mathewhe/aqua_rat huggingface dataset:
Question: The average height of 50 pupils in a class is 150 cm. Five of them whose height is 146 cm, leave the class and five others whose average height is 156 cm, join. The new average height of the pupils of the class (in cm) is ?
(A) 287 cm
(B) 151 cm
(C) 276 cm
(D) 287 cm
(E) 297 cm
Rationale: Total height = 150 * 50 = 7500 cm.
New average = [7500 - 5 * 146 + 5 * 156 ] / 50
= 151 cm.
Answer:B
Answer: (B) 151 cm
Question: If 3 (A's capital) = 5 (B's capital) = 7 (C's capital). Then the ratio of their capitals is?
(A) 65:21:15
(B) 45:21:15
(C) 35:21:18
(D) 35:11:15
(E) 35:21:15
Rationale: 3A = 5B = 7 C
A:B:C = 1/3:1/5:1/7
= 35:21:15
Answer: E
Answer: (E) 35:21:15
Question: Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is:
(A) 2:5
(B) 3:5
(C) 4:5
(D) 7:5
(E) 2:4
Rationale: Let the third number be x.
Then, first number = 120% of x =	120x	=	6x
100	5
Second number = 150% of x =	150x	=	3x
100	2
Ratio of first two numbers = 6x	:	3x = 12x : 15x = 4 : 5.
5	2
so the correct answer is option C)
Answer: (C) 4:5
Question: If the first day of a year (other than leap year) was Friday, then which was the last day of that year?
(A) Saturday
(B) Friday
(C) Tuesday
(D) Monday
(E) wednesday
Rationale: Explanation:
Given that first day of a normal year was Friday
Odd days of the mentioned year = 1 (Since it is an ordinary year)
Hence First day of the next year = (Friday + 1 Odd day) = Saturday
Therefore, last day of the mentioned year = Friday
Answer: Option B
Answer: (B) Friday
Question: A no. when divided by the sum of 555 and 445 gives 2times their difference as quotient & 30 as remainder. Find the no. is?
(A) 145646
(B) 236578
(C) 645353
(D) 456546
(E) 220030
Rationale: (555 + 445) * 2 * 110 + 30 = 220000 + 30 = 220030
E
Answer: (E) 220030
Question: On rainy mornings, Mo drinks exactly N cups of hot chocolate (assume that N is an integer). On mornings that are not rainy, Mo drinks exactly 5 cups of tea. Last week Mo drank a total of 36 cups of tea and hot chocolate together. If during that week Mo drank 14 more tea cups than hot chocolate cups, then how many rainy days were there last week?
(A) 5
(B) 3
(C) 4
(D) 2
(E) 6
Rationale: T= the number of cups of tea
C= the number of cups of hot chocolate
T+C = 36 T-C=14 -> T= 25. C=11.
Mo drinks 5 cups of tea a day then number of days that are not rainy = 25/5 = 5
So number of rainy days = 7-5 = 2
D is the answer.
Answer: (D) 2
Question: If x and y are integers such that x^2-2x+2y+4=2x^2-3x+y-2, we can deduce that y is
(A) not an even
(B) an even
(C) a perfect square
(D) an odd
(E) a prime
Rationale: x^2 - 2x + 2y + 4 = 2x^2 - 3x + y - 2
y = x^2 - x - 6
y = (x-3)(x+2) (Note that one factor is even and one factor is odd.)
Then y must be even.
The answer is B.
Answer: (B) an even
Question: Divide Rs. 1600 among A, B and C so that A receives 1/4 as much as B and C together and B receives 3/4 as A and C together. A's share is?
(A) 350
(B) 375
(C) 320
(D) 530
(E) 230
Rationale: A+B+C = 1600
A = 1/4(B+C); B = 3/4(A+C)
A/(B+C) = 1/4
A = 1/5 * 1600 => 320
Answer: C
Answer: (C) 320
Question: Let us say that a table tennis tournament was going on with knock out terms which means the one who loses the match is out of the tournament. 100 players took part in that tournament.
How many matches were played?
