mathewhe/aqua_rat huggingface dataset:
Question: Of the three-digit integers greater than 800, how many have two digits that are equal to each other and the remaining digit different from the other two?
(A)  90
(B)  82
(C)  43
(D)  45
(E)  36
Rationale: Three digit number can have only following 3 patterns:
A. all digits are distinct;
B. two digits are alike and third is different;
C. all three digits are alike.
We need to calculate B. B=Total - A - C
Total numbers from 800 to 999 = 199 (3-digit numbers greater than 800);
A. all digits are distinct = 2*9*8=144 (first digit can have only three values 7, 8, or 9);
C. all three are alike = 2(, 888, 999).
So, 199-144-2=43
Answer: C.
Answer: (C)  43
Question: HCF and LCM two numbers are 12 and 396 respectively. If one of the numbers is 24, then the other number is?
(A) 36
(B) 198
(C) 132
(D) 264
(E) 364
Rationale: 12 * 396 = 24 * x
x = 198
ANSWER:B
Answer: (B) 198
Question: If a man walks at a rate of 10kmph, he misses a train by 14minutes. However, if he walks at the rate of 12kmph, he reaches the station 10minutes before the arrival of the train. Find the distance covered by him to reach the station.
(A) 6 KM
(B) 15
(C) 12
(D) 4
(E) 8
Rationale: Let the required distance x km
difference in the times taken at two speeds = 12min = 1/5 hr
(x/10)-(x/12) = 1/10
x = 6
the required distance is 6 km
Answer is A
Answer: (A) 6 KM
Question: Today is Saturday. The day after 59 days will be
(A) Monday
(B) Tuesday
(C) Saturday
(D) Sunday
(E) None of these
Rationale: Explanation :
59 days = 8 weeks 3 days = 3 odd days
Hence if today is Saturday, After 59 days, it will be = (Saturday + 3 odd days)
= Tuesday. Answer : Option B
Answer: (B) Tuesday
Question: In a class of 10 students, the teacher writes a number on the board. The first student tells that number is divisible by 1, the second student tells that the number is divisible by 2, the third by 3, the forth by 4 and so on till 10. If the statement of one of the students is wrong then what is the least number possible.
(A) 320
(B) 340
(C) 360
(D) 380
(E) 400
Rationale: Statement of 7th student was wrong.
No is not divisible by 7.
LCM of 2,3,4,5,6,8,9,10 = 360
ANSWER:C
Answer: (C) 360
Question: A box contains 3 blue marbles, 3 red, 6 green marbles and 2 yellow marbles. If three marbles are picked at random, what is the probability that they are all blue?
(A) 1/364
(B) 2/455
(C) 1/91
(D) 4/455
(E) None of these
Rationale: Given that there are three blue marbles, three red marbles, six green marbles and two yellow marbles.
Probability that all the three marbles picked at random are blue = 3C₃/14C₃ = (1 * 3 * 2 * 1)/(14 * 13 * 12) = 1/364
ANSWER:A
Answer: (A) 1/364
Question: A shopkeeper purchased 90 kg of potatoes for Rs. 540 and sold the whole lot at the rate of Rs. 8 per kg. What will be his gain percent?
(A) 38 1/9 %
(B) 38 9/3 %
(C) 38 1/3 %
(D) 32 1/3 %
(E) 33 2/6 %
Rationale: C.P. of 1 kg = 540/90 = Rs. 6S.P. of 1 kg = Rs. 8Gain % = 2/6 * 100 = 200/6 = 33 2/6 %Answer: E
Answer: (E) 33 2/6 %
Question: Six years ago, the ratio of the ages of Kunal and Sagar was 6 : 5. Four years hence, the ratio of their ages will be 11 : 10. What is Sagar's age at present?
(A) 16 years
(B) 18 years
(C) 20 years
(D) 22 years
(E) 24 years
Rationale: Explanation:
Let the ages of Kunal and Sagar 6 years ago be 6x and 5x years respectively.
Then,
(6x + 6) + 4	=11
(5x + 6) + 4	=10
⇒ 10(6x + 10) = 11(5x + 10)
⇒ 5x = 10
⇒ x = 2.
