mathewhe/aqua_rat huggingface dataset:
Question: At what % above C.P must an article be marked so as to gain 33% after allowing a customer a discount of 5%?
(A) 49%
(B) 40%
(C) 48%
(D) 45%
(E) 38%
Rationale: Let C.P be Rs 100.then S.P be Rs 133
Let the market price be Rs x
Then 90% of x=133=>95x/100=133=>x=(133*100/95)=140
Market price = 40% above C.P
Answer is B.
Answer: (B) 40%
Question: An article is bought for Rs.675 and sold for Rs.775, find the gain percent?
(A) 73%
(B) 14.8%
(C) 33 1/3%
(D) 93 1/3%
(E) 33 1/3%
Rationale: Explanation:
675 ---- 100
100 ---- ? => 14.8%
Answer:B
Answer: (B) 14.8%
Question: What percent is 20% of 25%?
(A) 20%
(B) 30%
(C) 50%
(D) 60%
(E) 80%
Rationale: Required percentage = 20%/25% * 100 = 20/25 * 100 = 80%
Answer is E
Answer: (E) 80%
Question: There are 11 points marked on the circumference of a circle. How many hexagons can be formed by connecting 6 points of the 11 points?
(A) 450
(B) 454
(C) 458
(D) 462
(E) 466
Rationale: 11C6=462
The answer is D.
Answer: (D) 462
Question: A boy pays Rs. 369 for an article marked at Rs. 600, by enjoying two successive discounts. If the first discount is of 25%, how much should be the second discount?
(A) 20 %
(B) 10 %
(C) 25 %
(D) 18 %
(E) None of these
Rationale: Explanation:
First discount = 25% of 600 = Rs. 150.
Thus, the reduced price = 600 – 150 = Rs. 450.
Since the person actually paid Rs. 369, the value of the second discount must be equal to Rs. 81 (450 – 369).
Let the second discount be x
Thus, we get, 81 = x of 450
( 81/450)*100 = 18%
ANSWER D
Answer: (D) 18 %
Question: When Rahul was born, his father was 26 years older than his brother and his mother was 23 years older than his sister. If Rahul's brother is 4 years older than him and his mother is 3 years younger than his father, how old was Rahul's sister when he was born ?
(A) 7 years
(B) 5 years
(C) 4 years
(D) 6 years
(E) 8 years
Rationale: When Rahul was born, his brother's age = 4 years; his father's age = (4 + 26) years = 30 years,
his mother's age = (30 - 3) years = 27 years;
his sister's age = (27 - 23) years = 4 years.
Answer: Option C
Answer: (C) 4 years
Question: The length of a train and that of a platform are equal. If with a speed of 72 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is?
(A) 227
(B) 299
(C) 276
(D) 600
(E) 211
Rationale: Speed = [72 * 5/18] m/sec = 20 m/sec; Time = 1 min. = 60 sec.
Let the length of the train and that of the platform be x meters.
Then, 2x/60 = 20 è x = 20 * 60 / 2 = 600
Answer: D
Answer: (D) 600
Question: Which of the following is a non-negative?
(A) (b-0.9)(b-1)
(B) (b-0.9)(b-0.9)
(C) (b+0.9)(b+1)
(D) (b+1)(b-1)
(E) b(b+1)
Rationale: 5-sec approach:
D. (b-0.9)(b-0.9) = (b-0.9)^2. The square of a number is always non-negative.
Answer: B.
Answer: (B) (b-0.9)(b-0.9)
Question: When positive integer n is divided by 3, the remainder is 1. When n is divided by 11, the remainder is 9. What is the smallest positive integer k such that k+n is a multiple of 33?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 10
Rationale: n = 3p + 1 = 11q + 9
n+2 = 3p + 3 = 11q + 11
n+2 is a multiple of 3 and 11, so it is a multiple of 33.
The answer is A.
Answer: (A) 2
Question: A man can row upstream at 37 kmph and downstream at 53 kmph, and then find the speed of the man in still water?