(A) 88
(B) 99
(C) 50
(D) 85
(E) 57
Rationale: B
The number of matches will always sum up to one less than the number of players in a knock out tournament. You may calculate it in any manner. Thus 99 matches were played.
Answer: (B) 99
Question: In a certain game, you perform three tasks. You flip a quarter, and success would be heads. You roll a single die, and success would be a six. You pick a card from a full playing-card deck, and success would be picking a Hearts card. If any of these task are successful, then you win the game. What is the probability of winning?
(A) 1/48
(B) 5/16
(C) 11/12
(D) 11/16
(E) 23/48
Rationale: First lets get the overview
Event 1(A) = Flipping the quarter( Probability of both winning/loosing = 1/2)
Event 2(B) = Rolling a dice( Probability of winning = 1/6 ;Probability of loosing= 1 - 1\6 =5\6)
Event 3(C) = Drawing a card( SPADES) Probability of winning = 13/52=3/4 ;Probability of loosing= 1 - 3/4 =1/4)
So now as above we have three events A,BC.
1st method(This is lengthy method)
Possible cases in which it's a win( the highlighted green event is a win and red is loose.
1.ABC= 1/2*5/6*3/4
OR
2.ABC= 1/2*1/6*3/4
OR
3.ABC= 1/2*5/6*1/4
OR
4.ABC= 1/2*1/6*3/4
OR
5.ABC= 1/2*5/6*1/4
OR
6.ABC= 1/2*5/6*1/4
OR
7.ABC= 1/2*1/6*1/4
As we now OR means add
Adding up all of them we'll get the probability of winning ie 11/16
Answer : D
Answer: (D) 11/16
Question: Mangala completes a piece of work in 10 days, Raju completes the same work in 40 days. If both of them work together, then the number of days required to complete the work is
(A) 7 days
(B) 8 days
(C) 9 days
(D) 10 days
(E) 11 days
Rationale: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days.
That is, the required No. of days = 10 × 40/50 = 8 days.
B
Answer: (B) 8 days
Question: In the xy-coordinate system, if (m, n) and (m + 2, n + k) are two points on the line with the equation x = 2y + 3, then k =
(A) 1/2
(B) 1
(C) 2
(D) 5/2
(E) 4
Rationale: Since (m, n) and (m + 2, n + k) are two points on the line with the equation x = 2y + 5 they should satisfy m=2n +3 and m+2 =2 *(n+k)+3.
By 1st equation we have m-2n=3 and by 2nd equation m-2n = 2k+1 --->3 =2k+1 --->k=1.
The answer is, therefore, (B).
Answer: (B) 1
Question: Mrs. Rodger got a weekly raise of $145. If she gets paid every other week, write an integer describing how the raise will affect her paycheck.
(A) $225
(B) $165
(C) $234
(D) $145
(E) $178
Rationale: D
$145
Let the 1st paycheck be x (integer).
Mrs. Rodger got a weekly raise of $ 145.
So after completing the 1st week she will get $ (x+145).
Similarly after completing the 2nd week she will get $ (x + 145) + $ 145.
= $ (x + 145 + 145)
= $ (x + 290)
So in this way end of every week her salary will increase by $ 145.
Answer: (D) $145
Question: There are 69 people that own pets. 15 people own only dogs, 10 people own only cats, 5 people own only cats and dogs, 3 people own cats, dogs and snakes. How many total snakes are there?
(A) 2
(B) 4
(C) 8
(D) 39
(E) 32
Rationale: lets assign variables to all the areas in Venn Diagram of Three.
three different Units are DOG, Cat, Snake= Total = 69
Only Dog= d=15
Only Cat = c=10
Only Snake = s
Exactly Dog and Cat= 5
Exactly Dog and Snake = x
Exactly Cat and Snake = y
all three= 3
so 69=15+10+5+3+x+y+s
we need to know total snakes= x+y+s+3 = 39
answer:D
Answer: (D) 39
Question: Anne traveled from City A to City B in 6 hours, and her speed was between 24 miles per hour and 46 miles per hour. John traveled from City A to City B along the same route in 2 hours, and his speed was between 44 miles per hour and 81 miles per hour. Which of the following could be the distance, in miles, from City A to City B?