Sagar's present age = (5x + 6) = 16 years.
Answer: A
Answer: (A) 16 years
Question: Two employees X and Y are paid a total of Rs. 616 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?
(A) s.250
(B) s.280
(C) s.290
(D) s.299
(E) s.300
Rationale: Let the amount paid to X per week = x
and the amount paid to Y per week = y
Then x + y = 616
But x = 120% of y = 120y/100 = 12y/10
∴12y/10 + y = 616
⇒ y[12/10 + 1] = 616
⇒ 22y/10 = 616
⇒ 22y = 6160
⇒ y = 6160/22 = 560/2 = Rs.280
B
Answer: (B) s.280
Question: A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets Rs. 1000 more than D, what is B's share?
(A) Rs. 500
(B) Rs. 1500
(C) Rs. 2000
(D) Rs. 2500
(E) None of these
Rationale: Let the shares of A, B, C and D be Rs. 5x, Rs. 2x, Rs. 4x and Rs. 3x respectively.
Then, 4x - 3x = 1000
x = 1000.
B's share = Rs. 2x = Rs. (2 x 1000) = Rs. 2000.
Answer: Option C
Answer: (C) Rs. 2000
Question: In what time will a train 100 m long cross an electric pole, it its speed be 144 km/hr?
(A) 2.5
(B) 7.3
(C) 2.3
(D) 1.4
(E) 1.1
Rationale: Speed = 144 * 5/18 = 40 m/sec
Time taken = 100/40 = 2.5 sec.
Answer: A
Answer: (A) 2.5
Question: A cylindrical tank of diameter 35 cm is full of water. If 11 litres of water is drawn off, the water level in the tank will drop by:
(A) 11 3/7cm
(B) 11 2/7cm
(C) 11 1/7cm
(D) 11cm
(E) None of these
Rationale: Explanation:
Let the drop in the water level be h cm, then,
Volume of cylinder= πr2h
=>22/7∗35/2∗35/2∗h=11000
=>h=11000∗7∗4/ 22∗35∗35cm=80/7cm=11 3/7cm
Option A
Answer: (A) 11 3/7cm
Question: If the area of a circle is 144pi square feet, find its circumference.
(A) 65 pi feet
(B) 24 pi feet
(C) 42 pi feet
(D) 18 pi feet
(E) 64 pi feet
Rationale: The area is given by pi * r * r. Hence
pi * r *r = 144 pi
r *r = 81 ; hence r = 12 feet
The circumference is given by
2 *pi *r = 2 * pi * 12 = 24 pi feet
correct answer B
Answer: (B) 24 pi feet
Question: In how many ways can the six letters of the word "mammal" be arranged in a row?
(A) 20
(B) 40
(C) 31
(D) 60
(E) 64
Rationale: Since there are 3 "m"s , 2 "a"s and 1 "l" in the word "mammal", we have:
(3+2+1)! / (3! * 2! * 1!)=60
​Ans-D
Answer: (D) 60
Question: a light flashes every 6 seconds, how many times will it flash in ? of an hour?
(A) 550
(B) 600
(C) 650
(D) 700
(E) 750
Rationale: 1flash=6sec
for 1 min=10flashes
so for 1 hour=10*60=600 flashes.
ANSWER:B
Answer: (B) 600
Question: Suppose a game is played between two players A and B. On each turn of the game, exactly
one of A or B gets a point. Suppose A is better than B and has a probability of 2/3 of getting
a point on each turn of the game. The first person to get two points ahead in the game is the
winner. What is the probability that A wins the game?
(A) 5/9
(B) 4/7
(C) 2/3
(D) 4/5
(E) 8/9
Rationale: Let W0 be the event that Player A wins the game. The goal is to compute P(W0).
