mathewhe/aqua_rat huggingface dataset:
Question: Find the odd man out. 23, 27, 36, 52, 77, 111, 162
(A) 111
(B) 162
(C) 52
(D) 27
(E) 36
Rationale: 23 + 22 = 27
27 + 32 = 36
36 + 42 = 52
52 + 52 = 77
77 + 62 = 113
113 + 72 = 162
Hence, 113 should have come in place of 111Answer is A
Answer: (A) 111
Question: Jaclyn buys $50 000 worth of debentures in a company. She earns 9.5% p.a. simple interest, paid to her quarterly (that is, every 3 months). If the agreed period of the debenture was 18 months: calculate the amount of interest Jaclyn will earn for each quarter
(A) 1187.5
(B) 1234
(C) 1289
(D) 1345
(E) None of these
Rationale: Explanation:
I=(p x r x t)/100
Answer: A
Answer: (A) 1187.5
Question: If A = x% of y and B = y% of x, then which of the following is true?
(A) A is smaller than B.
(B) Relationship between A and B cannot be determined
(C) If x is smaller than y, then A is greater than B.
(D) None of these
(E) B is smaller than A
Rationale: Explanation:
A = (x/100)y = (xy/100).................(Equation 1)
B = (y/100)x = (yx/100).................(Equation 2)
From these equations, it is clear that A = B
Answer: Option D
Answer: (D) None of these
Question: The number of arrangements that can be made with the letters of the word MEAUDOWS so that the vowels occupy the odd places?
(A) A)522
(B) B)534
(C) C)576
(D) D)656
(E) E)476
Rationale: Explanation:
The word MEAUDOWS has 8 letters of which 4 are vowels.
V-V-V-V-
As the vowels have to occupy odd places, they can be arranged in the 4 odd places in 4! i.e., 24 ways. While the consonants can be arranged among themselves in the remaining 4 places in 4! i.e., 24 ways.
Hence the total ways are 24 * 24 = 576.
C)
Answer: (C) C)576
Question: A scientist used a unique two-color code to identify each of the test subjects involved in a certain study. If the scientist found that choosing from among eight colors produced enough color codes to identify all but 5 of the test subjects, how many test subjects were in the study? (Assume that the order of the colors in the codes does not matter.)
(A) 32
(B) 33
(C) 34
(D) 35
(E) 36
Rationale: 8C2 = 28
The number of test subjects is 28 + 5 = 33
The answer is B.
Answer: (B) 33
Question: A monk has a very specific ritual for climbing up the steps to the temple. First he climbs up to the middle step and meditates for 1 minute. Then he climbs up 8 steps and faces east until he hears a bird singing. Then he walks down 12 steps and picks up a pebble. He takes one step up and tosses the pebble over his left shoulder. Now, he walks up the remaining steps three at a time which only takes him 9 paces.
How many steps are there?
(A) 50 steps
(B) 49 steps
(C) 44 steps
(D) 35 steps
(E) 49 steps
Rationale: B
There are 49 steps.
He hears the bird singing on step 33. He picks up the pebble on the 21st step and tosses it on the 22nd step. The remaining 27 steps are taken three at a time which is 9 pac
Answer: (B) 49 steps
Question: Roberto has three children: two girls and a boy. All were born on the same date in different years. The sum of the ages of the two girls today is smaller than the age of the boy today, but a year from now the sum of the ages of the girls will equal the age of the boy. Three years from today, the difference between the age of the boy and the combined ages of the girls will be
(A) 1
(B) 2
(C) 3
(D) –2
(E) –1
Rationale: girl1: g1, girl2: g2, boy:b, these are the symbols for their ages today.
g1+g2<b
(1 year from now): (g1+1)+(g2+1) = b+1 ; g1+g2 = b-1
The difference between the girls's age and the boy's age is one today:
Assume ages, g1:20, g2:25, b:46 (notice the difference is currently 1); in 3 years the ages will be g1:23, g2:28, b:49 ; 49-(23+28) = -2
The Answer should be D.
Answer: (D) –2
Question: The average score of a cricketer in 2 matches is 20 and in other 3 matches is 30. Then find the average score in all the 5 matches?