(A) 95
(B) 115
(C) 125
(D) 145
(E) 180
Rationale: Anne travels the same distance as John but takes longer.
6 hours : 2 hours
the ratio is 6:2 or 3:1
this means john travels 3 times her speed.
so if Anne travels at minimum 25 mph, john must travel at minimum 75 mph
if john travels 75 mph minimum the minimum distance traveled in 2 hours is 150 miles.
therefore the only answer possible is E
Answer: (E) 180
Question: If x < 12, then it must be true that...
(A) -x < -12
(B) -x - 2 < 14
(C) -x + 2 < -10
(D) x + 2 < 10
(E) x - 5 < 16
Rationale: A. -x < -12 --> x>12. Not true.
B. -x - 2 < 14 --> x>-16. Not true, consider x=-20.
C. -x + 2 < -10 --> x>12. Not true.
D. x + 2 < 10 --> x<8. Not true, consider x=10.
E. x - 5 < 16 --> x<21. Since given that x<12, then x is for sure less than 13. Thus this statement must be true.
Answer: E.
Answer: (E) x - 5 < 16
Question: A man two flats for $675958 each. On one he gains 16% while on the other he loses 16%. How much does he gain or lose in the whole transaction?
(A) 2%
(B) 2.56%
(C) 3.12%
(D) 4.65%
(E) 5.12%
Rationale: In such a case there is always a loss
Loss% = (16/10)^2 = 64/25 = 2.56%
Answer is B
Answer: (B) 2.56%
Question: What is the cost of leveling the field in the form of parallelogram at the rate of Rs.50/10 sq.metre, whose base & perpendicular distance from the other side being 54m & 24m respectively?
(A) Rs.5480
(B) Rs.6080
(C) Rs.6180
(D) Rs.6480
(E) Rs.7000
Rationale: Area of the parallelogram = Length of the base * Perpendicular height
= 54 * 24 = 1296 m.
Total cost of levelling = Rs.6480
D
Answer: (D) Rs.6480
Question: A couple spent $211.20 in total while dining out and paid this amount using a credit card. The $211.20 figure included a 20 percent tip which was paid on top of the price which already included a sales tax of 10 percent on top of the price of the food. What was the actual price of the food before tax and tip?
(A) $120
(B) $140
(C) $150
(D) $160
(E) $180
Rationale: Let the price of the meal be x.
After a 10% sales tax addition, the price is 1.1*x
After a 20% tip on this amount, the total is 1.2*1.1*x = 1.32x
1.32x = $211.20
x = $160
The correct answer is D.
Answer: (D) $160
Question: A certain car can travel 40 minutes on a gallon of gasoline at 60 miles per hour. If the car had started with a full tank and had 12 gallons of gasoline left in its tank at the end, then what percent of the tank was used to travel 80 miles at 60 mph?
(A) 15%
(B) 20%
(C) 25%
(D) 30%
(E) 14%
Rationale: Total time for travelling 80 miles @ 60 mph = 80/60 = 4/3 hour = 80 minutes.
Given, the car uses 1 gallon for every 40 minutes of driving @ 60 mph. Thus in 80 minutes it will use = 2 gallons. Thus, full tank = 2+12= 14 gallons ---> 2/14= 14% of the fuel used. E is the correct answer.
Answer: (E) 14%
Question: There are two inlets and one outlet to a cistern. One of the inlets takes 2 hours to fill up the cistern and the other inlet takes twice as much time to fill up the same cistern. Both of the inlets are turned on at 9:00 AM with the cistern completely empty, and at 10:00AM, the outlet is turned on and it takes 1 more hour to fill the cistern completely. How much time does the outlet working alone takes to empty the cistern when the cistern is full?
