x^2+1/X^2=7
ANSWER:B
Answer: B
Question: Peter read W books last year, and Nikki read N books last year. If Peter read 35 more books than Nikki last year, which of the following reflects this relationship?
Options:
A)W > 35N
B)W < N − 35
C)W > N + 35
D)W = N − 35
E)W = N + 35
Rationale: Peter read W books last year, and Nikki read N books last year. If Peter read 35 more books than Nikki last year, which of the following reflects this relationship?
A. W > 35N
B. W < N − 35
C. W > N + 35
D. W = N − 35
E. W = N + 35
Since Peter read more books than Nikki we have W>N. Moreover since Peter reads 35 more books than Nikki easily we can have W=N+35.
So the answer is (E).
Answer: E
Question: There are 4 physics books and 1 chemistry book on shelf P and 3 physics books on shelf Q. One book is moved from shelf P to shelf Q. A student picks up a book from shelf Q. What is the probability that the chemistry book is taken by the student?
Options:
A)1/9
B)1/10
C)1/12
D)1/15
E)1/20
Rationale: P(a chemistry book is moved to shelf Q) = 1/5
P(a chemistry book is then chosen from shelf Q) = 1/4
P(the student takes a chemistry book) = 1/5 * 1/4 = 1/20
The answer is E.
Answer: E
Question: If 3a – 2b – 4c = 32 and √3a-√(2b+2c)=4, what is the value of a + b + c?
Options:
A)3
B)9
C)10
D)12
E)14
Rationale: when we look at the two equations, we can relize some similarity, so lets work on it..
3a – 2b – 2c = 32 can be written as √3a^2-√(2b+2c)^2=32
{√3a-√(2b+2c)}{√3a+√(2b+2c)}=32..
or 4*√3a+√(2b+2c)=32..
or √3a+√(2b+2c)=8..
now lets work on these two equations
1)√3a-√(2b+2c)=4..
2)√3a+√(2b+2c)=8..
A) add the two eq..
√3a+√(2b+2c)+√3a-√(2b+2c)=12..
2√3a=12..
or √3a=6..
3a=36..
a=12.
B) subtract 1 from 2..
√3a+√(2b+2c)-√3a+√(2b+2c)=4..
2√(2b+2c)=4..
√(2b+2c)=2..
2b+2c=4..
or b+c=2..
from A and B a+b+c=12+2=14..
D
Answer: D
Question: If a car had traveled 35 kmh faster than it actually did, the trip would have lasted 30 minutes less. If the car went exactly 105 km, at what speed did it travel?
Options:
A)50 kmh
B)55 kmh
C)60 kmh
D)65 kmh
E)70 kmh
Rationale: Time = Distance/Speed
Difference in time = 1/2 hrs
105/x - 105/(x + 35) = 1/2
Substitute the value of x from the options. --> x = 70 --> 105/70 - 105/105 = 3/2 - 1 = 1/2
Answer: E
Answer: E