(A) 26
(B) 27
(C) 30
(D) 35
(E) 42
Rationale: Average in 5 matches = (2*20 + 3*30)/2+3 = 40+90 / 5 = 130/5 = 26
Answer is A
Answer: (A) 26
Question: A man whose speed is 4.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey ?
(A) 1 kmph
(B) 5 kmph
(C) 6 kmph
(D) 4 kmph
(E) 7 kmph
Rationale: Explanation:
Speed of Man = 4.5 kmph
Speed of stream = 1.5 kmph
Speed in DownStream = 6 kmph
Speed in UpStream = 3 kmph
Average Speed = (2 x 6 x 3)/9 = 4 kmph.
Answer: D
Answer: (D) 4 kmph
Question: A die is rolled twice. What is the probability of getting a sum equal to 9?
(A) 2/3
(B) 2/9
(C) 1/3
(D) 1/9
(E) 1/7
Rationale: Explanation :
Total number of outcomes possible when a die is rolled = 6 (âˆµ any one face out of the 6 faces)
Hence, total number of outcomes possible when a die is rolled twice, n(S) = 6 Ã— 6 = 36
E = Getting a sum of 9 when the two dice fall = {(3, 6), {4, 5}, {5, 4}, (6, 3)}
Hence, n(E) = 4
P(E) = n(E)/n(S)=4/36=1/9
ANSWER IS D
Answer: (D) 1/9
Question: Bob invested $2000 in fund A and $1000 in fund B. Over the next two years, the money in Fund A earned a total interest of 12 percent for the two years combined and the money in fund B earned 30 percent annual interest compounded annually. Two years after bob made these investments. Bob's investment in fund A was worth how much more than his investment in fund B?
(A) $500
(B) $550
(C) $600
(D) $650
(E) $700
Rationale: Bob earned 2000*(1+0.12) in total by fund A and earned 1000*(1+0.3)^2 in total by fund B.
So 2000*(1.12) - 1000*(1.69)= 550.
The answer is, therefore, (B).
Answer: (B) $550
Question: Four persons enter the lift of a seven storey building at the ground floor. In how many ways can they get out of lift on any floor other than ground floor
(A) 720
(B) 1296
(C) 1540
(D) 1478
(E) 360
Rationale: Each person out of 4 has 6 floors (options) to get out of (since no one gets out on the ground floor), hence total ways is 6*6*6*6=6^4. Now, there is no need to actually calculate this value: 6^4 will have 6 as the units digit and there is only one option (B)
Answer: B.
Answer: (B) 1296
Question: For any positive integer r, the sum of the first r positive integers equals r(r+1)/2 . If s and r are positive integers and s > r, what is the sum of all the integers between s and r, inclusive?
(A)  s(s+1)/2 + r(r+1)/2
(B)  s(s+1)/2 - r(r-1)/2
(C)  s(s+1)/2 - r(r+1)/2
(D)  s(s+1)/2 + r(r-1)/2
(E)  s(n+1)/2 - r(s-1)/2
Rationale: The sum of all the integers between s and r,inclusiveis the sum of the first s positive integersminusthe sum of the first r-1 positive integers.
The sum of the first s positive integers is s(s+1)/2;
The sum of the first r-1 positive integers is (r-1)r/2;
Therefore the answer is s(s+1)/2 - (r-1)r/2.
Answer: B.
Answer: (B)  s(s+1)/2 - r(r-1)/2
Question: 24 machines can do a work in 10days. How many machines are needed to complete the work in 40days?
(A) 10
(B) 6
(C) 4
(D) 7
(E) 5
Rationale: Required number of machines = 24*10/40 = 6
Answer is B
Answer: (B) 6
Question: Firm A's revenues are described by the equation Ra = 17.12x and its costs by Ca = 12.87x + 2400.
Firm B's revenues are described by the equation Rb = 13.27x and its costs by Cb = 8.77x + 1500.
(x denotes the quantity of sales).