(A) 2 hours
(B) 2.5 hours
(C) 3 hours
(D) 3.5 hours
(E) 4 hours
Rationale: The combined inflow rate of the two inlets is 1/2 + 1/4 = 3/4 cistern/hour. Thus, working together, it takes 4/3 hours (time is reciprocal of rate) to fill the cistern.
From 9:00 AM to 10:00 AM, so in 1 hours, the inlet pipes will fill (time)*(rate) = 1*3/4 = 3/4 th of the cistern .
Then the outlet is turned on and the remaining 1/4 th of the cistern is filled in 1 hour.
Letting x to be the rate of the outlet, we would have: 3/4 - x = 1/4 --> x = 1/2 cistern/hour, which means that it takes 2 hours the outlet working alone to empty the cistern.
Answer: A
Answer: (A) 2 hours
Question: The 15 homes in a new development are each to be sold for one of three different prices so that the developer receives an average (arithmetic mean) of $200,000 per home. If 4 of the homes are to be sold for $170,000 each and 5 are to be sold for $200,000 each, what will be the selling price of each of the remaining 8 homes?
(A) $200,000
(B) $210,000
(C) $215,000
(D) $220,000
(E) $230,000
Rationale: IMO the answer has to be D.
5 houses are being sold for 200,000. 4 houses are being sold for $30,000 less, resulting in a loss of $120,000. To make the average selling price intact i.e. $200,000, the remaining 8 houses must be sold at such a profit that it compensates for the loss of 120,000. Hence 8x=120,000.
x=15,000.
The 8 houses are sold at $15,000 profit or at $215,000. (ANSWER C)
Answer: (C) $215,000
Question: Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is?
(A) 3/7
(B) 3/2
(C) 3/1
(D) 3/9
(E) 3/4
Rationale: Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 27 x meters, and length of the second train = 17 y meters. (27 x + 17 y) / (x + y)
= 23 ==> 27 x + 17 y = 23 x + 23 y
==> 4 x = 6 y
==> x/y
= 3/2.
Answer:B
Answer: (B) 3/2
Question: lexus car agency has 108 cars.he sold some cars at 9% profit and rest at 36% profit thus he gains 17% on the sale of all his cars.the no. of cars sold at 36% profit is?
(A) 36
(B) 37
(C) 38
(D) 39
(E) 40
Rationale: ratio of 36% profit cars to 9% profit cars = 8:19
so no. of cars sold at 36% profit = 108*8/27= 32 cars
ANSWER:A
Answer: (A) 36
Question: Find the odd man out.
8, 64, 1, 27, 125, 342, 216
(A) 1
(B) 342
(C) 64
(D) 125
(E) 216
Rationale: Explanation:
Each of the numbers except 342 is a perfect cubes.
Answer: B) 342
Answer: (B) 342
Question: How much time will a train of length 200 m moving at a speed of 72 kmph take to cross another train of length 300 m, moving at 36 kmph in the same direction?
(A) 50
(B) 77
(C) 55
(D) 44
(E) 11
Rationale: Answer: Option A
Explanation:
The distance to be covered = Sum of their lengths = 200 + 300 = 500 m.
Relative speed = 72 -36 = 36 kmph = 36 * 5/18 = 10 mps.
Time required = d/s = 500/10
= 50 sec.
Answer: A
Answer: (A) 50
Question: The height of a cylinder is 60 Cm and the diameter of its base is 5 Cm. The total surface area of the cylinder is
(A) 918.14
(B) 981.41
(C) 982.14
(D) 928.41
(E) None of them
Rationale: Given h = 60 Cm and r = 5/2 Cm
Total surface area = 2πrh + 2&pir(power2)
= 2πr(h+r)
= [2 × 22/7 × 5/2 × (60 + 5/2)] Cm(power2)
= [ 44/7 × 5/2 × ( (120 + 5)/2 ) ] Cm(power2)
= 22/7 × 5 × 125/2 Cm(power2)
= (55 × 125)/7 Cm(power2)
= 6875/7 Cm(power2)
= 982.14 Cm(power2)
Answer is C.