(A) 29
(B) 92
(C) 30
(D) 32
(E) 45
Rationale: US = 37
DS = 53
M = (53 + 37)/2 = 45
Answer:E
Answer: (E) 45
Question: In a Lake, there is a patch of lily pads. Every day, the patch doubles in size. It takes 39 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 39: fully covered
day 38: half covered
So 38 days
ANSWER:D
Answer: (D) 38
Question: a girl scout sold 5 macadamia cookies, 10 peanut butter cookies and 15 butter cookies. what is the ratio of the peanut butter cookies to the total sold?
(A) 1/2
(B) 1/3
(C) 5/10
(D) 10/15
(E) 5/15
Rationale: total # of cookies is 5+10+15=30; ratio of peanut butter cookies sold is 10/30 = 1/3
ANSWER:B
Answer: (B) 1/3
Question: If the volume of two cubes are in the ratio 125:1, the ratio of their edges is:
(A) 3:1
(B) 5:1
(C) 3:5
(D) 3:7
(E) None of these
Rationale: Explanation:
Let the edges be a and b of two cubes, then
a3/b3=125/1
=>(a/b)3=(5/1)3
a/b=5/1
=>a:b=5:1
Option B
Answer: (B) 5:1
Question: A and B invests Rs.3000 and Rs.4000 respectively in a business. If A doubles his capital after 6 months. In what ratio should A and B divide that year's profit?
(A) 9:10
(B) 9:8
(C) 3:4
(D) 39:49
(E) 38:49
Rationale: (3*6 + 6*6): (4*12)
54:48 => 9:8
ANSWER:B
Answer: (B) 9:8
Question: At what percentage above the C.P must an article be marked so as to gain 33% after allowing a customer a discount of 5%?
(A) 38%
(B) 40%
(C) 43%
(D) 48%
(E) 50%
Rationale: Let C.P = Rs. 100, Then S.P = Rs.133.
Let the marked price be x
Then , 95% of x = 133, 95 x/ 100 =133, x = 133*100/95 =140
Marked price = 40% above C.P
ANSWER:B
Answer: (B) 40%
Question: If each term in the sum a1+a2+a3+.....+an is either 7 or 77 and the sum equals 336, which of the following could be equal to n?
(A) 38
(B) 39
(C) 40
(D) 41
(E) 42
Rationale: Since, there is no 48 in the answer choices (336/7 = 48), we know there is at least one 77.
336 - 77 = 259
259/7 = 37
37+1 = 38
If 38 wasn't there, I would have subtracted 77 from 259 and continued in a similar way.
Ans. A
Answer: (A) 38
Question: A company has two models of computers, model M and model N. Operating at a constant rate, a model M computer can complete a certain task in 36 minutes and a model N computer can complete the same task in 18 minutes. If the company used the same number of each model of computer to complete the task in 1 minute, how many model M computers were used?
(A) 12
(B) 11
(C) 10
(D) 9
(E) 8
Rationale: Let's say 1 work is processing 36 gb of data.
Model M : 1 gb per min
Model N : 2 gb per min
Working together, 1 M and 1 N = 3 gb per min
So, 12 times as many computers would work at 36 gb per min.
So no. of M =12
Answer is A
Answer: (A) 12
Question: How many positive integer solutions does the equation 5x+10y = 100 have?
(A) 2
(B) 33
(C) 38
(D) 35
(E) 14
Rationale: formula: (constant)/(lcm of two nos)
=100/(5*10)=2
ANSWER:A
Answer: (A) 2
Question: Two trains 200m and 300m long run at the speed of 70kmph and 50kmph in opposite directions in parallel tracks. The time which they take to cross each other is?
(A) 10sec
(B) 15sec
(C) 18sec
(D) 20sec
(E) 22sec
Rationale: Relative speed = 70+50 = 120kmph * 5/18 = 100/3 m/s
Distance covered in crossing each other = 200+300 = 500m
Required time = 500*3/100 = 15sec
Answer is B
Answer: (B) 15sec
Question: If the three-digit number 5W2 is evenly divisible by 8, which of the following could be the digit W ?
