mathewhe/aqua_rat huggingface dataset:
Question: Joe's current weekly caloric intake is 20,000 calories. His physician has advised Joe to reduce the number of calories he consumes weekly to 14,000. By what percent does Joe need to reduce his weekly caloric intake?
(A)  20%
(B)  30%
(C)  50%
(D)  60%
(E)  70%
Rationale: A certain percentage of questions in the Quant section of the GMAT are just 'math questions' - you'll use a formula, do some calculations and you'll have the answer. This is one of those types of questions. You still have to write everything down and stay organized, but the work involved is relatively straight-forward.
Here, we're told that the original amount of calories is 20,000 and that the reduced amount of calories is 14,000. We're asked what PERCENT should the original amount of calories be REDUCED BY?
Original Calories= 20,000
Reduced Calories = 14,000
The percent of reduced calories is relative to the original calories as shown:
14,000/20,000 = 7/10 = 70%. So, 14,000 calories is 70% of 20,000 calories (100%). But the question is BY what PERCENT should the original amount of calories be REDUCED. 100% - 70% = 30%.
B
Answer: (B)  30%
Question: Evaluate: |4 - 8(3 - 12)| - |5 - 11| = ?
(A) 40
(B) 50
(C) 60
(D) 70
(E) 80
Rationale: According to order of operations, inner brackets first. Hence
|4 - 8(3 - 12)| - |5 - 11| = |4 - 8*(-9)| - |5 - 11|
According to order of operations, multiplication within absolute value signs (which may be considered as brackets when it comes to order of operations) next. Hence
= |4 + 72| - |5 - 11|
= |76| - |-6|
= 76 - 6 = 70
correct answer D)70
Answer: (D) 70
Question: A certain sum amounts to Rs.675 in 3 years and Rs.850 in 6 years. Find the rate % per annum?
(A) 10%
(B) 8%
(C) 11%
(D) 9%
(E) 7%
Rationale: 3 --- 675
6 --- 850
--------------
3 --- 175
N = 1 I = 55 R = ?
P = 675 - 175= 500
55 = (500*1*R)/100
R = 11%
Answer: C
Answer: (C) 11%
Question: If (a – b) is 7 more than (c + d) and (a + b) is 3 less than (c – d), then (a – c) is:
(A) 6
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: (a – b) – (c + d) = 7 and (c – d) – (a + b) = 3
=> (a – c) – (b + d) = 7 and (c – a) – (b + d) = 3
=> (b + d) = (a – c) – 7 and (b + d) = (c – a) – 3
=> (a – c) – 7 = (c – a) – 3 => 2(a – c) = 4 => (a – c) = 2
ANSWER:B
Answer: (B) 2
Question: Frank the Fencemaker needs to fence in a rectangular yard. He fences in the entire yard, except for one full side of the yard, which equals 40 feet. The yard has an area of 480 square feet. How many feet offence does Frank use?
(A) 14
(B) 47
(C) 54
(D) 180
(E) 64
Rationale: Area = Length x Breadth
480 = 40 x Breadth
So, Breadth = 12 Units
Fencing required is -
Breadth + Breadth + Length
12 + 12 + 40 => 64 feet
Answer must be (E) 64
Answer: (E) 64
Question: A man buys 12 lts of liquid which contains 10% of the liquid and the rest is water. He then mixes it with 10 lts of another mixture with 30% of liquid. What is the % of water in the new mixture?
(A) 80.91
(B) 76.45
(C) 77.45
(D) 74.45
(E) 73.45
Rationale: 10% in 12 lts is 1.2. So water = 12-1.2 = 10.8 lts. 30% of 10 lts = 3. So water in 2nd mixture = 10-3 = 7 lts. Now total quantity = 12 + 10 = 22 lts. Total water in it will be 10.8 + 7 = 17.8 lts. % of water = (100*17.8)/22 = 80.91. Answer:A
Answer: (A) 80.91
Question: If in a box of dimensions 6 m * 5 m * 4 m smaller boxes of dimensions 60 cm * 50 cm * 40 cm are kept in it, then what will be the maximum number of the small boxes that can be kept in it?
