mathewhe/aqua_rat huggingface dataset:
Question: A water tank, having the shape of a rectangular prism of base 100 square centimeters, is being filled at the rate of 1 liter per minute. Find the rate at which the height of the water in the water tank increases. Express your answer in centimeters per minute.
(A) 30 cm
(B) 10 cm
(C) 50 cm
(D) 90 cm
(E) 70 cm
Rationale: The volume of a rectangular prism is given by
area of base ? height
The rate at which the tank is being filled is 1 liter per minute which we need to convert
1 liter = 1 dm3
But 1 dm = 10 cm. Hence
1 liter = (10 cm)3 = 1000 cm3
The height h of the water is related to the volume by
volume = area of base *h
In one minute the volume increases by 1 liter or 1000 cm3 and the height increases by
h = volume / area of base = 1000 cm3 / 100 cm2 = 10 cm
correct answer B
Answer: (B) 10 cm
Question: A train 200 m long is running with a speed of 68 kmph. In what time will it pass a man who is running at 8 kmph in the same direction in which the train is going?
(A) 6 sec.
(B) 7 sec.
(C) 9 sec.
(D) 12 sec.
(E) None
Rationale: Solution
Speed of the train relative to man	=( 68 - 8 )
= 60 Kmph
= 60 x 5 / 18
=50/3 m/sec.
Time taken by it to cover 200 m at (50 /3)m/sec
= (200 x 3/50)sec
= 12 sec.
Answer D
Answer: (D) 12 sec.
Question: How many possible ways can 2 girls (Rebecca, Kate, Ashley) go on a date with 2 boys (Peter, Kyle, Sam)?
(A)  2
(B)  4
(C)  5
(D)  6
(E)  8
Rationale: Any one girl can go with 2 boys.
and 2rd girl can go with remaining 1 boy
2! i.e 2 (A) is the answer
Answer: (A)  2
Question: a man buys m no. of pens for rs. n each and sells n no. of pens for rs. m each. then what is the profit he have earned?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: c.p. of 1 pen=Rs n (given each)
so c.p. of m pens=rs mn
s.p. of 1 pen =rs m
so s.p. of n pens=rs mn
so profit =s.p.-c.p.=0(zero)
ANSWER:A
Answer: (A) 0
Question: With an average speed of 40 km/hr a car reaches its destination on time. If it goes with an average speed of 35 km/h, it is late by 15 minutes. The total journey is?
(A) 30 km
(B) 40 km
(C) 70 km
(D) 80 km
(E) 90 km
Rationale: Let the total journey be X km.
X/35 - X/40 = 15/60
Solving for X, we get X = 70
Therefore, total journey = 70 km.
ANSWER:C
Answer: (C) 70 km
Question: If (t-8) is a factor of t^2-kt-45, then k=
(A) 16
(B) 12
(C) 2
(D) 6
(E) 14
Rationale: t^2-kt-48 = (t-8)(t+m) where m is any positive integer.
if 48/8 = 6, then we know as a matter of fact that:
m = +6
and thus k = 8-6 = 12
t^2-kt-m = (t-a)(t+m) where a>m
t^2+kt-m = (t-a)(t+m) where a<m
t^2-kt+m = (t-a)(t-m)
t^2+kt+m = (t+a)(t+m)
B
Answer: (B) 12
Question: The perimeter of a semi circle is 144 cm then the radius is?
(A) 22
(B) 28
(C) 97
(D) 26
(E) 12
Rationale: 36/7 r = 144 => r
= 28
Answer:B
Answer: (B) 28
Question: Arun, Akash, Amir and Aswanth go for a picnic. When Arun stands on a weighing machine, Akash also climbs on, and the weight shown was 132 kg. When Akash stands, Amir also climbs on, and the machine shows 130 kg. Similarly the weight of Amir and Aswanth is found as 102 kg and that of Akash and Aswanth is 116 kg. What is Aswanth’s weight?