Answer: (C) 982.14
Question: It takes twelve minutes to load a certain video on a cellphone, and fifteen seconds to load that same video on a laptop. If the two devices were connected so that they operated in concert at their respective rates, how many seconds would it take them to load the video, rounded to the nearest hundredth?
(A) 13.32
(B) 13.87
(C) 14.25
(D) 14.69
(E) 14.92
Rationale: The laptop can load the video at a rate of 1/15 of the video per second.
The phone can load the video at a rate of 1/(60*12) = 1/720 of the video per second.
The combined rate is 1/15 + 1/720 = 49/720 of the video per second.
The time required to load the video is 720/49 = 14.69 seconds.
The answer is D.
Answer: (D) 14.69
Question: 21 ball numbered 1 to 21. A ballis drawn and then another ball is drawn without replacement.
(A) 7/21
(B) 7/23
(C) 9/42
(D) 2/21
(E) 3/23
Rationale: The probability that first toy shows the even number,
=1021=1021
Since, the toy is not replaced there are now 9 even numbered toys and total 20 toys left.
Hence, probability that second toy shows the even number,
=920=920
Required probability,
=(1021)×(920)=(1021)×(920)
=9/42
C
Answer: (C) 9/42
Question: If 5x=6y=z, what is x+y, in terms of z?
(A) z/2
(B) 2z
(C) z/3
(D) 11z/30
(E) z/9
Rationale: 5x=6y=z
x = z/5
and y = z/6
x+y = z/5 + z/6 = 11z/30
Answer is D
Answer: (D) 11z/30
Question: The arithmatic mean of 2 no is 34 and geomatric mean of two no is 16 then nos will be
(A) 64,4
(B) 64,6
(C) 64,8
(D) 62,4
(E) 60,4
Rationale: A.M of a and b=>(a+b)/2=34=> a+b=68---(1)
G.M of a and b=>sqrt(a,b)=16=> ab=256
(a-b)^2=(a+b)^2-4ab= (68)^2-(4*256)=>4624-1024=> 3600
(a-b)^2=3600=> a-b=60------(2)
Solving (1) and (2), we get
b=4, a=64
ANSWER:A
Answer: (A) 64,4
Question: Two trains are moving in opposite directions with speed of 210 km/hr and 90 km/hr respectively. Their lengths are 1.10 km and 0.9 km respectively. the slower train cross the faster train in --- seconds
(A) 56
(B) 48
(C) 47
(D) 26
(E) 24
Rationale: Explanation:
Relative speed = 210+90 = 300 km/hr (Since both trains are moving in opposite directions)
Total distance = 1.1+.9 = 2km
Time = 2/300 hr = 1/150 hr = 3600/150 seconds =24 seconds
Answer: Option E
Answer: (E) 24
Question: A man can row 14 Kmph in still water. It takes him twice as long to row up as to row down the river. Find the rate of stream?
(A) 17.6 Km/hr
(B) 18.6 Km/hr
(C) 19.6 Km/hr
(D) 18.6 m/hr
(E) None of these
Rationale: Explanation:
Let man's rate upstream be x kmph
Then his rate downstream = 2x kmph
Rate in still water = 1/2 (2x + x)
3x/2= 14 Kmph
3x = 28
x = 9.3
Rate of upstream = 9.3 Km/hr
Rate of downstream =18.6 Km/hr
Answer: Option B
Answer: (B) 18.6 Km/hr
Question: In how many ways can the letters F, E, E, L be arranged so that the two E's are not next to each other?
(A) 5
(B) 6
(C) 72
(D) 96
(E) 128
Rationale: 1 F
2 E
1 L
Number of ways these letters can be arranged = 4!/2! (2! to account 2 same Es) = 12
Consider 2 Es as 1 entity and thus the number of arrangements for (EE)FL = 3! = 6
Total allowed cases = 12-6 =6
B is the correct answer.
Answer: (B) 6
Question: The vertices of a rectangle in the standard (x,y) coordinate place are (0,0), (0,5), (8,0) and (8,5). If a line through (2,2) partitions the interior of this rectangle into 2 regions that have equal areas, what is the slope of this line?
