mathewhe/aqua_rat huggingface dataset:
Question: In a apartment, 20% of the people speak English, 60% speak Hindi and 60% speak both. If a people is selected at random, what is the probability that he has speak English or Hindi?
(A) 1/5
(B) 2/3
(C) 2/5
(D) 2/7
(E) 2/9
Rationale: P (E) = 20 / 100 = 1 / 5 , P (H) = 60 / 100 = 3 / 5 and P (E âˆ© H) = 60 / 100 = 3 / 5
P (E or H) = P (E U H)
= P (E) + P (H) - P (E âˆ© H)
= (1 / 5) + (3 / 5) - (3 / 5) = 4 / 10 = 1/5
A
Answer: (A) 1/5
Question: The difference between the length and breadth of a rectangle is 30 m. If its perimeter is 240 m, then its area is:
(A) 1520 m2
(B) 2420 m2
(C) 3375 m2
(D) 2520 m2
(E) None
Rationale: EXPLANATION
We have: (l â€“ b) = 30 and 2(l + b) = 240 or (l + b) = 120.
Solving the two equations, we get: l = 75 and b = 45.
Area = (l x b) = (75x 45) m2 = 3375 m2.
Answer C
Answer: (C) 3375 m2
Question: A straight line in the xy- plane has slope 4 . On this line the x-coordinate of the point is 50 and y-coordinate is 300 then what is the y intercept of the plane?
(A) 150
(B) 110
(C) 100
(D) 200
(E) 50
Rationale: Eq of line = Y = MX +C
M= 4
X=50
Y=50*4 + C,
Substitute Y by 300 as given in question.
300=200+C , C =100
correct option is C
Answer: (C) 100
Question: If a truck is travelling at a speed of 54 kmph, crosses a pole in 1 sec, then the length of train is?
(A) 13 m
(B) 14 m
(C) 15 m
(D) 16 m
(E) 17 m
Rationale: Explanation:
D = 54 * 5/18 * 1 = 15 m
Answer: Option C
Answer: (C) 15 m
Question: What is the sum of all the prime factors of 220 and 330?
(A) 15
(B) 21
(C) 35
(D) 41
(E) 64
Rationale: Prime factorization of both the numbers is as follows
220 = 2 * 2 * 5 * 11
sum of the prime factors of 220 = 20
330 = 2 *3 * 5 * 11
sum of prime factors of 330 = 21
addition of both = 20 + 21 = 41
ANSWER D
Answer: (D) 41
Question: Two twins sisters Sita and Geeta were standing back to back and suddenly they started running in opposite direction for 4 miles and then turn to left and run for another 3 miles.
what is the distance between the the two twins when they stop ?
(A) 10 miles
(B) 11 miles
(C) 18 miles
(D) 16 miles
(E) 13 miles
Rationale: A
10 miles
Answer: (A) 10 miles
Question: If x and y are positive integers, then xy - y is
(A) Always odd
(B) Odd whenever y is odd
(C) Odd whenever x+y is even
(D) Even whenever y is odd
(E) It cannot be determined
Rationale: x and y are positive integers, then xy - y..
Let's take even as 4 and odd as 5.
IMO option A is correct answer..
If you consider your fourth scenario, that turns out to be even.
Hence option B should be correct.
Answer: (B) Odd whenever y is odd
Question: If x, y, and z are all factors of 21, which of the following must be true?
(A) The product xyz > 21
(B) Either x = y, y = z, or x = z
(C) x – y – z = even
(D) The product xyz is odd
(E) yz/x is an integer
Rationale: All the factors of 21 are odd numbers.
The product of odd numbers is odd.
The answer is D.
Answer: (D) The product xyz is odd
Question: Ratio of the ages of Mahesh and Nilesh is 5 : x. Mahesh is 18 years younger to Ramesh. After nine years Ramesh will be 47 years old. If the difference between the ages of Mahesh and Nilesh is same as the age of Ramesh, what is the value of x?