If A's volume of sales increases from 1000 to 2000 over the same period that B's volume increases from 2000 to 4000, the percent increase in profits for the firm with the biggest dollar increase in profits is
(A) 20%
(B) 30%
(C) 60%
(D) 50%
(E) 33%
Rationale: Ok, I do not know whether it is exactly what you want to hear but I did it that way: first look at difference between revenue and variable cost => take the bigger one (b) which gives you: 4.5x-1500 just plug in 2000 and 3000. you get 7500 and 12000 (difference 4500). 4500> 0.5*7500 so 30%
B
Answer: (B) 30%
Question: If X = 2 + 1/(1+1/(1-1/2))then the value of 5x+7/3?
(A) 9 2/3
(B) 10 1/3
(C) 11
(D) 11 2/3
(E) 14
Rationale: X = 2 + 1/(1+1/(1-1/2))
= 2 + 1/(1+2)
= 2 + 1/3
X = 7/3 ==> 5X + 7/3 => 5(7/3) + 7/3
==> 35/3 + 7/3
==> 42/3
==> 14.
E)
Answer: (E) 14
Question: Which of the following expressions CAN be equal to 0 when x^2 − x = 6 ?
(A) x^2 − 3x +2
(B) x^2 − 2x -4
(C) x^2 − 5x +5
(D) x^2 − 3x +1
(E) x^2 − 4x +2
Rationale: x^2 − x = 6
x^2 − x - 6= 0
x=3 or x=-2
Only one choice results in a possibility of 0 when you plug in 3 or -2 for x except rest of all
x^2 − 3x + 2
Answer is A
Answer: (A) x^2 − 3x +2
Question: How many ltrs of water must beadded to 16 ltrs of milk and water containing 10% water to make it 20% water in it?
(A) 1 liter
(B) 2 liter
(C) 3 liter
(D) 4 liter
(E) 4.5 liter
Rationale: By rule of alligation,
% Concentration
of water in pure water (100) % Concentration
of water in the given mixture (10)
Mean % concentration
(20)
20 - 10 = 10 100 - 20 = 80
=> Quantity of water : Quantity of the mixture = 10 : 80 = 1 : 8
Here quantity of the mixture = 16 litres
=> Quantity of water : 16 = 1 : 8
=> Quantity of water =16×18=2 liter
B
Answer: (B) 2 liter
Question: A father said to his son, "I was as old as you are at present at the time of your birth." If the father's age is 28 years now, the son's age five years back was:
(A) 9 years
(B) 4 years
(C) 33 years
(D) 8 years
(E) 39 years
Rationale: Let the son's present age be x years.
Then, (28 - x) = x
2x = 28 => x = 14
Son's age 5 years back = (14 - 5) = 9 years.
ANSWER:B
Answer: (B) 4 years
Question: What Approximate Values should comein place of the question mark (?) in each of the following equations ?
85% of 225 + 56% of 450 + 32.98 x 5.001 = ?
(A) 600
(B) 625
(C) 608
(D) 605
(E) 610
Rationale: Explanation :
85x225/100+56x450/100+33x5 = 85 x 2.25 + 56 x 4.5 + 165 = 608
Answer : Option C
Answer: (C) 608
Question: Two concentric circles form a ring. The inner and outer circumferences of ring are (352/7) m and (518/7) m respectively. Find the width of the ring.
(A) 2
(B) 4
(C) 6
(D) 8
(E) None of them
Rationale: Let the inner and outer radii be r and R meters.
Then 2(22/7)r = (352/7) = r =((352/7) X (7/22) X (1/2))=8m.
2(22/7)R=(528/7) = R=((528/7) X (7/22) X (1/2))= 12m.
Therefore, Width of the ring = (R - r) = (12 - 8) m = 4 m.
Answer is B.
Answer: (B) 4
Question: In the x-y plane, the area of the region bounded by the graph of |x+y| + |x-y| = 2 is
(A) 1
(B) 12
(C) 16
(D) 20
(E) 24
Rationale: I've never seen such kind of question in GMAT before.
OK there can be 4 cases:
|x+y| + |x-y| = 2
A. x+y+x-y = 2 --> x=1
B. x+y-x+y = 2 --> y=1
C. -x-y +x-y= 2 --> y=-1
D. -x-y-x+y=2 --> x=-1
The area bounded by 4 graphs x=1, x=-1, y=1, y=-1 will be square with the side of 4 so the area will be 1*1=1.