(A) 0
(B) 1/4
(C) 4/7
(D) 1
(E) 7/4
Rationale: CONCEPT: The readers need to know that a rectangle can be divided into two equal area by a Straight line only when the straight line passes through the Centre of the Rectangle (Intersection of its two diagonals)Draw a figure and know it for yourself.
The point of Intersections of the diagonals will be the midpoint of any diagonal i.e. Midpoint of (0,0), and (8,5) OR Midpoint of (0,5) and (8,0)
i.e. Either [(0+8)/2, (0+5)/2] OR [(0+8)/2, (5+0)/2] =[4, 2.5]
Slope of line passing through points (2,2) and (4,2.5) = (2.5-2)/(4-2) = 0 0.5/2= 1/4
B
Answer: (B) 1/4
Question: A single discount equivalent to the discount series of 20%, 20% and 5% is?
(A) 31.9
(B) 39.2
(C) 31.6
(D) 31.5
(E) 31.1
Rationale: 100*(80/100)*(20/100)*(95/100) = 60.8
100 - 60.8 = 39.2
Answer:B
Answer: (B) 39.2
Question: 45 is the product of two negative numbers. If the greater number is doubled, it is 1 more than the lesser number. What is the greater number?
(A) -6
(B) -5
(C) -8
(D) -1
(E) -2
Rationale: Test the options.
(B) - 5
Double of -5 is -10 and 1 less is -9.
-9 * -5 = 45 (Correct)
Correct
Answer (B)
Answer: (B) -5
Question: Ten people take a test and the scores are 40, 45, 45, 50, 50, 60, 70, 75, 95, 100.
Find the amount of people that scored between the median and mean scores of the tests.
(A) Two
(B) Four
(C) One
(D) Three
(E) Five
Rationale: The median = (the average of two middle terms) = (50 + 60)/2 = 55.
The mean = (the sum)/(# of terms) = 630/10 = 63.
Only 60 is between 55 and 63.
Answer: C.
Answer: (C) One
Question: The least number of complete years in which a sum of money put out at 20% compound interest will
be more than doubled is
(A) 4 years
(B) 5 years
(C) 6 years
(D) 7 years
(E) None of these
Rationale: Explanation:
As per question we need something like following
P(1+R100)n>2P(1+20100)n>2(65)n>265×65×65×65>2
So answer is 4 years
Answer: A
Answer: (A) 4 years
Question: (X+2) is an even number and Y is a positive odd number. Which of the following expressions cannot be even?
(A) (X+2)Y
(B) (X+2)Y^2
(C) (X+2)Y^3
(D) Y^4
(E) (X+2)
Rationale: Y^4
D
Answer: (D) Y^4
Question: A dishonest milkman sells his milk at cost price but he mixes it with water and thereby gains 25%.
What is the percentage of water in the mixture?
(A) 25%
(B) 20%
(C) 22%
(D) 24%
(E) None of these
Rationale: Explanation :
--------------------------------------------------------------------------------Solution 1 - Using the concepts learned in
Profit and Loss--------------------------------------------------------------------------------If a trader professes to sell
his goods at cost price, but uses false weights, thenGain%=[Error(True Value−Error)×100]%Here Gain=
25%Here error = quantity of water he mixes in the milk = xHere the true value = true quantity of milk =
TSo the formula becomes 25 = x(T−x)×100⇒1=x(T−x)×4⇒T−x=4x⇒T=5xpercentage of water in the
mixture = xT×100=x5x×100=15×100=20%--------------------------------------------------------------------------------
Solution 2 - Using the concepts learned in Mixtures and Alligations---------------------------------------------------
-----------------------------Let CP of 1 litre milk = Rs.1Given that SP of 1 litre mixture = CP of 1 Litre milk =
Rs.1Given than Gain = 25%Hence CP of 1 litre mixture =
100(100+Gain%)×SP=100(100+25)×1=100125=45
By the rule of alligation, we have
CP of 1 litre milk CP of 1 litre water
1 0
CP of 1 litre mixture
4/5
4/5 - 0 = 4/5 1- 4/5 = 1/5
=> Quantity of milk : Quantity of water = 4/5 : 1/5 = 4 : 1
Hence percentage of water in the mixture = 15×100=20%
Answer : Option B
Answer: (B) 20%
Question: A grocer has a sale of Rs. 5000 Rs. 5500, Rs. 6000, Rs. 6500 and Rs. 7000 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6125?