(A) 500
(B) 1000
(C) 900
(D) 800
(E) 700
Rationale: 6 * 5 * 4 = 60/100 * 50/100 * 40/100 * x
1 = 1/10 * 1/10 * 1/10 * x => x = 1000
ANSWER:B
Answer: (B) 1000
Question: If a and b are each greater than x and y, which of the following must be true?
I. a + b < x + y
II. ab > xy
III.a + b > x + y
(A) I only
(B) II only
(C) I and II
(D) III only
(E) I, II and III
Rationale: I. a + b > x + y. Since a and b are each greater than x and y, then the sum of a and b will also be greater than the sum of x and y.
II. ab > xy. Not necessarily true, consider a = b = 0 and x = y = -1 --> ab = 0 < 1 = xy.
III. |a| + |b| > |x| + |y|. Not necessarily true, consider a = b = 0 and x = y = -1 --> |a| + |b| = 0 < 2 = |x| + |y|.
Answer: D.
Answer: (D) III only
Question: A rummy( card game) player has 13 cards in his hand with 2 Aces, one of spades and other of hearts. All other cards are unique. How many ways can he hold the 13 cards?
(A) 14!
(B) 11!
(C) 12!
(D) 10!
(E) 13!
Rationale: Even though the player has 2 Aces, both of them are of different colour and sign. So we can't consider them as a single object. Ace (spade)Ace(heart) is different to Ace(heart)Ace(spades). So there are 13! Ways to arrange the cards. Answer is E. 13!.
Answer: (E) 13!
Question: The units digit of (35)^(87) + (93)^(55) is:
(A) 2
(B) 4
(C) 6
(D) 8
(E) 0
Rationale: The units digit of powers of 3, cycles in a group of 4: {3, 9, 7, 1}
55 has the form 4k+3, so the units digit of 93^55 is 7.
The units digit of powers of 5 is always 5.
7+5 = 12, so the units digit is 2.
The answer is A.
Answer: (A) 2
Question: If X gets 25% more than Y and Y gets 20% more than Z, the share of Z out of Rs. 740 will be:
(A) Rs. 300
(B) Rs. 200
(C) Rs. 240
(D) Rs. 350
(E) None of these
Rationale: Z share = Z,
Y = 1.2Z
X = 1.25×1.2Z,
X+Y+Z =740
(1.25× 1.2+1.2+1)Z=74
3.7Z=740, Z=200
Answer: . B.
Answer: (B) Rs. 200
Question: When 27 is divided by positive integer n, the remainder is 4. For how many values of n is this true?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: When 27 is divided by n, the remainder is 4 i.e. 4 apples left over after grouping, so n must be greater than 4.
It also means that 23 is completely divisible by n.
The factors of 23 are 1 and 23.
Out of these, n can be 23.
Answer (B).
Answer: (B) 1
Question: Two pipes can fill the cistern in 10hr and 12 hr respectively, while the third empty it in 25hr. If all pipes are opened simultaneously, then the cistern will be filled in
(A) 7.5 hr
(B) 6.98 hr
(C) 8.5 hr
(D) 10 hr
(E) None of these
Rationale: Solution:
Work done by all the tanks working together in 1 hour.
1/10+1/12−1/25=1/7
Hence, tank will be filled in 6.98 hour
Option(B)
Answer: (B) 6.98 hr
Question: A carpenter constructed a rectangular sandbox with a capacity of 10 cubic feet. If the carpenter were to make a similar sandbox twice as long, twice as wide, and twice as high as the first sandbox, what would be the capacity, in cubic feet, of the second sandbox?
(A)  20
(B)  40
(C)  60
(D)  80
(E)  100
Rationale: A quick note on doubling. When you double a length you have 2*L1. When you double all lengths of a rectangle you have (2*L1)(2*L2) = A. An increase of 2^2 or 4. When you double all lengths of a rectangular prism you have (2*L1)(2*L2)(2*L3) = V. An increase of 2^3 or 8.