Answer: A
Answer: (A) 1
Question: Father is aged three times more than his son Ronit. After 8 years, he would be two and a half times of Ronit's age. After further 8 years, how many times would he be of Ronit's age?
(A) 2 times
(B) 2 1/5 times
(C) 3 times
(D) 4 times
(E) 5 times
Rationale: Let Ronit's present age be x years. Then, father's present age =(x + 3x) years = 4x years.
(4x + 8) = 5 (x + 8)
2
8x + 16 = 5x + 40
3x = 24
x = 8.
Hence, required ratio = (4x + 16)/(x + 16) = 48/24	= 2.
A)
Answer: (A) 2 times
Question: emblem is coded as 216;
crude is coded as 125
Cricket will be ?
(A) 243
(B) 143
(C) 343
(D) 383
(E) 393
Rationale: coding follows (no. of letters)^3
emblem = 216 = 6^3
crude = 125 = 5^3
Cricket = 7^3 =343
ANSWER:C
Answer: (C) 343
Question: The difference between the place values of 7 and 3 in the prime number 527435 is
(A) 4
(B) 5
(C) 45
(D) 6970
(E) None
Rationale: Solution
(place value of 7)-(place value of 3)
= (7000 - 30)
= 6970.
Answer D
Answer: (D) 6970
Question: What is the remainder when 25473 is divided by 5?
(A) 3
(B) 2
(C) 4
(D) 5
(E) 0
Rationale: If the digit in unit place is divisible by 5, then number will be divisible by 5.
3 is not divisible by 5,so the number is not divisible by 5.
The nearest multiple of 5 is 25470
25473-25470=3.
Answer:3
Answer: (A) 3
Question: The ages of 2 persons differ by 16 years. If 6 years ago the elder one be 3 times as old as the younger one, find the present age of younger person.
(A) 10
(B) 14
(C) 20
(D) 15
(E) 32
Rationale: age of the younger person = x
age of the elder person = x+16
3(x-6) = x+16-6
x= 14
Answer is B
Answer: (B) 14
Question: From the starting point in a boat race, one competitor started to sail north at a speed of 1.6 Km/h, the other competitor started to sail west at a speed of 1.2 Km/h. What is the distance in Km between the two competitors after 5 hours?
(A) 10.
(B) 12.
(C) 12.5.
(D) 14.
(E) 15.4.
Rationale: Both competitors are sailing making angle of 90 degrees.
After 5 hrs one competitor will cover a distance of = 1.6 *5= 8 KM
And, other competitor will cover a distance of = 1.2*5= 6KM
distance between them after 5 hrs = (8^2+ 6^2)^1/2= 10 KM
A is the answer
Answer: (A) 10.
Question: What is the least number, which is perfect square but contains 2700 as its factor?
(A) 8100
(B) 10900
(C) 54000
(D) 2500
(E) 2700
Rationale: 900 * 3 * 3 = 8100
ANSWER A
Answer: (A) 8100
Question: Machine A can finish a job in 4 hours, Machine В can finish the job in 2 hours, and Machine С can finish the job in 6 hours. How many hours will it take for A, B, and С together to finish the job?
(A) 4/3
(B) 6/5
(C) 8/7
(D) 10/9
(E) 12/11
Rationale: The combined rate is 1/4+1/2+1/6 = 11/12 of the job per hour.
The time to complete the job is 12/11 hours.
The answer is E.
Answer: (E) 12/11
Question: Three hoses work to fill a tub at at different rate. Hose Q and B, working together, can fill the tub in 6/5 of an hour. Hoses Q and C can fill it in 3/2 an hour. Houses B and C can fill it in 2 hours. How long does it take all 3 hoses, working together, to fill the tub?
Edited for accurate solution
(A) 3/10
(B) 2/5
(C) 1/2
(D) 1
(E) 6/5
Rationale: Convert the given time to rate and you will be able to add it up.