(A) 5
(B) 4
(C) 3
(D) 2
(E) 1
Rationale: Tried to locate a '0' ending multiple of 8 between 500599
Only 560 is present
560 is divisible by 8, so (560 - 8) is also divisible by 8 = 5
ANSWER A
Answer: (A) 5
Question: If 350!/10^n is an integer, what is the largest possible value of n?
(A) 88
(B) 82
(C) 86
(D) 87
(E) 80
Rationale: The question actually asks the highest power of 10 which divides 350! ( For a number to be an integer - Without any remainder all the trailing zeroe's must be divided by the denominator)
10 = 2 x 5
350 factorial will have 86 as -
350/5 = 70
70/5 = 14
14/5 =2
So answer will be (C) 86
Answer: (C) 86
Question: A person travels through 5 cities - A, B, C, D, E. Cities E is 2 km west of D. D is 3 km north-east of A. C is 5 km north of B and 4 km west of A. If this person visits these citiesin the sequence B - C - A - E - D, what is the effective distance between cities B and D?
(A) 12
(B) 13
(C) 14
(D) 15
(E) 16
Rationale: make diagram first, then traverse according to B C A E D
u can find 5+4=9 (B to A)
A to E is not given but u can see it as 1.5 or 2 km so B to E is 10 km
now E to D is 2 km
total=5+4+1.5+2=12.5
or 5+4+2+2=13
ANSWER:B
Answer: (B) 13
Question: In a group of ducks and Cows, the total number of legs are 16 more than twice the no. of heads. Find the total no.of buffaloes.
(A) 10
(B) 12
(C) 8
(D) 12
(E) 14
Rationale: Let the number of buffaloes be x and the number of ducks be y
=> 4x + 2y = 2 (x + y) + 16
=> 2x = 16 => x = 8
C
Answer: (C) 8
Question: What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 12%?
(A) 20%
(B) 29%
(C) 32%
(D) 80%
(E) 90%
Rationale: SP2 = 2/3 SP1
CP = 100
SP2 = 88
2/3 SP1 = 88
SP1 = 132
100 --- 32 => 32%
Answer: C
Answer: (C) 32%
Question: If the cost price of 12 pencils is equal to the selling price of 8 pencils, the gain percent is:
(A) 30
(B) 40
(C) 50
(D) 60
(E) 70
Rationale: C
50%
Let C.P. of each pencil be $ 1.
Then, C.P. of 8 pencils = $8; S.P. of 8 pencils = $12.
Gain % = 4/8 * 100 = 50%
Answer: (C) 50
Question: A box contains 100 balls, numbered from 1 to 100. If three balls are selected at random and with replacement from the box, what is the probability that the sum of the three numbers on the balls selected from the box will be odd?
(A) 1/4
(B) 3/8
(C) 1/2
(D) 5/8
(E) 3/4
Rationale: The sum of the three numbers on the balls selected from the box to be odd one should select either three odd numbered balls (Odd+Odd+Odd=Odd) or two even numbered balls and one odd numbered ball (Even+Even+Odd=Odd);
P(OOO)=(1/2)^3;
P(EEO)=3*(1/2)^2*1/2=3/8 (you should multiply by 3 as the scenario of two even numbered balls and one odd numbered ball can occur in 3 different ways: EEO, EOE, or OEE);
So finally P=1/8+3/8=1/2.
Answer: C.
Answer: (C) 1/2
Question: The units digit of (10)^(87) + (5)^(46) is:
(A) 2
(B) 4
(C) 6
(D) 8
(E) 0
Rationale: any power of anything ending in 5 always has a units digit of 5. So the first term has a units digit of 5. Done.
The second term anything power to 10 unit digit will be zero
then 5 + 0 = 5,
E
Answer: (E) 0
Question: If a 6 cm cube is cut into 1 cm cubes, then what is the percentage increase in the surface area of the resulting cubes?
(A) 300%
(B) 400%
(C) 500%
(D) 600%
(E) 750%
Rationale: The area A of the large cube is 6*6*6 = 216 square cm.
The area of the 216 small cubes is 216*6 = 6A, an increase of 500%.
The answer is C.