This leads to the basic relationship:
Line: 2*original size
Rectangle: 4*original size
Rectangular Prism: 8*original size answer is D
Answer: (D)  80
Question: A house seller can deduct 5 percent from the total sales value. If he has sold 5 houses, and the price of two houses is between $150,000 and $250,000, one of them is $400,000 house, two houses are between $500,000 and 750,000, what is the range of his revenue?
(A) 790
(B) 785
(C) 795
(D) 800
(E) 810
Rationale: taking away '000 thousand sfor easy calculation
(1) 2(150)+400+2(500) = 1700
1700*0.95=1615 (Revenue considering the minimum values with the discount)
(2) 2(250)+400+2(750) = 2400 (Revenue considering the maximum values without the discount)
So, the the revenue range could be = 2400 - 1615 = 785
B
Answer: (B) 785
Question: Salaries of Ravi and Sumit are in the ratio 2 : 3. If the salary of each is increased by Rs. 4000, the new ratio becomes 40 : 57. What is Sumit's salary?
(A) 32000
(B) 38000
(C) 35000
(D) 33000
(E) 39000
Rationale: Let the original salaries of Ravi and Sumit be Rs. 2x and Rs. 3x respectively.
Then, 2x + 4000/3x + 4000 = 40/57
57(2x + 4000) = 40(3x + 4000)
6x = 68,000
3x = 34,000
Sumit's present salary = (3x + 4000) = Rs.(34000 + 4000) = Rs. 38,000.
Answer is B.
Answer: (B) 38000
Question: Rs. 800 becomes Rs. 956 in 3 years at a rate of S.I. If the rate of interest is increased by 4%, what amount will Rs. 800 become in 3 years?
(A) 1059
(B) 1028
(C) 1052
(D) 1028
(E) 1012
Rationale: S.I. = (956 - 800) = Rs. 156.
Rate = (100 * 156) / (800 * 3) = 6 1/2 %
Now rate = (6 1/2 + 4) = 10 1/2 %
New S.I. = (800 * 21/2 * 3/100) = Rs. 252
New amount = (800 + 252) = Rs. 1052.Answer:C
Answer: (C) 1052
Question: Three pipes A, B and C can fill a tank from empty to full in 30 minutes, 20 minutes and 10 minutes respectively. When the tank is empty, all the three pipes are opened. A, B and C discharge chemical solutions P, Q and R respectively. What is the proportion of solution R in the liquid in the tank after 3 minutes?
(A) 6/19
(B) 6/11
(C) 6/12
(D) 6/10
(E) 6/38
Rationale: Part filled by (A + B + C) in 3 minutes = 3(1/30 + 1/20 + 1/10) = 11/20
Part filled by C in 3 minutes = 3/10
Required ratio = 3/10 * 20/11 = 6/11
Answer:B
Answer: (B) 6/11
Question: 9 men working 8 hours per day dig 30 m deep. How many extra men should be put to dig to a depth of 50 m working 6 hours per day?
(A) 33
(B) 66
(C) 88
(D) 11
(E) 281
Rationale: (9 * 8)/30 = (x * 6)/50 => x = 20
20 – 9 = 11
Answer: D
Answer: (D) 11
Question: The total cost of 100 paper plates and 200 paper cups is $6.00 At the same rates what is the total cost of 20 of the plates and 40 of the cups?
(A) $.90
(B) $1.00
(C) $1.20
(D) $1.50
(E) $1.60
Rationale: U dont need to go through all this
What u have with u is
100 P + 200 C = $6.00
Just divide the equation by 5 and you will get what u are looking for
20P + 40 C = $1.20
Therefore OA is C
Answer: (C) $1.20
Question: What is the least number of squares tiles required to pave the floor of a room 15 m 17 cm long and 9 m 2 cm broad?
(A) 617
(B) 746
(C) 808
(D) 812
(E) 814
Rationale: Length of largest tile = H.C.F. of 1517 cm and 902 cm = 41 cm.
Area of each tile = (41 x 41) cm2.
Required number of tiles = (1517 x 902)/(41X41) = 814.
Answer: Option E
Answer: (E) 814
Question: A train is 400 meter long is running at a speed of 60 km/hour. In what time will it pass a bridge of 800 meter length?