(A) 72.9
(B) 62.2
(C) 14.2
(D) 13.7
(E) 14.5
Rationale: Let the present ages of Mahesh, Nilesh and Ramesh be m, n and r respectively.
m/n = 5/x ------ (1)
m = r - 18 ------ (2)
r + 9 = 47 ------ (3)
m - n = r ----- (4)
(3) => r = 47 - 9 = 38 years
(2) => m = 38 -18 = 20 years
(1) => 20/n = 5/x => n = 4x
(4) => 4x - 20 = 38
=> 4x = 58 => x = 14.5
Answer:E
Answer: (E) 14.5
Question: Which one of the following can't be the square of natural number ?
(A) 128881
(B) 128242
(C) 131044
(D) 130321
(E) 130322
Rationale: Square of a natural number cannot end with 2 .
Hence 128242 cannot be the square of natural number
Answer is B
Answer: (B) 128242
Question: Every digit of a number written in binary is either 0 or 1. To translate a number from binary, multiply the nth digit (reading from right to left) by 2^(n-1)
What is the largest prime number (written in binary) that is a factor of both 10110000 and 101100000 ?
(A)  10
(B)  11
(C)  101
(D)  1011
(E)  10001
Rationale: Binary Divison can provide a quick answer if you are comfortable with it.
as option E is the biggest binary number we try with it first :
100010000/ 1011 =10000
1000100000/ 1011 =100000
so answer is option is D
Answer: (D)  1011
Question: If x = - |x| , then which one of the following statements could be true?
I. x <1
II. x < 0
III. x > 0
(A)  None
(B)  I only
(C)  II only
(D)  I and II
(E)  II and III
Rationale: Answer copied from NOVA guide
Statement I could be false because 1/2 = −(1/2) = −1/2 .
Statement II could be true because the right side of the equation is always negative [ ± x = –(a positive number) = a negative number].
Now, if one side of an equation is always negative, then the other side must always be negative,
otherwise the opposite sides of the equation would not be equal.
Since Statement III is the opposite of Statement II, it must be false. But let’s show this explicitly:
Suppose x were positive. Then x = x, and the equation x = ± x becomes x = –x. Dividing both sides of this equation by x yields 1 = –1. This is contradiction.
Hence, x cannot be positive. The answer is C).
Answer: (C)  II only
Question: Of the 14,210 employees of the anvil factory, 3/7 are journeymen. If half of the journeymen were laid off, what percentage of the total remaining employees would be journeymen?
(A)  14.3%
(B)  16.67%
(C)  33%
(D)  28.6%
(E)  49.67%
Rationale: The exam gives us a number that is easily divisible by 7 to pique our curiosity and tempt us into calculating actual numbers (also because otherwise the ratio would be incorrect). Since the question is about percentages, the actual numbers will be meaningless, as only the ratio of that number versus others will be meaningful. Nonetheless, for those who are curious, each 1/7 portion represents (14210/7) 2,030 employees. This in turn means that 4,060 employees are journeymen and the remaining 10,150 are full time workers.
If half the journeymen were laid off, that would mean 1/7 of the total current workforce would be removed. This statistic is what leads many students to think that since half the journeymen are left, the remaining journeymen would represent half of what they used to be, which means 1/7 of the total workforce. If 1/7 of the workforce is journeymen, and 1/7 is roughly 14.3%, then answer choice A should be the right answer. In this case, though, it is merely the tempting trap answer choice.
What changed between the initial statement and the final tally? Well, you let go of 1/7 of the workforce, so the total number of workers went down. The remaining workers are still 1/7 of the initial workers, but the group has changed. The new workforce is smaller than the original group, specifically 6/7 of it because 1/7 was eliminated. The remaining workers now account for 1/7 out of 6/7 of the force, which if we multiply by 7 gives us 1 out of 6. This number as a percentage is answer choice B, 14.3%.
Using the absolute numbers we calculated before, there were 4,060 journeymen employees out of 14,210 total. If 2,030 of them are laid off, then there are 2,030 journeyman employees left, but now out of a total of (14,210-2,030) 12,180 employees. 2,030/12,180 is exactly 1/6, or 16.67%. The answer will work with either percentages or absolute numbers, but the percentage calculation will be significantly faster and applicable to any similar situation.