(A) 58kg
(B) 78 kg
(C) 44 kg
(D) 48 kg
(E) None
Rationale: arun+akash=132-----eq1
akash+amir=130------eq2
amir+aswanth=102------eq3
akash+aswanth=116-------eq4
solving eq 2 and 4
we get amir-aswanth=14-------eq5
now solving eq 3 and 5
we get aswanth=44
ANSWER:C
Answer: (C) 44 kg
Question: The ratio between the speeds of two trains is 5: 6. If the second train runs 300 kms in 5 hours, then the speed of the first train is ?
(A) 60 km/hr
(B) 50 km/hr
(C) 55 km/hr
(D) 65 km/hr
(E) None of these
Rationale: Explanation:
Let the speeds of two trains be 5X and 6X km/hr.
6/X=300/5=>X=10 Km/hr
So speed of first train is 10*5 = 50 km/hr
Option B
Answer: (B) 50 km/hr
Question: A and B can do a piece of work in 21 and 24 days respectively. They started the work together and after some days A leaves the work and B completes the remaining work in 9 days. After how many days did A leave?
(A) 5 days
(B) 6 days
(C) 7 days
(D) 8 days
(E) 9 days
Rationale: In 9 days B completes 9/24 i.e., 3/8th of the work.
Hence 1 - 3/8 = 5/8th of the work is completed by A and B together.
i.e., x (1/21 + 1/24) = 5/8 => x = 7 days.
ANSWER:C
Answer: (C) 7 days
Question: How many pieces of 75 cm can be cut from a rope 55.5 meters long?
(A) 30
(B) 40
(C) 60
(D) None
(E) 74
Rationale: Explanation :
Total pieces of 75 cm that can be cut from a rope of 55.5 meters long is
= (55.5 meters)/(75 cm)
= (55.5 meters)/(0.75 meters)
= 74
Answer : E
Answer: (E) 74
Question: The workforce of Company X is 60% female. The company hired 20 additional male workers, and as a result, the percent of female workers dropped to 50%.How many employees did the company have after hiring the additional male workers?
(A) 145
(B) 188
(C) 189
(D) 190
(E) 191
Rationale: let x be the total worker then 0.6x =female worker and 0.4x is male worker then 20 male worker added
06x/(0.4x +20) = 50/100 or 60x = 50*( 0.4x+100) = 20x+ 5000 or 40x = 5000 , x = 500/4= 125
total worker = 125 +20= 145
A
Answer: (A) 145
Question: D is the set of all the multiples of 3 between 20 and 100. E is the set of all the factors of 400. Set D and Set E have how many numbers in common?
(A) 0
(B) 1
(C) 3
(D) 5
(E) 12
Rationale: D is a set of multiples of 3.
400 is NOT a multiple of 3, hence none of its factors is a multiple of 3.
Therefore, those two sets won't have any overlap.
Answer: A.
Answer: (A) 0
Question: judith is practicing her dance steps along with her friends. In a particular sequence, all of them form a row. At that point, judithis standing on the 5th position from either end of the row.
Can you find out how many girls are practicing together?
(A) 4
(B) 9
(C) 7
(D) 6
(E) 8
Rationale: As judith is 5th from either end of the row, it means that 4 girls are on one of her sides and 4 are present on the other.
4 + 4 + 1(judith herself) = 9.
Hence,9 girls are practicing the dance together.
correct answer is B)9
Answer: (B) 9
Question: What is the value of 3x^2 − 1.8x + 0.4 for x = 0.6?
(A) −0.3
(B) 0
(C) 0.4
(D) 1.08
(E) 2.46
Rationale: 3x^2-1.8x+0.4 for x=0.6
=3(0.6*0.6)-3*0.6*(0.6)+0.4
=0+0.4
=0.4
ANSWER:C
Answer: (C) 0.4
Question: The contents of a certain box consist of 24 mangos and 30 kiwis. How many kiwis must be added to the box so that exactly 30% of the pieces of fruit in the box will be mangos?