Total Rate of Q and B = Rate of Q + Rate of B = 1/(6/5) = 5/6
Total Rate of Q and C = Rate of Q + Rate of C = 1/(3/2) = 2/3
Total Rate of B and C = Rate of B + Rate of C = 1/2
Adding all three,
2(Rate of Q + Rate of B + Rate of C) = 5/6 + 2/3 + 1/2 = 2
Rate of Q + Rate of B + Rate of C = 1 tub/hour
Time taken by all three together to fill up the tub is 1 hour=D
Answer: (D) 1
Question: A sum of money amounts to Rs. 9800 after 5 years and Rs. 12005 after 8 years at the same rate of simple interest. The rate of interest per annum is:
(A) 5%
(B) 8%
(C) 12%
(D) 15%
(E) 10%
Rationale: S.I. for 3 years = Rs. (12005 - 9800) = Rs. 2205.
S.I. for 5 years = Rs.	((2205/3)x 5)	= Rs. 3675
Principal = Rs. (9800 - 3675) = Rs. 6125.
Hence, rate =((100 x 3675)/(6125 x 5))%	= 12%
Answer :C
Answer: (C) 12%
Question: A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is:
(A) 110 m
(B) 120 m
(C) 190 m
(D) 150 m
(E) 180 m
Rationale: Answer: Option D
Let the length of the train be x meters and its speed be y m/sec.
They, x / y = 15 => y = x/15
x + 100 / 25 = x / 15
x = 150 m.
Answer: (D) 150 m
Question: W and X start a business with Rs.5000 and Rs.20000 respectively. Hoe should they share their profits at the end of one year?
(A) 4:1
(B) 1:3
(C) 1:4
(D) 1:5
(E) 2:1
Rationale: They should share the profits in the ratio of their investments.
The ratio of the investments made by W and X =
5000 : 20000 => 1:4 .
Answer:C
Answer: (C) 1:4
Question: In x-y plane, there is a right triangle ABC (∠B=90o). If the length of AC is 25 and the slope of line segment AC is 4/3, what is the length of AB?
(A) 12
(B) 18
(C) 24
(D) 20
(E) 40
Rationale: Slope = Change in Vertical Direction/Change in Horizontal Direction = 4/3
Change in Vertical Direction = 4x = AB
Change in Horizontal Direction = 3x = BC
AB^2 + BC^2 = 25^2
16x^2 + 9x^2 = 625
25x^2 =625
x^2 = 25
x = 5
Therefore AB = 5*4 =20
Answer: D
Answer: (D) 20
Question: A walks around a circular field at the rate of one round per hour while B runs around it at the rate of four rounds per hour. They start in the same direction from the same point at 7.30 a.m. They shall first cross each other after___ minutes?
(A) 11 min
(B) 12 min
(C) 10 min
(D) 15 min
(E) 20 min
Rationale: Since A and B move in the same direction along the circle, so they will first meet each other when there is a difference of one round between the two.
Relative speed of A and B = 4 - 1 = 3 rounds per hour.
Time taken to complete one round at this speed = 1/3 hr = 20 min.
E
Answer: (E) 20 min
Question: Working alone at its constant rate, pump A pumped out ¼ of the water in a tank in 2 hours. Then pumps B and C started working and the three pumps, working simultaneously at their respective constant rates, pumped out the rest of the water in 3 hours. If pump B, working alone at its constant rate, would have taken 18 hours to pump out the rest of the water, how many hours would it have taken pump C, working alone at its constant rate, to pump out all of the water that was pumped out of the tank?
(A) 6
(B) 12
(C) 15
(D) 18
(E) 24
Rationale: Rate of pump A = 1/8
3 hours are required to pump out the remaining (3/4)ths of tank --> 1 hr to pump out 1/4
Rate of A + Rate of B + Rate of C = 1/4
Rate of B + Rate of C = 1/4 - 1/8 = 1/8
B takes 18 hours to pump out the remaining (3/4)ths of tank --> 6 hrs per (1/4)ths --> 24 hrs to pump out fully.
Rate of B = 1/24
1/24 + Rate of C = 1/8
Rate of C = 1/8 - 1/24 = 1/12
Time required to pump out all the water by C = 12 hrs
Answer: B
Answer: (B) 12
Question: A FIVE DIGIT NUMBER IS FORMED BY USING THE DIGITS 1,2,3,4&5 WITH OUT REPETITIONS . WHAT IS THE PROBABILITY THE NUMBER IS DIVISIBLE BY4?