The underlying principle of percentages (and, on a related note, ratios) can be summed up in the brainteaser I like to ask my students: If you’re running a race and you overtake the 2nd place runner just before the end, what position do you end up in?
The correct answer is 2nd place.
Percentages, like ratios and other concepts of relative math, depend entirely on the context. Whether 100% more of something is better than 50% more of something else depends on the context much more than the percentages quoted. When it comes to percentages on the GMAT, the goal is to understand them enough to instinctively not fall into the traps laid out for you.
A
Answer: (A)  14.3%
Question: If a and b are positive numbers, and a^3 + b^3 = 140, then the greatest possible value of a is between:
(A) 0 and 2
(B) 2 and 3
(C) 3 and 4
(D) 4 and 5
(E) 5 and 8
Rationale: If a = 5.1 and b is a bit less than 2, then a^3 + b^3 can equal 140.
If a > 8, then a^3 + b^3 > 140.
The answer is E.
Answer: (E) 5 and 8
Question: Set A {3,3,3,4,5,5,5} has a standard deviation of 1. What will the standard deviation be if every number in the set is multiplied by 3?
(A) A)1
(B) B)2
(C) C)4
(D) D)3
(E) E)16
Rationale: Points to remember -
1. If oneAdd/Subtractthe same amont from every term in a set, SD doesn't change.
2. If oneMultiply/Divideevery term by the same number in a set, SD changes by same number.
Hence the answer to the above question is D
Answer: (D) D)3
Question: Two trains of length 100 meters and 200 meters are 630 meters apart. They are moving towards each other on parallel tracks, at speeds of 90 km/h and 72 km/h. After how many seconds will the trains meet?
(A) 12
(B) 14
(C) 16
(D) 18
(E) 20
Rationale: The speeds are 90000/3600 = 25 m/s and 72000/3600 = 20 m/s
The relative speed is 45 m/s.
time = 630 / 45 = 14 seconds
The answer is B.
Answer: (B) 14
Question: Becky sets up a hot dog stand in her busy neighborhood and purchases x pounds of hot dogs for q dollars per pound. If she has to throw away s pounds of hot dogs due to spoilage and she sells the rest of the hot dogs for d dollars per pound, which of the following represents the net profit on the sale of the hot dogs?
(A) (x – s)q – sd
(B) xq – (xd – sd)
(C) xd – sq
(D) (x – s)d – xq
(E) (s – q)d – xq
Rationale: Answer D:
The amount of hotdogs she can sell is x-s. The price per pound is d, so the revenue is (x-s)d. The total costs are x time q, so the profit is (x-s)d-xq.
Answer: (D) (x – s)d – xq
Question: Allen walks at an average speed of 4km/h, to the park and then return to the home he walks at an average speed of 8km/h. Which of the following is the closest approximation of Allen's average speed, in kilometers per hour, for the trip?
(A) 8
(B) 32
(C) 25
(D) 16
(E) 4
Rationale: Since we're not given a distance to work with, we can TEST any distance that we like. Here, since the speeds are 4 km/hour and 8 km/hour, using a multiple of both 4 and 8 would make the math easiest.
Let's set the Distance up the hill at 16 km.
So, going park, we have....
D = (R)(T)
16 = (4)(T)
16/4 = 4 = T
4 hours to go park
Going home, we have....
D = (R)(T)
16 = (8)(T)
16/8 = 2 = T
2 hours to go home
Total Distance = 32 km
Total Time = 4+2 = 6 hours
Average Speed = 32/2 = 16 km/hour
D
Answer: (D) 16
Question: Each child has 8 crayons and 15 apples. If there are 7 children, how many crayons are there in total?
(A) 22
(B) 56
(C) 12
(D) 36
(E) 10
Rationale: 8*7=56.Answer is B.
Answer: (B) 56
Question: A train 400 m long can cross an electric pole in 20 sec and then find the speed of the train?