(A) 24
(B) 26
(C) 30
(D) 46
(E) 50
Rationale: mango = (mango + kiwi + x)*0.3
24 = (30 + 24 + x)*0.3
x = 26.
Answer: B.
Answer: (B) 26
Question: A computer program generates a sequence of numbers a1, a2, a3, ... such that a1=1, a2=2, and ak=a(k-2)*4-1 for 2 < k < n for n=10. Find a6.
(A) 19
(B) 27
(C) 31
(D) 36
(E) 41
Rationale: a1=1
a2=2
a3=1*4-1=3
a4=2*4-1=7
a5=3*4-1=11
a6=7*4-1=27
27
Answer: (B) 27
Question: In an examination, there were 2,000 candidates, out of which 900 candidates were girls and rest were Boys. If 38% of the boys and 32% of the girls passed, then the total percentage of failed candidates is?
(A) 35.67%
(B) 64.75%
(C) 68.57%
(D) 69.57%
(E) none of these
Rationale: Girls = 900, Boys = 1100
Passed = ( 38% of 1100 ) + ( 32% of 900)
= 418 + 288 = 706
Failed = 2000 - 706 = 1294
Failed % = [(1294/2000) x 100]%
= 64.7%.
ANSWER:B
Answer: (B) 64.75%
Question: If 45% of z is 60% of y and y is 75% of x, what percent of x is z?
(A) 200
(B) 160
(C) 100
(D) 65
(E) 50
Rationale: (45/100)z = (60/100)y
and y = (75/100)x i.e. y = (3/4)x
i.e. (45/100)z = (60/100)*(3/4)x
i.e. z = (60*3)x/(45*4)
i.e. z = (1)x = (100/100)x
i.e. z is 100% of x
Answer: Option C
Answer: (C) 100
Question: If Rs.7500 are borrowed at C.I at the rate of 4% per annum, then after 2 years the amount to be paid is :
(A) Rs.8082
(B) Rs.7800
(C) Rs.8100
(D) Rs.8112
(E) None
Rationale: Explanation:
Amount = Rs. [7500(1+4/100)2]= Rs. [7500×26/25×26/25]=Rs.8112.
Correct Option: D
Answer: (D) Rs.8112
Question: If S is the sum of reciprocals of a list of consecutive integers from 25 to 34, inclusive, S is approximately equal to
(A) 0.1
(B) 0.2
(C) 0.33
(D) 0.4
(E) 0.5
Rationale: We need to find the approximate value of 1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34. Now, the sum of these 10 terms will be very close to 10 times 1/30, which is 0.033*10=0.33.
Answer: C.
Answer: (C) 0.33
Question: 250 metres long yard, 51 trees are palnted at equal distances, one tree being at each end of the yard. What is the distance between 2consecutive trees
(A) 10
(B) 12
(C) 14
(D) 16
(E) 5
Rationale: 51 trees have 50 gaps between them,
Required distance (250/50) = 15
E
Answer: (E) 5
Question: sue has 3 apples. Billy has 5 apples. If billy steals all of sues apples and eats 1 how many does he have left?
(A) 2
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: 7 D
Answer: (D) 7
Question: If x+|x|+y=7 and x+|y|-y=5 what is x+y=?
(A) 1
(B) -1
(C) 3
(D) 5
(E) 13
Rationale: If x<0 and y<0, then we'll have x-x+y=7 and x-y-y=6. From the first equation y=7, so we can discard this case since y is not less than 0.
If x>=0 and y<0, then we'll have x+x+y=7 and x-y-y=6. Solving gives x=4>0 and y=-1<0 --> x+y=3. Since in PS questions only one answer choice can be correct, then the answer is C (so, we can stop here and not even consider other two cases).
Answer: C.