Let W1 be the event that Player A wins the game given that she is ahead by one point. Let
W-1 be the event Player A wins the game given that she is behind by one point. Then, the
probability that Player A wins the game is
P(W0) = P(A is ahead by 1 point)P(W1) + P(A is behind by 1 point)P(W-1)
= (2/3)P(W1) + (1/3)P(W-1): (1)
Now,
P(W1) = P(Player A gets a point on the next turn) + P(Player B gets a point on the next turn)P(W0)
= (2/3) + (1/3)P(W0);
and
P(W-1) = P(Player A gets a point on the next turn)P(W0) = (2/3)P(W0):
Substituting these equations into (1) we have
P(W0) = (2/3)[(2/3) + (1/3)P(W0)] + (1/3)(2/3)P(W0) = 4/9 + (4/9)P(W0):
Therefore, P(W0) = (4/9)(9/5) = 4/5
correct answer D
Answer: (D) 4/5
Question: If the ratio of apples to bananas is 5 to 2 and the ratio of bananas to cucumbers is 1 to 3, what is the ratio of apples to cucumbers?
(A) 2:3
(B) 5:3
(C) 5:6
(D) 1:4
(E) 3:4
Rationale: The ratio of bananas to cucumbers is 1 to 3 which equals 2 to 6.
The ratio of apples to bananas to cucumbers is 5 to 2 to 6.
The ratio of apples to cucumbers is 5 to 6.
The answer is C.
Answer: (C) 5:6
Question: A man's speed with the current is 20 kmph and speed of the current is 3 kmph. The Man's speed
against the current will be
(A) 11 kmph
(B) 12 kmph
(C) 14 kmph
(D) 17 kmph
(E) None of these
Rationale: Explanation:
Speed with current is 20,
speed of the man + It is speed of the current
Speed in sƟll water = 20 - 3 = 17
Now speed against the current will be
speed of the man - speed of the current
= 17 - 3 = 14 kmph
Answer: C
Answer: (C) 14 kmph
Question: Jake, Lena, Fred, John and Inna need to drive home from a corporate reception in an SUV that can seat 7 people. If only Inna or Jake can drive, how many seat allocations are possible?
(A) 30
(B) 42
(C) 120
(D) 360
(E) 720
Rationale: 5 people ,7 seats, only 2 can drive
if inna is in one seat remaining, 4 people can be arranged in 4p4 i.e 4! =24 ways
since any one can drive total ways = 24 *2= 48 ways
4 seats can be chosen out of remaining 6 seats in 6c4 ways = 6!/(4!*2!)= 15 ways
48*15=720
ANSWER:E
Answer: (E) 720
Question: A certain sum amounts to Rs.1725 in 3 years and Rs.1875 in 5 years. Find the rate % per annum?
(A) 2
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: 3 --- 1725
5 --- 1875
--------------
2 --- 150
N = 1 I = 75 R = ?
P = 1725 - 225 = 1500
75 = (1500*1*R)/100
R = 5%.Answer: B
Answer: (B) 5
Question: Jaclyn buys $20 000 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) 475
(B) 234
(C) 289
(D) 345
(E) None of these
Rationale: Explanation:
I=(p x r x t)/100
= 30000*9.5/100*(18/12)^1/6 = 475
Answer: A
Answer: (A) 475
Question: A train 280m long is running at 70kmph. In how much time will it pass a platform 210m long?
(A) 1.5 seconds
(B) 9.56 seconds
(C) 28.56 seconds
(D) 30.56 seconds
(E) 3.5 seconds
Rationale: Distance travelled = 280 + 210m = 490mSpeed = 70 * 5/8 = 205/4mTime = 490 * 4/205 = 9.56 SecondsAnswer : B.
Answer: (B) 9.56 seconds
Question: A person purchases 90 shirts and sells 40 shirts at a gain of 10% and 50 shirts at a gain of 20%. If he sold all of them at a uniform profit of 15%, then he would have got $40 less. The cost price of each shirt is:
(A) 10
(B) 30
(C) 80
(D) 40
(E) 90
Rationale: C
80
Let C.P. of shirt be $x.
Then, C.P. of 90 shirts = $90x.
[(110% of 40x) + (120% of 50x)] - (115% of 90x) = 40
44x + 60x - 103.5x = 40
0.5x = 40 => x = 80
Answer: (C) 80
Question: A trained covered x km at 40 kmph and another 2x km at 20 kmph. Find the average speed of the train in covering the entire 3x km.