(A) 87 Kmph
(B) 28 Kmph
(C) 72 Kmph
(D) 18 Kmph
(E) 29 Kmph
Rationale: Length = Speed * time
Speed = L/T
S = 400/20
S = 20 M/Sec
Speed= 20*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 72 Kmph
Answer:C
Answer: (C) 72 Kmph
Question: Two sets A and B consists only of positive integers such that mean of set A is 40 . If set R consist of all the elements of both A and B such that mean of R is 80 then the mean of set B is =>
(A) [A] 65
(B) [B] 60
(C) [C 70
(D) [D] 55
(E) [E] cannot be determined
Rationale: For this question, we have zero information about the size of two sets, sets AB. These two sets may have the same size or may be wildly different. Thus, the answer is (E), the mathematical answer cannot be determined. This is a very weak math question. As someone who writes GMAT practice questions, I would give this a grade of anD-as a question.
Answer E
Answer: (E) [E] cannot be determined
Question: A train 280 m long passed a pole in 28 sec. How long will it take to pass a platform 660 m long?
(A) 52
(B) 94
(C) 71
(D) 68
(E) 88
Rationale: Speed = 280/28 = 10 m/sec.
Required time = (280 + 660)/10 = 94 sec.
Answer: B
Answer: (B) 94
Question: A baker makes chocolate cookies and peanut cookies. His recipes allow him to make chocolate cookie in batches of 7 and peanut cookies in batches of 6. If he makes exactly 97 cookies, what is the minimum number of chocolate chip cookies he makes?
(A) 7
(B) 14
(C) 21
(D) 35
(E) 49
Rationale: 7C+6P=97
We need to maximize P to minimize C so that the eq is also satisfied
Try substitution for CP to solve so that eqn is satisfied
The least value of C for which equation gets satisfied is 5
i.e. 7*1+6*15=7+90=97
Hence A is the answer
Answer: (A) 7
Question: A paper is in a square form whose one side is 20 cm. Two semi circles are drawn on its opposites as diameters. If these semi circles are cut down what is the area of the remaining paper?
(A) 8.76
(B) 8.79
(C) 8.75
(D) 8.74
(E) 8.72
Rationale: (5 * 3.5)/2 = 8.75
Answer: C
Answer: (C) 8.75
Question: 9 persons a, b, c, ... and i are to be lined up in a row. If a, b, and c adhere always together, how many possible cases are there?
(A) 24
(B) 36
(C) 48
(D) 72
(E) 144
Rationale: firstly it is not GEOMETRY but COMBINATIONS, so changing the TAG accordingly..
total 9 are there..
take a,b, and c as one,so total =7..
these 7 can be arranged in 7! ways..
a,b, and c can be arranged within themselves in 3! ways ..
TOTAL = 7!*3!=30240
E
Answer: (E) 144
Question: Of the 13 employees in a certain department, 1 has an annual salary of 38,000, 2 have an annual salary of 45,600 each, 2 have an annual salary of 42,500 each, 3 have an annual salary of 40,000 each and 5 have an annual salary of 48,500 each. What is the median annual salary for the 13 employees?
(A) 38,000
(B) 40,000
(C) 42,600
(D) 45,600
(E) 48,500
Rationale: Median is just the value in the middle when you arrange all values in the ascending order
In this question, the 7th value would be the median (Since there are 13 employees)
38, 40, 40, 40, 42.5, 42.5,45.6
So, answer is D.
Answer: (D) 45,600
Question: The botanic garden is planting bulbs for the spring flower show. The head gardener is trying to decide how to place three Tulips bulbs, three Daffodil bulbs, and three Crocus bulbs along the front row. How many different arrangements can he make of these bulbs in the front row?
(A) 27
(B) 108
(C) 216
(D) 512
(E) 1,680
Rationale: total number of bulbs is 9, hence possible arrangements is 9!
But all the 3 bulbs are 3 each, hence
i.e.,9!/3!3!3!=1680 ways
answer is E.
Answer: (E) 1,680
Question: What sum of money put at C.I amounts in 2 years to Rs.8880 and in 3 years to Rs.9261?
(A) 8164
(B) 8877
(C) 2877
(D) 2678
(E) 1011
Rationale: 8880 ---- 381
100 ---- ? => 4.29%
x *104.29/100 * 104.29/100 = 8880
x*1.0876=8880
x=8880/1.0876 => 8164.38
Answer: A
Answer: (A) 8164
Question: Find the area of a parallelogram with base 24 cm and height 16 cm?