Answer: (C) 500%
Question: The winning relay team in a high school sports competition clocked 48 minutes for a distance of 13.2 km. Its runners A, B, C and D maintained speeds of 18 kmph, 19 kmph, 20 kmph, and 21 kmph respectively. What is the ratio of the time taken by B to than taken by D?
(A) 5:16
(B) 5:17
(C) 9:8
(D) 8:9
(E) None of these
Rationale: Explanation :
Since it is a relay race, all the runners ran the same distance.
Hence for a same distance, (ratio of times) = 1/(ratio of speeds).
Hence ratio of times taken by B t& D = 21 : 19
Answer : E
Answer: (E) None of these
Question: Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 45 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
(A) 40
(B) 93
(C) 26
(D) 23
(E) 12
Rationale: Relative speed = 45 + 45 = 90 km/hr.
90 * 5/18 = 25 m/sec.
Distance covered = 500 + 500 = 1000 m.
Required time = 1000 /25 = 40 sec.
Answer:A
Answer: (A) 40
Question: Stacy and Heather are 5 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) 2.5mile
(B) 1.9mile
(C) 1.7mile
(D) 1.5mile
(E) 1.18mile
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 5 -2.4 = 2.6
Time taken = Distance/ Speed = 2.6/11 = 0.23 hrs
Heather will cover = 5*0.23 = 1.18miles.
Answer E
Answer: (E) 1.18mile
Question: In how many ways can 6 people, A, B, C, D, E, F be seated in a row such that C and D are not seated next to each other as well as A and B are not seated next to each other?
(A) 384
(B) 396
(C) 576
(D) 624
(E) 696
Rationale: Total # of arrangements of 6 people in a row is 6!;
Now, let's find # of arrangements where C and D as well as A and B ARE seated next to each other. Consider them as a single unit: {AB}, {CD}, E, F. Now, these 4 units can be arranged in 4!, but we should multiply this number by 2*2 as A and B, as well as C and D within their unit can be arranged in two ways: {AB} or {BA}, and {CD} or {DC}. Hence total for this case is 4!*2*2;
So, {# of arrangements}={total}-{restriction}=6!-4!*2*2=624.
Answer: D.
Answer: (D) 624
Question: When four dice are thrown, what is the probability that the same number appears on each of them ?
(A) 1/36
(B) 1/18
(C) 1/216
(D) 1/5
(E) 1/8
Rationale: Explanation :
When four dice are rolled the total no of outcomes are : 64
All dice show up same number in the following cases: (1,1,1,1), (2,2,2,2), (3,3,3,3), (4,4,4,4), (5,5,5,5), (6,6,6,6)
So in above six cases, all dice will show up the same number.
Required probability: 6/64 = 1/216
Answer : C
Answer: (C) 1/216
Question: If the least common multiple of two prime numbers x and y is 10, where x < y, then the value of 3x + y is
(A) 7
(B) 9
(C) 11
(D) 12
(E) 21
Rationale: LCM (x,y) = 10 and both x an y are prime.
The only values of x and y can be 2 and 5 (x = 2 and y = 5)
3x + y = 3*2 + 5 = 11
Correct Option: C
Answer: (C) 11
Question: The ages of two persons differ by 24 years. If 5 years ago, the elder one be 5 times as old as the younger one, their present ages (in years) are respectively
(A) 20,20
(B) 20,10
(C) 25,15
(D) 35,11
(E) None of these
Rationale: Explanation:
Let their ages be x and (x + 24) years.
5 (x - 5) = (x + 24 - 5) or 4x = 44 or x = 11.
Their present ages are 35 years and 11 years
Option D
Answer: (D) 35,11
Question: Express a speed of 36 kmph in meters per second?
(A) 10 mps
(B) 17 mps
(C) 97 mps
(D) 17 mps
(E) 18 mps
Rationale: 36 * 5/18
= 10 mps
Answer: A
Answer: (A) 10 mps
Question: Every year an amount increases by 1/8th of itself. How much will it be after two years if its present value is Rs.64000?