(A) 72 seconds
(B) 27 seconds
(C) 40 seconds
(D) 128 seconds
(E) 18 seconds
Rationale: Speed = 60 Km/hr = 60*(5/18) m/sec = 150/9 m/sec
Total distance = 400+ 800 = 1200 meter
Time = Distance/speed
= 1200 * (9/150) = 72 seconds
Answer: A
Answer: (A) 72 seconds
Question: The percentage profit earned by selling an article for Rs. 1920 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make 25% profit?
(A) Rs. 2000
(B) Rs. 2200
(C) Rs. 2400
(D) Rs. 2600
(E) None of these
Rationale: Let C.P. be Rs. x.
Then, (1920 - x)/x * 100 = (x - 1280)/x * 100
1920 - x = x - 1280
2x = 3200 => x = 1600
Required S.P. = 125 % of Rs. 1600 = 125/100 * 1600 = Rs. 2000.
ANSWER:A
Answer: (A) Rs. 2000
Question: Stacy and Heather are 15 miles apart and walk towards each other along the same route. Stacy walks at constant rate that is 1 mile per hour fast than heather's constant rate of 5 miles/hour. If Heather starts her journey 24 minutes after Stacy, how far from the original destination has Heather walked when the two meet?.
(A) 6.5mile
(B) 5.7mile
(C) 7.0mile
(D) 8.0mile
(E) 12 mile
Rationale: Ss - Stacy's speed = 6m/hr
Sh - Heather's speed = 5m/hr
In 24 minutes Stacy will cover = (24/60)*6 = 2.4miles
Now since both are walking in opposite directions, add their speeds - 6+5 =11m/hr and distance to cover is 15 -2.4 = 12.6
Time taken = Distance/ Speed = 12.6/11 = 1.145 hrs
Heather will cover = 5*1.145 = 5.72miles.
Answer B
Answer: (B) 5.7mile
Question: Look at this series: 2, 4, 6, 8, 10, ... What number should come next?
(A) 11
(B) 12
(C) 13
(D) 14
(E) 15
Rationale: Explanation: This is a simple addition series. Each number increases by 2.
Answer: Option B
Answer: (B) 12
Question: A man gets a simple interest of Rs.500 on a certain principal at the rate of 5% p.a in two years. Find the compound interest the man will get on twice the principal in two years at the same rate.
(A) 256.29
(B) 256.22
(C) 256.28
(D) 256.21
(E) 256.25
Rationale: Let the principal be Rs.P
S.I at 5% p.a in 8 years on Rs.P = Rs.500
(P)(8)(5)/100 = 500
P = 1250
C.I on Rs.2P i.e., Rs.2500 at 5% p.a in two years
=2500{ [1 + 5/100]2 - 1} = 2500{ 212 - 202 /202}
= 2500/400(441 - 400)
= 25/4(41) = 1025/4 = Rs.256.25
Answer:E
Answer: (E) 256.25
Question: The area of a square garden is A square feet and the perimeter is p feet. If a=2p+14.25, what is the perimeter of the garden, in feet?
(A) 38
(B) 36
(C) 40
(D) 56
(E) 64
Rationale: Perimeter of square = P
Side of square = P/4
Area of Square = (P^2)/16 =A
Given that A = 2P + 14.25
(P^2)/16 = 2P + 9
P^2 = 32P + 228
P^2 -32P -228 = 0
P^2 -38P + 6P -228 = 0
P(P-38)+6(P+38) = 0
(P-38)(P+6) = 0
P = 38 or- 6
Discarding negative value , P = 38
Answer is A
Answer: (A) 38
Question: A gym offers 11 levels of fitness classes, and in an attempt to reward those who progress toward higher levels of fitness it charges $50 less per course for each level of fitness. Jessica completed all 11 levels by taking one course at each level, and her total cost was $4675. What is the cost X for a course at the gym's highest level?