(A) 298 cm2
(B) 384 cm2
(C) 279 cm2
(D) 297 cm2
(E) 278 cm2
Rationale: Area of a parallelogram = base * height
= 24 * 16
= 384 cm2
Answer: B
Answer: (B) 384 cm2
Question: A fresh water aquarium contains Molly fish and Guppy fish at a ratio of 15:16. If 35 additional Guppy fish were put in the aquarium, the ratio of Molly fish to Guppy fish would be 15:21. How many Molly fish does the aquarium contain?
(A) 90
(B) 105
(C) 120
(D) 135
(E) 150
Rationale: 15x/21x = 15y/(16y+35)
15x=15y
x=y
21x=16y+35
5y=35
y=7
M=7*15=105
ANSWER:B
Answer: (B) 105
Question: After M students took a test, the average score was 65%. If the test has 50 questions, what is the least number of questions that the next student has to get right to bring the average score up to 70%?
(A) 2.5M + 35
(B) M + 37.5
(C) 0.65M + 70
(D) 70 - 0.65M
(E) 35+0.65M
Rationale: The total number of correct answers for M students is (0.65)*50*M=32.5*M
For an average of 70%: (total correct answers) / (M+1) = 0.7*50=35
Let x be the number of correct answers for the next student.
(x + 32.5M) / M+1 = 35
x + 32.5M= 35M+35
x = 2.5M + 35
The answer is A.
Answer: (A) 2.5M + 35
Question: Find the value of y from (12)^3 x 6^4 ÷ 432 = y?
(A) 2450
(B) 2560
(C) 2650
(D) 3500
(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) 5184
Question: Jim bought edging to go around a circular garden with a radius of 4 feet. Later he decided to
double the diameter of the garden. How many more feet of edging must he buy?
(A) 28.84' additional edging
(B) 48.84' additional edging
(C) 38.84' additional edging
(D) 18.84' additional edging
(E) 25.12' additional edging
Rationale: circumference of small garden = 2 x 3.14 x 4 = 25.12'
double of the circumference of small garden = 2 x 25.12' = 50.24'
More feet to be buy = 50.24 - 25.12 = 25.12
Answer : E
Answer: (E) 25.12' additional edging
Question: There are 50 players in a chess group, and each player plays each of the others once. Given that each game is played by two players, how many total games will be played?
(A) 1000
(B) 3000
(C) 1225
(D) 6000
(E) 9000
Rationale: 50 players are there.
two players play one game with one another.
so 50C2=50*49/2
=1225
SO OPTION C is correct
Answer: (C) 1225
Question: The diameter of a cylindrical tin is 14 cm and height is 2 cm. Find the volume of the cylinder?
(A) 33
(B) 45
(C) 66
(D) 77
(E) 98
Rationale: r = 7 h = 5
π * 7 * 7 * 5 = 98 π cc
Answer:E
Answer: (E) 98
Question: What approximate value should come in place of the question mark (?) in the following equation?
16√524 + 1492 - 250.0521?
(A) 1600
(B) 1800
(C) 1900
(D) 2400
(E) 1400
Rationale: ? ≈ 16 × 23 + 1490 – 250 ≈ 1600
Answer A
Answer: (A) 1600
Question: A retail item is offered at a discount of b percent (where b > 10), with a 5% state sales tax assessed on the discounted purchase price. If the state sales tax were not assessed, what percent discount from the item’s original retail price, in terms of b, would result in the same final price?
(A) b+5/1.05
(B) b/1.05 +5
(C) 1.05b-5
(D) b-5/1.05
(E) 1.05(p – 5)
Rationale: Let x be the price of the item.
Final price after discount and sales tax = x * (1 - b/100) * 1.05
Let c be the percent discount which would result in the same final price.
Then,
x * (1 - b/100) * 1.05 = x * (1 - c/100)
=> 1.05 - 1.05b/100 = 1 - c/100
=> c/100 = 1.05b/100 - .05
=> c = 1.05b - 5
Hence ,option C is correct.
Answer: (C) 1.05b-5
Question: A train 1600 m long passes a man, running at 6 km/hr in the same direction in which the train is going, in 60 sec. The speed of the train is?