(A) 12 kmph
(B) 88 kmph
(C) 24 kmph
(D) 17 kmph
(E) 19 kmph
Rationale: Total time taken = x/40 + 2x/20 hours
= 5x/40 = x/8 hours
Average speed = 3x/(x/8) = 24 kmph
Answer: C
Answer: (C) 24 kmph
Question: If 20 shirts can be purchased for 5 dollars, how many shirts can be purchased for 10 dollars?
(A) 10
(B) 30
(C) 60
(D) 40
(E) 20
Rationale: 200/5=40
Ans = D
Answer: (D) 40
Question: How many seconds will a 500 meter long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
(A) 299 meters
(B) 278 meters
(C) 500 meters
(D) 276 meters
(E) 299 meters
Rationale: Let length of tunnel is x meter
Distance = 800+x meter
Time = 1 minute = 60 seconds
Speed = 78 km/hr = 78*5/18 m/s = 65/3 m/s
Distance = Speed*Time
800+x = (65/3) * 60
800+x = 20 * 65 = 1300
x = 1300 - 800 = 500 meters
Answer: C
Answer: (C) 500 meters
Question: ABCD is a parallelogram on xy rectangular coordinate plane, three of the four vertices of parallelogram are (5,15) , (5,20) and (-5,15). Which can be the coordinate of fourth vertex?
(A) (-5,-5)
(B) (5,15)
(C) (-5,-20)
(D) (-5,10)
(E) (15,20)
Rationale: A(-5, 15)
B(5, 15)
C(5, 20)
X(-5, 20): Parallelogram=Square=AXCB, where AX||CB, AX=CB, XC||AB, XC=AB
Y(-5, 5): Parallelogram=AYBC, where AY||BC, AY=BC, AC||YB, AC=YB
Z(15, 20): Parallelogram=ACZB, where AC||ZB, AC=ZB, CZ||AB, CZ=AB
Ans:E
Answer: (E) (15,20)
Question: If p/6 = r/2 and r = 0.75s, what is the ratio of p to r to s?
(A) 2 : 3 : 4
(B) 8 : 12 : 9
(C) 9 : 6 : 8
(D) 6 : 4 : 3
(E) 18 : 6 : 8
Rationale: p/6=r/2, r=0.75s, what is p:r:s?
we get p/r=6/2 and r/s=3/4, so
6/3*3/2 and 2/2*3/4
18/6 and 6/8
E
Answer: (E) 18 : 6 : 8
Question: One year ago the ratio of Yamini’s and Gamini’s ages was 6 : 7 respectively. Four years hence this ratio would become 7 : 8. How old is Gamini?
(A) 35 years
(B) 30 years
(C) 31 years
(D) Cannot be determined
(E) None of these
Rationale: Y : G = 6 : 7; One year before
Y : G = 7 : 8; After 4 years
Now, 1 → 5
∴ 7 → 35
Therefore, the age of Gamini now is 35 + 1 = 36 years
Answer E
Answer: (E) None of these
Question: A man buys 20 lts of liquid which contains 30% of the liquid and the rest is water. He then mixes it with 20 lts of another mixture with 20% of liquid. What is the % of water in the new mixture?
(A) 59
(B) 95
(C) 80
(D) 75
(E) 65
Rationale: 30% in 20 lts is 6. So water = 20-6 = 14lts.20% of 20 lts = 4. So water in 2nd mixture = 20-4 = 16 lts. Now total quantity = 20 + 20 = 40 lts. Total water in it will be 14 + 16 = 30 lts. % of water = (100*30)/40 = 75.
ANSWER:D
Answer: (D) 75
Question: The base of a right triangle is 8 and hypotenuse is 10. Its area is?
(A) 12
(B) 80
(C) 59
(D) 24
(E) 25
Rationale: Explanation:
h2=(10)2-(8)2-(6)2->h=6
1/2*8*6=24
ANSWER IS D
Answer: (D) 24
Question: At what price must an article costing Rs.75 be marked in order that after deducting 5% from the list price. It may be sold at a profit of 25% on the cost price?