(A) $175
(B) $245
(C) $425
(D) $675
(E) $725
Rationale: Let the cost of a course in level 1 = x
=> Cost of level 2 = x-(50*1)... and so on
=> cost of level 11 = x-(50*10) = x-500
=> Total cost X of 1 course in each of the 11 levels = x+(x-50)+(x-100)+.....+(x-500)
= 11x -50 (1+2+....+10)
= 11x - (50*55)
=> 11x-2750 = 4675
11x = 7425
x= 675
x-500=175
Answer A
Answer: (A) $175
Question: If the average marks of three batches of 62, 60 and 45 students respectively is 50, 55, 60, then the
average marks of all the students is
(A) 54.48
(B) 54.68
(C) 54.6
(D) 54.49
(E) None of these
Rationale: Explanation:
(62Ã—50)+(60Ã—55)+(45Ã—60)/(62+60+45)=54.49
Answer: Option D
Answer: (D) 54.49
Question: Seven children — A, B, C, D, E, F, and G — are going to sit in seven chairs in a row. Child A has to sit next to both BG, with these two children immediately adjacent to here on either side. The other four children can sit in any order in any of the remaining seats. How many possible configurations E are there for the children?
(A) 240
(B) 480
(C) 720
(D) 1440
(E) 3600
Rationale: MAGOOSHOFFICIAL SOLUTION:
First, we will consider the restricted elements — children ABG have to be in three seats in a row. How many “three in a row” seats are there in a row of seven seats?
X X X _ _ _ _
_ X X X _ _ _
_ _ X X X _ _
_ _ _ X X X _
_ _ _ _ X X X
There are five different “three in a row” locations for these three children. Now, for any given triplet of seats, we know A has to be in the middle, so the children could be seated B-A-G or G-A-B — just those two orders. This means the total number of configurations for these three children is 5*2 = 10.
Now, consider the non-restricted elements, the other four. Once ABG are seated, the remaining four children can be seated in any order among the remaining four seats — that’s a permutation of the 4 items —- 4P4 = 4! = 24. For any single configuration of ABG, there are 24 ways that the other children could be seated in the remaining seats.
Finally, we’ll combine with the Fundamental Counting Principle. We have 10 ways for the first three, and 24 ways for the remaining four. That’s a total number of configurations E of 24*10 = 240.
Answer = A
Answer: (A) 240
Question: In how many different ways can 2 girls and 2 boys form a circle such that the boys and the girls alternate?
(A) 8
(B) 1
(C) 7
(D) 5
(E) 2
Rationale: Explanation :
In a circle, 2 boys can be arranged in 2! ways
Given that the boys and the girls alternate.
Hence there are 2 places for girls which can be arranged in 2! ways
Total number of ways = 1! x 2! = 1 x 2 = 2. Answer : Option E
Answer: (E) 2
Question: A sum amounts to Rs.8820 in 2 years at the rate of 5% p.a. If interest was compounded yearly then what was the principal?
(A) s.4000
(B) s.5000
(C) s.4500
(D) s.4800
(E) s.8000
Rationale: CI=8820,R=5,N=2
CI=P[1+R/100]^2
=P[1+5/100]^2
8820=P[21/20]^2
8820[20/21]^2
8000
ANSWER:E
Answer: (E) s.8000
Question: Due to construction, the speed limit along an 10-mile section of highway is reduced from 55 miles per hour to 30 miles per hour. Approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
(A) A) 6.24
(B) B) 8
(C) C) 10
(D) D) 9.1
(E) E) 24
Rationale: Old time in minutes to cross 10 miles stretch = 10*60/55 = 10*12/11 = 10.9
New time in minutes to cross 10 miles stretch = 10*60/30 = 10*2 = 20
Time difference = 9.1
Ans:D
Answer: (D) D) 9.1
Question: A boat goes 100 km downstream in 10 hours, and 75 m upstream in 15 hours. The speed of the stream is?
(A) 25 ½ kmph
(B) 28 ½ kmph
(C) 42 ½ kmph
(D) 20 ½ kmph
(E) 22 ½ kmph
Rationale: M = 100
S = x
DS = 10
US = 5
S = (10 - 5)/2
S= 2 2 ½ kmph
Answer: E
Answer: (E) 22 ½ kmph
Question: Water consists of hydrogen and oxygen, and the approximate ratio, by mass, of hydrogen to oxygen is 2:16. Approximately how many grams of hydrogen are there in 117 grams of water?