(A) Rs.81000
(B) Rs.80000
(C) Rs.75000
(D) Rs.64000
(E) Rs.68000
Rationale: 64000* 9/8 * 9/8 = 81000
ANSWER:A
Answer: (A) Rs.81000
Question: How many 3-digit numbers can be formed with the digits 1,4,7,8 and 9 if the digits are not repeated?
(A) 20
(B) 40
(C) 60
(D) 80
(E) 100
Rationale: Three digit numbers will have unit's, ten's and hundred's place.
Out of 5 given digits any one can take the unit's place.
This can be done in 5 ways ------- (i)
After filling the unit's place, any of the four remaining digits can take the ten's place.
This can be done in 4 ways ------- (ii)
After filling in ten's place, hundred's place can be filled from any of the three remaining digits.
This can be done in 3 ways ------- (iii)
=> By counting principle, the number of 3 digit numbers =5Ã—4Ã—3==5Ã—4Ã—3= 60
ANSWER C
Answer: (C) 60
Question: 16 ltr of water is added with 24 ltr of a solution containing 90%of alcohol in the water. The %of alcohol in the new mixture is?
(A) 48%
(B) 52%
(C) 54%
(D) 60%
(E) 70%
Rationale: We have a 24 litre solution containing 90% of alcohol in the water.
=> Quantity of alcohol in the solution
=24Ã—90/ 100
Now 16 litre of water is added to the solution.
=> Total quantity of the new solution = 24 + 16 = 40
Percentage of alcohol in the new solution
=24Ã—90/100
40
Ã—
100
=24Ã—9010040Ã—100
=24Ã—2.25/100
=54%
C
Answer: (C) 54%
Question: In how many ways can you seat 6 people on a bench if one of them does not want to sit at either end?
(A) 360
(B) 400
(C) 440
(D) 480
(E) 520
Rationale: One person can choose 4 possible chairs to sit. The remaining 5 people can sit in 5! ways.
The number of arrangements is 4*5! = 480.
The answer is D.
Answer: (D) 480
Question: Find the smallest number which should be divided with 3872 to make it a perfect square.
(A) 8
(B) 6
(C) 2
(D) 4
(E) 1
Rationale: 3872 = 11*11*2*2*2*2*2
Required smallest number = 2
2 is the smallest number which should be divided with 3872 to make it a perfect square.
ANSWER:C
Answer: (C) 2
Question: x is a positive integer less than 400. When x is divided by 7, the remainder is 1; when x is divided by 3, the remainder is 2. How many x are there?
(A) 21
(B) 22
(C) 23
(D) 24
(E) 25
Rationale: the nubmer which when divided by 7 leaves remainder 1 should be of the form 7k+1
this number when divided by 3 leaves remainder 2.
so,
(7k+1)-2 should be divisible by 3 or 7k-1 should be divisible by 3.
we now put the values of k starting from 0 to find first number divisible by 3
we find 1st number at k= 1
thus smallest number will be 7(1)+1 = 8
now,
next number will be = 8+ lcm of 37
i.e 29
now we will find number of all such values less than 500 by using the formula for last term of an a.p
8+(n-1)21=400
n=23.42
or n= 23
Answer:- C
Answer: (C) 23
Question: Robert's salary was decreased by 50% and subsequently increased by 50%. how much percentage does he lose?
(A) 10%
(B) 20%
(C) 25%
(D) 30%
(E) 50%
Rationale: let original salary be $100
new final salary = 150% of (50% of $100) = (150/100)*(50/100)*100 = $75
decrease = 25%
correct option is C
Answer: (C) 25%
Question: A scuba diver descends at a rate of 40 feet per minute. a diver dive from a ship to search for a lost ship at the depth of 3000feet below the sea level..how long will he take to reach the ship?
(A) 70 minutes
(B) 72 minutes
(C) 75 minutes
(D) 76 minutes
(E) 77 minutes
Rationale: Time taken to reach = 3000/40= 75 minutes
ANSWER:C
Answer: (C) 75 minutes
Question: The positive difference between Sam and Lucy’s ages is b, and the sum of their ages is x. If Lucy is older than Sam, then which of the following represents Lucy’s age?