(A) 62.5
(B) 62.0
(C) 62.6
(D) 62.1
(E) 98.68
Rationale: CP = 75
SP = 75*(125/100) = 93.75
MP*(95/100) = 93.75
MP = 98.68
Answer:E
Answer: (E) 98.68
Question: Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?
(A) 20.8 sec
(B) 10.7 sec
(C) 10.3 sec
(D) 10.8 sec
(E) 10.2 sec
Rationale: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other
= 140 + 160 = 300 m.
Required time = 300 * 9/250
= 54/5
= 10.8 sec.
Answer:D
Answer: (D) 10.8 sec
Question: A train speeds past a pole in 20 seconds and passes through a tunnel 500 m long in 40 seconds. Its length is :
(A) 200 m
(B) 400 m
(C) 500 m
(D) 700 m
(E) None of the above
Rationale: Sol.Let the length of the train be x metres and its speed be y m/sec. Then, x / y = 20 ⇒ y = x / 20∴ (x + 500) / 40 = x / 20 ⇔ x = 500 m. Answer C
Answer: (C) 500 m
Question: In how many ways can 16 different gifts be divided among four children such that each child receives exactly three gifts?
(A) 16^4
(B) (4!)^4
(C) 16!/(3!)^4
(D) 16!/4!
(E) 4^16
Rationale: Total 16 different Gifts, and 4 children.
Thus any one child gets 16C3 gifts,
then the other child gets 13C3 gifts(16 total - 3 already given),
then the third one gets 10C3 gifts,
and the last child gets 7C3 gifts.
Since order in which each child gets the gift is not imp, thus, ans :
16C3 * 13C3 * 10C3 * 7C3 = 16! / (3!)^4
Ans : C.
Answer: (C) 16!/(3!)^4
Question: The following sets each have a mean of 50 and the standard deviations are given in variable form.
Set I = {20, 20, 20, 80, 80, 80}, standard deviation = A
Set II = {20, 30, 40, 60, 70, 80}, standard deviation = B
Set III = {50, 50, 50, 50, 50, 50}, standard deviation = C
Rank these three standard deviations from least to greatest.
(A) A, B, C
(B) B, C, A
(C) C, A, B
(D) B, A, C
(E) C, B, A
Rationale: The answer should be E as the mean is least deviated in Set III followed by Set II and then Set I.
Answer: (E) C, B, A
Question: A can give B 100 meters start and C 170 meters start in a kilometer race. How much start can B give C in a kilometer race?
(A) 11.77 meters
(B) 55.77 meters
(C) 77.77 meters
(D) 113.77 meters
(E) None of these
Rationale: Explanation:
A runs 1000 meters while B runs 900 meters and C runs 830 meters.
Therefore, B runs 900 meters while C runs 830 meters.
So, the number of meters that C runs when B runs 1000 meters = (1000 x 830)/900 = 922.22 meters
Thus, B can give C (1000 - 922.22) = 77.77 meters start
Answer: C
Answer: (C) 77.77 meters
Question: A Card marked 1 and 2 on its two faces. Two colors, white and black are used to paint the two faces of the card. If the card is painted with the different colors, in how many ways can the card be painted?
(A) 3
(B) 6
(C) 2
(D) 12
(E) 27
Rationale: If the base of the card is white, then in order the card to be painted with the different colors, the top must be white.Another side can be painted in Black.
But we can have the base painted in either of the two colors, thus the total number of ways to paint the card is 2*1=2.
Answer: C.
Answer: (C) 2
Question: If the sample interest on a sum of money 20% per annum for 2 years is $400, find the compound interest on the same sum for the same period at the same rate?
(A) $460
(B) $510
(C) $440
(D) $500
(E) $550
Rationale: Rate = 20%
Time = 2years
S.I. = $400
Principal = 100*400/20*2 = $1000
Amount = 1000(1+20/100)^2 = $1440
C.I. = 1440-1000 = $440
Answer is C
Answer: (C) $440
Question: A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office. In how many ways can the company assign 3 employees to 2 different offices?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: for each employee there are two possibilities: first office and second office.