(A) 7
(B) 9
(C) 11
(D) 13
(E) 15
Rationale: (2/18)*117 = 13 grams
The answer is D.
Answer: (D) 13
Question: Felix earned 70% more per month than Oscar. If Felix’s salary is decreased 10% and Oscar’s salary is increased by 10%, then Felix would be earning what percent more than Oscar?
(A) 10%
(B) 9.09%
(C) 40%
(D) 39.09%
(E) It cannot be determined from the information given.
Rationale: This Q is all about taking the correct BASE for taking %s..
the very first step requires taking some numbers for each..
ONE should be 100...
it is easy to take 30 and 100 here..
but the BASE is 100 here, so the salary can be 100 and 170..
100 increases 10% =110..
170 decreases 10%=153..
so the increase is 43..
again the BASE is 110, so answer 43/110 * 100= 39.09% D
without calculations,
answer cannot be equal to or greater than 40, as 43 is on 110..
so D is the only one left
Answer: (D) 39.09%
Question: If g and d are both integers, g>d, and -3g>19, then the largest value of d would be?
(A) -5
(B) -6
(C) -7
(D) -8
(E) -10
Rationale: No, your thinking is incorrect. When we know that g>d and g<-6.33, the largest value of g can be -7 while if g=-7, then largest value of d < -7 will be -8.For negative numbers, -7 > -8 and -8> -10.
You are right in saying that d can take any value less than -7 ---> d could be -8, -9, -10 .... and out of all these values, -8 is the greatest.
Look at the numbers on the number line. For any 2 numbers, the ones on the right are greater than the ones on the left:
.......-11 -10 -9 -8 -7 -6 -5 ..... 0 1 2 3 4 5 6 ... (-11< -10, -10< -8, 4< 5 etc).
So, as per the question if d<g and g = -7 , then d's largest 'possible' value has to be -8.
-10 is smaller than -8=D
Answer: (D) -8
Question: A father tells his son, "I was of your present age when you were born." If the father is 36 now, how old was the boy 5 years back?
(A) 15 years
(B) 13 years
(C) 17 years
(D) 20 years
(E) None of the above
Rationale: present age of father 36
present age of son x
36-x=x
x=18
five yrs back sons age 18-5=13
ANSWER:B
Answer: (B) 13 years
Question: What percentage loss will a merchant incur if he marks his goods up by x% over his cost price and then offers a discount of x% on his selling price?
(A) 0 %
(B) 2x/100 %
(C) x^2/100 %
(D) x %
(E) 2x %
Rationale: Answer is C.
Taking smart numbers:
Let, C.P = 100$ and X = 20% over C.P
then Mark Up = 120$
After discount of X%
S.P= 80% of 120
S.P = 96$
Therefore Loss is 4$ and hence Loss in % = 4%
Plugging numbers in options.
A. 0 % ---------------------------Not truebecause loss is 4%
B. 2x/100 % --------------------2*20/100 = 0.4%.Hence Not True
C. x^2/100 % ------------------ 20^2/100 = 4%.True ANSWER IS C
D. x % --------------------------- 20%.Hence Not True
E. 2x % -------------------------- 2*20 = 40%.Hence Not True ANSWER IS C
Answer: (C) x^2/100 %
Question: If 'A' means '-', 'B' means '/', 'C' means '+', and 'D' means 'X' then
Find the value of the following:
21 B 7 C 9 D 10 A 13
(A) 80
(B) 75
(C) 85
(D) 95
(E) 66
Rationale: A
80
Explanation:
21 B 7 C 9 D 10 A 13
= 21 / 7 + 9 X 10 - 13
= 3 + 90 - 13
= 80
Answer: (A) 80
Question: B takes 12 more days than A to finish a task. B and A start this task and A leaves the task 12 days before the task is finished. B completes 60% of the overall task. How long would B have taken to finish the task if he had worked independently?
(A) 48 days
(B) 36 days
(C) 28 days
(D) 32 days
(E) 30 days
Rationale: DETAILED SOLUTION
Let us say A and B split their share of the task and started doing their respective shares simultaneously.