(A) s. 6500
(B) s. 7000
(C) s. 7271
(D) s. 4997
(E) s. 5000
Rationale: Total sale for 5 months = Rs. (5000 + 5500 + 6000 + 6500 + 7000) = Rs. 30000
Required sale = Rs. [ (6125 x 6) - 30000 ]
= Rs. (36750 - 30000)
= Rs.6750.
C)
Answer: (C) s. 7271
Question: A man can row upstream at 26 kmph and downstream at 40 kmph, and then find the speed of the man in still water?
(A) 22
(B) 37
(C) 30
(D) 33
(E) 18
Rationale: US = 26
DS = 40
M = (40 + 26)/2 = 33
Answer:D
Answer: (D) 33
Question: Population of a city in 20004 was 1000000. If in 2005 there isan increment of 15%, in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45%, then find the population of city atthe end of the year 2007
(A) 975335
(B) 974563
(C) 976442
(D) 974257
(E) 1083875
Rationale: Required population = P (1 + R1/100)(1 - R2/100)(1 + R3/100)
= P (1 + 15/100)(1 - 35/100)(1 + 45/100)
= 1083875
E
Answer: (E) 1083875
Question: Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?
(A) 9
(B) 10
(C) 12
(D) 20
(E) 14
Rationale: Due to stoppages, it covers 9 km less.
Time taken to cover 9 km =(9* 60)/54min	= 10 min.
Answer:B
Answer: (B) 10
Question: 3^2 + 3^2 + 3^2 + 3^2 =
(A) 3^3
(B) 3^6
(C) 4^8
(D) 4^9
(E) 4^12
Rationale: Hi shakticnb,
Certain Quant questions on the GMAT are just about 'organizing' the information in a specific way. If you find yourself getting confused by a prompt, think about how you might change the way that the information is presented to you.
Here, for example, we're asked for....
3^2 + 3^2 + 3^2 + 3^2 =
Now, the GMAT doesn't really expect us to calculate this sum (but we could if we had to), but we are expected to find a way to organize this information... If, instead of all of those exponents, we had...
X + X + X + X =
What would the sum be?
Clearly, it would be 4(X) = 4X.....since we're just combining 'like' terms. Take that same idea with this prompt and you have...
3^2 + 3^2 + 3^2 + 3^2 =
3(3^2)
This can be re-written as...
(3^1)(3^2)
...and now we can use exponent rules; since we're MULTIPLYING 'bases' that are the same, we ADD the exponents...
(3^1)(3^2) = 3^3
Final Answer:
A
Answer: (A) 3^3
Question: If x < 12, then it must be true that...
(A) -x < -12
(B) -x - 2 < 14
(C) -x + 2 < -10
(D) x + 2 < 10
(E) x - 7 < 18
Rationale: A. -x < -12 --> x>12. Not true.
B. -x - 2 < 14 --> x>-16. Not true, consider x=-20.
C. -x + 2 < -10 --> x>12. Not true.
D. x + 2 < 10 --> x<8. Not true, consider x=10.
E. x - 7 < 18 --> x<25. Since given that x<12, then x is for sure less than 13. Thus this statement must be true.
Answer: E.
Answer: (E) x - 7 < 18
Question: A certain farmer pays $30 per acre per month to rent farmland. How much does the farmer pay per month to rent a rectangular plot of farmland that is 370 feet by 605 feet? (43,560 square feet = 1 acre)
(A) $5,330
(B) $3,360
(C) $1,350
(D) $360
(E) $154.1
Rationale: Basically the question an error. 1 acre = 43,560 square feet and if it is then the answer is 154.1 (E)
Answer: (E) $154.1