(A) (x-b)/2
(B) b - x/2
(C) 2b+ x
(D) (x + b)/2
(E) (b - x)/2
Rationale: let Lucy's age be L and sam's age be S
as given,
L-S=b-- 1
L+S=x --2
adding both the equations 2L=a+z
L= (b+x)/2 answer is D
Answer: (D) (x + b)/2
Question: If K is the sum of reciprocals of the consecutive integers from 33 to 38, inclusive, then K is closest in value to which of the following?
(A) 1/12
(B) 1/10
(C) 1/8
(D) 1/7
(E) 1/4
Rationale: 1/33 , 1/34 , 1/35 , 1/36 , 1/37 , 1/38
Hypothetically , assume all 6 Numbers to be 1/33
Hence sum of it would result in = 6/33 ( almost equals 1/6 , or slightly more than 1/6 - )
If all 6 nos were to be 1/38 ... Sum of which would result in 6/38 = 3/19 .
Hence answer should lie between 1/6 and 1/7 (3/21)
D i.e 1/7
Answer: (D) 1/7
Question: In an election, candidate A got 55% of the total valid votes. If 15% of the total votes were declared invalid and the total numbers of votes is 560000, find the number of valid vote polled in favor of candidate?
(A) 261800
(B) 355800
(C) 356500
(D) 356800
(E) 357000
Rationale: Total number of invalid votes = 15 % of 560000
= 15/100 × 560000
= 8400000/100
= 84000
Total number of valid votes 560000 – 84000 = 476000
Percentage of votes polled in favour of candidate A = 55 %
Therefore, the number of valid votes polled in favour of candidate A = 55 % of 476000
= 55/100 × 476000
= 26180000/100
= 261800
A)
Answer: (A) 261800
Question: Mike earns $17.5per hour and Phil earns $10.5 per hour. Approximately how much less, as a percentage, does Phil earn than Mike per hour?
(A) 25%
(B) 32.5%
(C) 37%
(D) 37.5%
(E) 40%
Rationale: What % less of 17.5 is 10.5
let it be x % less ,then
=17.5(1-x/100)=10.5
1-x/100=10.5/17.5
x=200/5
x=40%
Ans E
Answer: (E) 40%
Question: Two trains are moving at 60 kmph and 70 kmph in opposite directions. Their lengths are 150 m and 100 m respectively. The time they will take to pass each other completely is?
(A) 6 12/13 sec
(B) 7 1/7 sec
(C) 7 2/2 sec
(D) 8 1/2 sec
(E) 7 1/9 sec
Rationale: 70 + 60 = 130 * 5/18 = 325/9 mps
D = 150 + 100 = 250 m
T = 250 * 9/325 = 90/13 = 6 12/13 sec
Answer: A
Answer: (A) 6 12/13 sec
Question: Which of the following is a prime number ?
(A) 72
(B) 86
(C) 88
(D) 97
(E) 98
Rationale: Clearly, 97 is a prime number.
Option D
Answer: (D) 97
Question: Ratio of Ravi's and Ashok's present ages is 4:5 After 6 years it will be 5:6. What is Ravi's present age?
(A) 16 Years
(B) 15 Years
(C) 20 Years
(D) 24 Years
(E) 25 Years
Rationale: Let present ages are 4x and 5x
After 6 years hence
4x+6/5x+6=5/6
After solving above eqn
X=6
So ravis present age become 4*6=24
ANSWER:D
Answer: (D) 24 Years
Question: What is the remainder when 46*49 is divided by 8?
(A)  1
(B)  3
(C)  4
(D)  6
(E)  7
Rationale: we can make use of the rule :
Remainder of { (a * b)/n}} = Remainder of (a/n) * Remainder of (b/n)
Here
Remainder of { 46 * 49)/8}} = Remainder of (46/8) * Remainder of (49/8) = 6 * 1 = 6
Answer :D
Answer: (D)  6
Question: Nick's average (arithmetic mean) test score on 4 tests is 78. What must be the student's score on a 5th test for the Nick's average score on the 5 tests to be 80?