Therefore,
N=2^3=8
ANS:D
Answer: (D) 8
Question: A train covers a distance of 12 km in 10 min. If it takes 7 sec to pass a telegraph post, then the length of the train is?
(A) 298
(B) 288
(C) 140
(D) 776
(E) 991
Rationale: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec.
Length of the train = 20 * 7
= 140 m.
Answer:C
Answer: (C) 140
Question: Let y = 2m + x^2 and m = 5x + 2. If m^2 =49, then which of the following can be a value of 2y + 3m?
(A) 48
(B) 56
(C) 61
(D) 51
(E) 71
Rationale: m^2 = 49 => m=7
7= 5x+2 => x=1
y= 2*7+1^2 = 15
2y+3m = 2*15+3*7 = 51
Answer : D
Answer: (D) 51
Question: There were two candidates in an election. Winner candidate received 62% of votes and won the election by 288 votes. Find the number of votes casted to the winning candidate?
(A) 748
(B) 744
(C) 725
(D) 727
(E) 272
Rationale: W = 62% L = 38%
62% - 38% = 24%
24% -------- 288
62% -------- ? => 744
Answer:B
Answer: (B) 744
Question: The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero?
(A) 17
(B) 16
(C) 17
(D) 19
(E) 62
Rationale: Average of 20 numbers = 0
Sum of 20 numbers = (0 * 20) = 0
It is quite possible that 19 of these numbers may be positive and if their sum is a, then 20th number is (-a).
Answer: D
Answer: (D) 19
Question: A trained covered x km at 40 kmph and another 2x km at 20 kmph. Find the average speed of the train in covering the entire 5x km.
(A) 20kmph
(B) 25kmph
(C) 30kmph
(D) 35kmph
(E) 40kmph
Rationale: Total time taken = x/40 + 2x/20 hours
= 5x/40 = x/8 hours
Average speed = 5x/(x/8)
= 40 kmph
Answer:E
Answer: (E) 40kmph
Question: A cube of side one meter length is cut into small cubes of side 10 cm each. How many such small cubes can be obtained?
(A) 288
(B) 127
(C) 2999
(D) 277
(E) 299
Rationale: Along one edge, the number of small cubes that can be cut
= 100/10 = 10
Along each edge 10 cubes can be cut. (Along length, breadth and height). Total number of small cubes that can be cut = 10 * 10 * 10 = 1000.Answer: C
Answer: (C) 2999
Question: An "integrated" team consists of 2 members from the engineering team and 2 members from the design team. If the engineering team has 6 members and the design team has 4 members, how many "integrated" team formations are possible?
(A) 36
(B) 54
(C) 76
(D) 90
(E) 112
Rationale: Possible Integrated teams=6!/2!∗4!*4!/2!∗2=15*6=90
So,Correct Answer D
Answer: (D) 90
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) 5
(B) 4
(C) 6
(D) 8
(E) 32
Rationale: M = 45
S = 1.5
DS = 6
US = 3
AS = (2 * 6 * 3) /9 = 4
Answer: B
Answer: (B) 4
Question: A cycle is bought for Rs.900 and sold for Rs.1140, find the gain percent?
(A) 11
(B) 27
(C) 99
(D) 77
(E) 18
Rationale: 900 ---- 240
100 ---- ? => 27%
Answer: B
Answer: (B) 27
Question: In one year, the population, of a village increased by 30% and in the next year, it decreased by 30%. If at the end of 2nd year, the population was 13650, what was it in the beginning?
(A) 7787
(B) 8000
(C) 15000
(D) 1277
(E) 2081
Rationale: x*130/100 * 70/100 = 13650
X*0.91=13650
X=13650/0.91
=> 15000
Answer:C
Answer: (C) 15000
Question: The equation x = 2y^2 + 5y - 19, describes a parabola in the xy coordinate plane. If line l, with slope of 3, intersects the parabola in the upper-left quadrant at x = -5, the equation for l is
(A) 3x + y + 15 = 0
(B) y - 3x - 11 = 0
(C) -3x + y - 19 = 0
(D) -2x - y - 7 = 0
(E) -3x + y + 13.5 = 0
Rationale: The question is made to look difficult though it is pretty simple if you focus on just the line and use process of elimination. (Remember that GMAT does not focus on parabolas so basically, the question should be quite do-able even if someone doesn't know how to handle parabolas.)