Adding both eqn we get 2x +IxI+IyI = 13
Now considering X <0 and y>0
2x-x +y = 13
we get x+y =5
Hence answer should be D
Answer: (D) 5
Question: A textile manufacturing firm employees 100 looms. It makes fabrics for a branded company. The aggregate sales value of the output of the 100 looms is Rs 5,00,000 and the monthly manufacturing expenses is Rs 1,50,000. Assume that each loom contributes equally to the sales and manufacturing expenses are evenly spread over the number of looms. Monthly establishment charges are Rs 75000. If one loom breaks down and remains idle for one month, the decrease in profit is:
(A) 13000
(B) 7000
(C) 10000
(D) 3500
(E) None of these
Rationale: Explanation :
Profit = 5,00,000âˆ’(1,50,000+75,000) =Rs. 2,75,000.
Since, such loom contributes equally to sales and manufacturing expenses.
But the monthly charges are fixed at Rs 75,000.
If one loan breaks down sales and expenses will decrease.
New profit :-
=>500000Ã—(99/100)âˆ’150000Ã—(99/100)âˆ’75000.
=>Rs 2,68,000.
Decrease in profit
=>2,75,000âˆ’2,71,500
=>Rs. 3,500.
Answer : D
Answer: (D) 3500
Question: The fourth proportional to 12, 20 and 30 is?
(A) 21
(B) 66
(C) 55
(D) 50
(E) 61
Rationale: (20*30)/12
= 50
Answer:D
Answer: (D) 50
Question: The sum of the present ages of father and his son is 60 years. Six years ago, father's age was five times the age of the son. After 6 years, son's age will be?
(A) 22
(B) 287
(C) 26
(D) 20
(E) 28
Rationale: Let the present ages of son and father be x and (60 - x) years respectively.
Then, (60 - x) - 6 = 5(x - 6)
6x = 84 => x = 14
Son's age after 6 years = (x + 6) = 20 years.Answer: D
Answer: (D) 20
Question: The sides of the triangle are in the ratio 5:6:7 and its perimeter is 720cm. The length of the longest side is?
(A) 150cm
(B) 200cm
(C) 162cm
(D) 220cm
(E) 280cm
Rationale: Ratio of sides = 5:6:7
Largest side = 720*7/18 = 280cm
Answer is E
Answer: (E) 280cm
Question: Three business people wish to invest in a new company. Each person is willing to pay one third of the total investment. After careful calculations, they realize that each of them would pay $8,200 less if they could find two more equal investors. How much is the total investment in the new business?
(A) $61,500
(B) $54,000
(C) $21,000
(D) $ 5,400
(E) $ 3,600
Rationale: Total Investment between 5: (x/5)
Total investment including 8200 less between 3 people(x-(8200*3))/3
Set both eq. equal to each other.
61,500
Answer A)
Answer: (A) $61,500
Question: What should come in place of the question mark (?) in the following number series?
16 8 12 30 105 ?
(A) 387.5
(B) 470.5
(C) 367.5
(D) 472.5
(E) None of these
Rationale: Explanation:
16*1/2=8
8*3/2=12
12*5/2=30
30*7/2=105
105*9/2=472.5
Answer:D
Answer: (D) 472.5
Question: While playing a certain dice game, Chris wins if the sum of the two dice is 5, at which point the game is over. If the game allows Chris three rolls in an attempt to win, what is the probability that Chris will win?
(A) 1/2
(B) 17/36
(C) 217/729
(D) 11/36
(E) 25/216
Rationale: Probability of winning game = 1- Probability of losing game
Probability of losing game = (Probability of not getting sum 7 in any of the three attempts)
Ways of getting sum 5 = (1,4)(2,3)(3,2)(4,1)= 4 ways
Total ways of getting outcome on two dice =6*6=36
Probability of getting sum as 5 in any attempt =4/36=1/9
Probability of NOT getting sum as 5 in any attempt = 1-(1/9)= 8/9
Probability of losing game =(8/9)*(8/9)*(8/9)=512/729
I.e. Probability of wining game = 1-(512/729) = 217/729
Answer : Option C
Answer: (C) 217/729
Question: How many 3 digit numbers are completely divisible 6 ?