(A)  80
(B)  82
(C)  84
(D)  86
(E)  88
Rationale: E. 88
Nick must score at least an 80 for sure. If he scores an 8, then he will need to score 2 pots for each of the 4 other tests tomake upthe difference. They each were at 78 (at least the average is, but this is a small point and doesn't matter to the answer). So 4 tests that were each 2 points short of the 80 average that is desired means the next test must be 8 points higher than the desired average, so 80+8 = 88.
Answer: (E)  88
Question: Guadalupe owns 2 rectangular tracts of land. One is 300 m by 500 m and the other is 250 m by 630 m. The combined area of these 2 tracts is how many square meters?
(A) 3,360
(B) 307,500
(C) 621,500
(D) 704,000
(E) 2,816,000
Rationale: One is 300 m by 500 m and the other is 250 m by 630 m :
(300*500)+(250*630) = 150000+157500
307500
ANSWER:B
Answer: (B) 307,500
Question: What is the ratio between perimeters of two squares one having 3 times the diagonal then the other?
(A) 3:5
(B) 3:3
(C) 3:9
(D) 3:1
(E) 3:2
Rationale: d = 3d d = d
a√2 = 3d a√2 = d
a = 3d/√2 a = d/√2
=>3:1
Answer: D
Answer: (D) 3:1
Question: Sound is said to travel in air at about 1100 feet per second. A man hears the axe striking the tree, 11/5 seconds after he sees it strike the tree. How far is the man from the wood chopper?
(A) 3449
(B) 3777
(C) 2998
(D) 2420
(E) 2778
Rationale: Speed of the sound = 1100 ft/s
Time = 11/5 second
Distance = Speed × Time = 1100 ×115=220×11=2420 ft
Answer : D
Answer: (D) 2420
Question: Which of the following is closest to 10^150 – 10^30 ?
(A) 10^210
(B) 10^180
(C) 10^150
(D) 10^90
(E) 10^6
Rationale: 10^150 – 10^30
10^30 * (10^120 – 1)
as we know 10^2 - 1 means 100-1 and we get 99, which is approximately 100. hence (10^120 – 1) would remain as 10^120.
and 10^30 * 10^120 = 10^150. Answer is C.
Answer: (C) 10^150
Question: If two numbers are in the ratio 6:7. If 10 is Reduced to both of the numbers then the ratio becomes 5:6 then find the smallest number?
(A) 50
(B) 30
(C) 60
(D) 70
(E) 80
Rationale: Explanation:
6:7
6x - 10 : 7x - 10 = 5 : 6
6[6x - 10] = 5[7x - 10]
36x - 60 = 35x - 50
36x - 35x = 60 - 50
x = 10
the small number is = 6
6x = 60 (Answer = 60)
Short cut method:
a:b = 6:7
c:d = 5:6
1.Cross multiplication with both ratios
a * d ~ b * c = 6 * 6 ~ 7 * 5 = 36 ~ 35 = 1
2. If 10 is reduced both the number means 10 * 5 = 50 and 10 * 6 = 60,
Then 50 ~ 60 = 10
===> 1 -----> 10
===> 6 -----> 60 (Answer is = 60)
Answer: Option C
Answer: (C) 60
Question: In some quantity of ghee, 60% of pure ghee and 40% of is vanaspati. If 10kg of pure ghee is added, then the strength of vanaspati ghee becomes 20%. The original quantity was?
(A) 5kg
(B) 10kg
(C) 15kg
(D) 20kg
(E) 25kg
Rationale: Let the original quantity be x kg
vanaspati ghee in x kg = 40/100 *x = 2x/5 kg
(2x/5)/(x+10) = 20/100
2x/(5x+50) = 1/5
5x = 50
x = 10kg
Answer is B
Answer: (B) 10kg
Question: There are 20 balls in a jar. You take out 2 blue balls without putting them back inside, and now the probability of pulling out a blue ball is 1/5. How many blue balls were there in the beginning?
(A) 12.
(B) 9.
(C) 8.
(D) 7.
(E) 6.
Rationale: 12 = 3 blue balls + 18 / 2
Answer: A
Answer: (A) 12.