(A) 42 km/hr
(B) 44 km/hr
(C) 46 km/hr
(D) 48 km/hr
(E) 50 km/hr
Rationale: Speed of the train relative to man = 1600/60 = 80/6 m/sec.
= 80/6 * 18/5 = 48 km/hr
Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr.
x - 6 = 48 => x = 42 km/hr.
Answer: A
Answer: (A) 42 km/hr
Question: In a company of 16 employees, 8 employees earn $38,000, 4 employees earn $42,000, and the 4 highest-paid employees earn the same amount. If the average annual salary for the 16 employees is $44,000, what is the annual salary for each of the highest-paid employees?
(A) $54,000
(B) $55,000
(C) $56,000
(D) $57,000
(E) $58,000
Rationale: 8*38,000+4*42,000+4x=16*44,000
4x=704,000-304,000-168,000
4x=232,000
x=58,000
The answer is E.
Answer: (E) $58,000
Question: What is the area of a square field whose diagonal of length 20 m?
(A) 288
(B) 289
(C) 200
(D) 112
(E) 178
Rationale: d2/2 = (20 * 20)/2
= 200
Answer: C
Answer: (C) 200
Question: How many times are the hands of a clock at right angle in a day?
(A) 22
(B) 24
(C) 44
(D) 48
(E) None
Rationale: EXPLANATION
In 12 hours, they are at right angles 22 times.
In 24 hours, they are at right angles 44 times.
Answer C
Answer: (C) 44
Question: Three 6 faced dice are thrown together. The probability that no two dice show the same number on them is
(A) 5/6
(B) 5/9
(C) 5/5
(D) 5/2
(E) 5/1
Rationale: No two dice show same number would mean all the three faces should show different numbers. The first can fall in any one of the six ways. The second die can show a different number in five ways. The third should show a number that is different from the first and second. This can happen in four ways.
Thus 6 * 5 * 4 = 120 favourable cases.
The total cases are 6 * 6 * 6 = 216.
The probability = 120/216 = 5/9.Answer: B
Answer: (B) 5/9
Question: If 0.5% of A =70 paise, then the value of A is ?
(A) Rs. 170
(B) Rs. 140
(C) Rs. 1.70
(D) Rs. 4.25
(E) None
Rationale: Answer
∵ 0.5/100 of A = 70/100
∴ A = Rs. (70 / 0.5) = Rs. 140
Correct Option: B
Answer: (B) Rs. 140
Question: Two brothers took the GMAT exam, the higher score is X and the lower one is Y. If the difference between the two scores is 1/5, what is the value of X/Y ?
(A) 3.
(B) 5
(C) 1/2.
(D) 1/3.
(E) There isn't enough data to answer the question.
Rationale: Answer is B : 5
X - Y = (X + Y)/2
Solving for X/Y = 5
Answer: (B) 5
Question: The distance from City A to City B is 120 miles. While driving from City A to City B, Cara drives at a constant speed of 30 miles per hour. Dan leaves City A 60 minutes after Cara. What is the minimum constant speed in miles per hour that Dan must exceed in order to arrive in City B before Cara?
(A) 42
(B) 44
(C) 46
(D) 48
(E) 40
Rationale: The time it takes Cara to drive to City B is 120 / 30 = 4 hours.
Dan needs to take less than 3 hours for the trip.
Dan needs to exceed a constant speed of 120 / 3 = 40 miles per hour.
The answer is E.
Answer: (E) 40
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.
(A) 348
(B) 277
(C) 960
(D) 872
(E) 121
Rationale: 60(x + 1) = 64x
X = 15
60 * 16 = 960 km
Answer: C
Answer: (C) 960
Question: An article is bought for Rs.675 and sold for Rs.900, find the gain percent?
(A) 33 1/8%
(B) 33 9/3%
(C) 33 1/3%
(D) 93 1/3%
(E) 33 2/3%
Rationale: 675 ---- 225
100 ---- ? => 33 1/3%
Answer:C
Answer: (C) 33 1/3%
Question: |x+3| – |4-x| = |9+x| How many solutions will this equation have?
(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) = 1
B
Answer: (B) 1