A)
B)
C)
D)
E)
(A) 1/5
(B) 5/6
(C) 4/5
(D) 7/3
(E) 2/7
Rationale: FOLLOW SEND PM
Re: A FIVE DIGIT NUMBER IS FORMED BY USING THE DIGITS 1,2,3,4&5 WITH OUT R [#permalink] Post 08 Oct 2010, 05:15
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anilnandyala wrote:
A FIVE DIGIT NUMBER IS FORMED BY USING THE DIGITS 1,2,3,4&5 WITH OUT REPETITIONS . WHAT IS THE PROBABILITY THE NUMBER IS DIVISIBLE BY4?
A)1/5
B)5/6
C)4/5
D)7/3
E)2/7
P = Number of desired outcomes / number of possible outcomes
Number of desired outcomes:
To be divisible by 4, the number has to end with the last two digits forming a number divisible by 4. Given the numbers in the question this leaves us with:
12
24
32
52
For each of them I now have to put the remaining numbers in front: 3x2x1 --> 6 combinations for each number set = 6x4 (we have 4 sets from above) = 24
Number of possible outcomes:
The total number of possibilities to form a 5 digit number from the question= 5x4x3x2x1=120
P = 24/120 = 1/5 --> A
Answer: (A) 1/5
Question: In a Lake, there is a patch of lily pads. Every day, the patch doubles in size. It takes 48 days for the patch to cover the entire lake, how many days would it take the patch to cover half of the lake?
(A) 36
(B) 2^4*3
(C) 24
(D) 38
(E) 47
Rationale: Working backward from the day it's covered:
day 48: fully covered
day 47: half covered
So 47 days
ANSWER:E
Answer: (E) 47
Question: Find large number from below question The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder
(A) 1234
(B) 1435
(C) 1456
(D) 1567
(E) 1635
Rationale: Let the smaller number be x. Then larger number = (x + 1365).
x + 1365 = 6x + 15
5x = 1350
x = 270
Large number = 270+1365 = 1635
E
Answer: (E) 1635
Question: 20 beavers, working together in a constant pace, can build a dam in 3 hours. How many B hours will it take 12 beavers that work at the same pace, to build the same dam?
(A) 2.
(B) 4.
(C) B=5.
(D) B=6.
(E) B=8.
Rationale: C. 5 hrs
If there were 10 beavers it could have taken double B= 6hrs.. so closest to that option is 5.C
Answer: (C) B=5.
Question: A train running at the speed of 54 km/hr crosses a pole in 9 seconds. What is the length of the train?
(A) 135
(B) 278
(C) 255
(D) 150
(E) 287
Rationale: Speed=(54 * 5/18) m/sec = (15) m/sec Length of the train
= (Speed x Time) = (15 * 9) m
= 135 m.
Answer:A
Answer: (A) 135
Question: How many different sets of positive square integers K, each greater than 1, add up to 75?
(A)  1
(B)  4
(C)  7
(D)  11
(E)  13
Rationale: E = 13 is the correct answer.
Answer: (E)  13
Question: A can do a piece of work in 25 days and B in 20 days. They began the work together but 5 days before the completion of the work, A leaves. The work was completed in?
(A) 19 1/3 days
(B) 10 1/3 days
(C) 13 1/3 days
(D) 15 1/3 days
(E) 13 2/3 days
Rationale: (x – 5)/25 + x/20 = 1
x = 13 1/3 days
ANSWER:C
Answer: (C) 13 1/3 days
Question: A train running at the speed of 142 km/hr crosses a pole in 12 seconds. Find the length of the train.
(A) 540
(B) 288
(C) 200
(D) 340
(E) 712
Rationale: Speed = 162*(5/18) m/sec = 45m/sec
Length of Train (Distance) = Speed * Time
45 * 12 = 540 meter
Answer: A
Answer: (A) 540
Question: 4 bells first begin to toll together with anintervals of 5,10,15 & 20 sec. How many times does they toll together in an hr?