We need equation of l. Its slope must be 3.
Slope in option A and D is not 3 so we are left with B, C and E
The line has a point (-5, y) on it where y is positive (since the point lies in upper left quadrant).
In options B and E, if you put x = -5, you get -ve value for y co-ordinate. So ignore them.
Answer must be (C)
Answer: (C) -3x + y - 19 = 0
Question: A man buys 50 pens at marked price of 46 pens from a whole seller. If he sells these pens giving a discount of 1% , what is the profit percent?
(A) 7.6 %
(B) 7.7 %
(C) 7.32 %
(D) 3.6 %
(E) 7.8 %
Rationale: Explanation:
Let Marked price be Re. 1 each
C.P. of 50 pens = Rs. 46
S.P. of 50 pens = 99% of Rs. 50 = Rs. 49.50
Profit % = (Profit /C.P.) x 100
Profit% = (3.50/46) x 100 = 7.6 %
ANSWER: A
Answer: (A) 7.6 %
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: If a tap could fill entire tank in 20 hrs due to leakage, then in how much time
tank can be emptied by leakage if tap can fill entire tank in 12 hrs without leakage
(A) 30hrs
(B) 24hrs
(C) 36hrs
(D) 48hrs
(E) 52hrs
Rationale: time take to fill[withleakage] =20hrs so workdone in 1hr=1/20
time tkae to fill[without leakage]=12hrs so workdone in 1hr=1/12
if u subtract both u'll get time taken by leakage to empty...
1/20-1/12=2/60 = 1/30 so 30hrs
ANSWER:A
Answer: (A) 30hrs
Question: What is the tenth digit of (5!*5! - 5!*3!)/5?
(A) 1
(B) 2
(C) 0
(D) 6
(E) 7
Rationale: (5!*5! + 5!*3!)/5
=5!(5! + 3!)/5
=120 (120+6)/5
=3024
Units digit of the above product will be equal to 2
Answer B
Answer: (B) 2
Question: A man can row at 5 kmph in still water. If the velocity of the current is 1 kmph and it takes him 1 hour to row to a place and come back. how far is that place.
(A) 4 km
(B) 1.4 km
(C) 2.4 km
(D) 3.4 km
(E) 4.4 km
Rationale: Explanation:
Let the distance is x km
Rate downstream = 5 + 1 = 6 kmph
Rate upstream = 5 - 1 = 4 kmph
then
x/6 + x/4 = 1 [because distance/speed = time]
=> 2x + 3x = 12
=> x = 12/5 = 2.4 km
ANSWER IS C
Answer: (C) 2.4 km
Question: A man bought 10 crates of apples for $120 total. If he lost 2 of the crates, at what price would he have to sell each of the remaining crates in order to earn a total profit of 50 percent of the total cost?
(A) $22.50
(B) $25
(C) $28
(D) $30
(E) $35
Rationale: As given, after lost, the remaining 8 crates total cost = $120
So, 1 crate cost = 120/8 =15
To get 50% profit, 1 crate cost should be =15+15*50/100 =$22.5
Answer : A
Answer: (A) $22.50
Question: If the quantity 3^4+ 3^6 + 3^8 is written as (a + b)(a – b), in which both a and b are integers, which of the following could be the value of b?
(A) 57
(B) 26
(C) 52
(D) 81
(E) 25
Rationale: (a+b)(a-b) = a^2 - b^2
3^4+ 3^6 + 3^8 = 3^4 (1+3^2+3^4)
if the above expression is solved even then every term of the expression will remain a multiple of 3^4 which is out of parenthesis
hence, b must be a multiple of 3^4 i.e. 81
Answer: option D
Answer: (D) 81