Let’s say A takes A days to finish the task. Therefore, B takes A + 12 days to finish the entire task.
A has to finish 40% of the task, since B is doing the rest. So A will only take 2A/5 number of days.
B only has to finish 60% of the task, so B will take (3(A+12)/5) number of days.
But as we know, B starts working along with A and finishes 12 days after A stops working.
So, (3(A+12)/5) = ((2A)/5+12)
3A + 36 = 2A + 60
A = 24; B = 36 days.
Answer choice B
Answer: (B) 36 days
Question: If point A coordinates are (-7, -3) point B coordinates are (7 ,4 ) if C is along the line A-B so that AC = 1/2 CB. What are the coordinates of point C.
(A) (-2, - 2/3)
(B) (2, -2/3)
(C) (2/3, -2)
(D) (0, 2)
(E) (2, 2/3)
Rationale: Look at the diagram below:
Line segment.pngSince, AC= 1/2 CB, then AC = 1/3 AB. This implies that point C is closer to A than to B, which on the other hand implies that the x-coordinate of C must be less than (-7+7)/2=0.5. Only D and A fits, but as (0 , 2) is clearly not on line segment AB, then the answer must be D.
Answer: D.
Answer: (D) (0, 2)
Question: A seven-digit combination lock on a safe has zero exactly three times, does not have the digit 1 at all. What is the probability that exactly 3 of its digits are odd?
(A) 9/16
(B) 1/2
(C) 1/3
(D) 1/4
(E) 1/6
Rationale: Remaining number of digits after three '0' digits= 4
Constraint- no more '0' and no more '1'
Well, these four digits can be odd or even
1/2*1/2*1/2*1/2= 1/16
Ways to choose 3 odd digits out of total 4 digits= 4C3= 4
4* 1/16= 1/4
D is the answer
Hi! Since we are talking about remaining 4 digits. Each digit can either be odd or even (Total ways to select = 2. desired outcome= 1)
so let's say we want to choose first 3 digits as odd digits and last digit as even. The probability will be :-
1/2 *1/2*1/2*1/2= 1/16
But out of remaining 4 digit , any 3 can be odd and one even as there are no constraints in the question. Therefore, total ways of choosing 3 odd digits out of 4 total digits= 4C3
So, the probability = 4*1/16= 1/4
answer is D
Answer: (D) 1/4
Question: When XYZ Co discontinued an agency arrangement with John, management held his commission of Rs. 25000/- for one month. Earlier John had availed an advance agency fees of 8280/- from company. But Robert forgot that. After one month John asked his fees and accountant gives Rs.18500/- to him. What is the incentive amount given to John ?
(A) A)1780
(B) B)1250
(C) C)10780
(D) D)10500
(E) E)8600
Rationale: Total fees = Rs.25000/-
Advance fees = 8280/-
Balance fees = 25000-8280= 16720
Paid amount = 18500/-
Incentive amount = 18500-16720 = 1780/-
Answer is A
Answer: (A) A)1780
Question: If a^2 + b^2 = 144 and ab ≠ 0, then the greatest possible value for b is between
(A) 16 and 13
(B) 12 and 3
(C) 11 and 4
(D) 10 and 5
(E) 9 and 6
Rationale: Since a ≠ 0, greatest possible value for b will be less than 12 but closer to it.
So it lies between 11 and 12
ANSWER:B
Answer: (B) 12 and 3
Question: A is thrice as good a workman as B & therefore is able to finish a job in 45 days less than B. In how many days they can finish the job if they work together?
(A) 10
(B) 11.25
(C) 12
(D) 13.45
(E) 14
Rationale: A is thrice as good a workman as B =>A = 3B
The ratio of efficiencies of A and B = 3:1
The ratio of the days taken by A and B to finish work is = 1: 3
B takes 45 days to finish the work => 3 parts = 45 days
A alone takes => 45/3x 1 = 15 days
A and B alone can finish the work is = AB/A+B
= 15 X 45/15 + 45
= 11.25
B
Answer: (B) 11.25