(A) 50
(B) 60
(C) 67
(D) 78
(E) 98
Rationale: 5|5, 10, 15, 20
2|1, 2, 3, 4
|1, 1, 3, 2
L.C.M of 5, 10, 15, 20 is 60
60 times
B
Answer: (B) 60
Question: A tradesman by means of his false balance defrauds to the extent of 50%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?
(A) 149%
(B) 125%
(C) 130%
(D) 175%
(E) 143%
Rationale: g% = 50 + 50 + (50*50)/100
= 125%
Answer: B
Answer: (B) 125%
Question: Which of the following inequalities is equivalent to -24 > -4 - 10x?
(A)  x < 1
(B)  x < 2
(C)  x < 3
(D)  x < 4
(E)  x < 5
Rationale: You can work with the inequality in the same way as you do when you have the equal to sign. You can take terms to the other side by flipping their sign, you can multiply/divide the inequality by the same term on both sides of the equation etc.
The only important thing to note is the following:
When you multiply/divide by a negative number, the sign of the inequality flips.
To illustrate,
-24 > -4 - 10x
-20 > - 10x (Correct)
2 > x (Correct)
the correct option is B
Answer: (B)  x < 2
Question: A company hired a printer to produce a total of x + 1 envelopes. The job consisted of two types of envelopes, 2¢ envelopes and 7¢ envelopes. If the company requested 3 more 2¢ envelopes than 7¢ envelopes, which of the following expressions denotes the cost, in cents, of the total x + 1 envelopes ?
(A) (7x-20)/2
(B) 2x+22
(C) 5x+7
(D) (6x+14)/2
(E) 5x-7
Rationale: We can take
X+1 = 9
X= 8
So 2c envelopes will be 6
and 7c envelopes will be 3
So total cost will be 33
Then that is our target
Plug x =8 in answer choices
Only E works
Correct Answer : E
Answer: (E) 5x-7
Question: A person can go from place “P” to “Q” by 7 different modes of transport, but is allowed to return back to “P” by any mode other than the one used earlier. In how many different ways can he complete the entire journey?
(A) 42
(B) 55
(C) 77
(D) 29
(E) 10
Rationale: Explanation:
The person can travel from “P” to “Q” in any of the 7 different modes of transport. However, while returning, he cannot use the mode which he used earlier. Thus, while returning, he has the option of only 6 different modes of transport. Hence, the total number of ways would be 7 * 6 = 42.
ANSWER: A
Answer: (A) 42
Question: 6) A marketing firm determined that , of 160 households surveyed, 80 used neither Brand A nor Brand B soap.60 used only Brand A soap and for every household that used both brands of soap, 3 used only brand B soap.how many of the 200 household surveyed used both brands of soap?
(A) a) 15
(B) b) 20
(C) c) 30
(D) d) 40
(E) e) 5
Rationale: 80 = At least one of Soap A or B
Both brands = x
Brand B = 3x
=> 60 + x + 3x = 120
=> 4x = 20
=> x = 5
Answer - E
Answer: (E) e) 5
Question: Rs. 20 is the true discount on Rs. 260 due after a certain time. What will be the true discount on the same sum due after half of the former time, the rate of interest being the same?
(A) Rs. 10
(B) Rs. 10.40
(C) Rs. 15.20
(D) Rs. 13
(E) Rs. 14
Rationale: given TD=20, S=260 from these we can know PW=S-TD=260-20=240
given TD for sum is 20
SI on PW is TD
=>SI on 240 is 20
now given TD is half of the former time
=> SI on 240 is 10
=> TD on 250(i.e 240+10) is 10 (since given TD on sum=PW+TD is half the former time)
=> TD on 260=(10/250)*260=Rs10.40
ANSWER:B
Answer: (B) Rs. 10.40
Question: A case contains c cartons. Each carton contains b boxes, and each box contains 300 paper clips. How many paper clips are contained in 2 cases?
(A) 300bc
(B) 300b/c
(C) 600bc
(D) 600b/c
(E) 600/bc
Rationale: 2 cases * c cartons/case * b boxes/carton * 300 clips/box = 600bc paper clips
The answer is C.
Answer: (C) 600bc