(A) 146
(B) 148
(C) 150
(D) 152
(E) None of these
Rationale: Explanation :
100/6 = 16, remainder = 4. Hence 2 more should be added to 100 to get the minimum
3 digit number divisible by 6.
=> Minimum 3 digit number divisible by 6 = 100 + 2 = 102
999/6 = 166, remainder = 3. Hence 3 should be decreased from 999 to get the maximum
3 digit number divisible by 6.
=> Maximum 3 digit number divisible by 6 = 999 - 3 = 996
Hence, the 3 digit numbers divisible by 6 are 102, 108, 114,... 996
This is Arithmetic Progression with a = 102 ,d = 6, l=996
Number of terms = (l−a)/d + 1 = (996 − 102)/6 + 1 = 894/6 + 1 = 149 + 1 = 150. Answer : Option C
Answer: (C) 150
Question: David invested certain amount in three different schemes. A, B and C with the rate of interest 10% p.a., 12% p.a. and 15% p.a. respectively. If the total interest accrued in one year was Rs. 3200 and the amount invested in scheme C was 150% of the amount invested in scheme A and 240% of the amount invested in scheme B, what was the amount invested in scheme B?
(A) 5000
(B) 5007
(C) 5006
(D) 5026
(E) 5002
Rationale: Let x, y and z be the amount invested in schemes A, B and C respectively. Then,
(x * 10 * 1)/100 + (y * 12 * 1)/100 + (z * 15 * 1)/100 = 3200
10x + 12y + 15z = 320000
Now, z = 240% of y = 12/5 y
And, z = 150% of x = 3/2 x
x = 2/3 z = ( 2/3 * 12/5) y = 8/5 y
16y + 12y + 36y = 320000
y = 5000
Sum invested in scheme B = Rs. 5000.
Answer:A
Answer: (A) 5000
Question: The total age of A and B is 16 years more than the total age of B and C. C is how many year younger than A
(A) 11
(B) 16
(C) 13
(D) 14
(E) 15
Rationale: Explanation:
Given that A+B = 16 + B + C
=> A ? C = 16 + B ? B = 16
=> C is younger than A by 16 years
Answer: Option B
Answer: (B) 16
Question: Call a number parents if it is composite but not divisible by 2, 3, or 5. The three smallest guardian numbers are 49, 77, and 91. There are 168 prime numbers less than 1000. How many parent numbers are there less than 1000?
(A) a) 90
(B) b) 97
(C) c) 100
(D) d) 106
(E) e) 108
Rationale: Start with the numbers from 1 - 1000. We have 1000 numbers.
Subtract the primes:
1000 - 168 = 832
Now, subtract the even numbers, divisible by 2. There are 500 even numbers in the set, but the first, 2 itself, has already been subtracted with the primes. There are 499 non-prime even numbers in the set, including 1000 itself. (1000 itself really shouldn't be included, because are looking for numbers less than 1000, but it gets subtracted in this step anyway, so it doesn't matter.)
832 - 499 = 333
Now, numbers divisible by 3. There are 333 factors of three between 1 and 1000, but first of all, one of those is the prime number 3, already subtracted, so exclude that --- 332. Of those, half are even, already counted, so that leaves 332/2 = 166 non-prime odd multiples of 3.
333 - 166 = 167
Now, multiples of 5. There are 200 multiples of 5 up to 1000. Half are even, divisible by 10, so eliminate them --- 100 odd multiples of 5. Eliminate the prime number 5 itself, already counted --- 99 non-prime multiples of 5. Now, 1/3 of these are divisible by three, already counted, so we 2/3 of this number ==> 66. There are 66 non-prime multiples of 5 that are not divisible by 3.
167 - 66 = 101
The last number that needs to be subtracted --- not prime, not composite, not a multiple of 2 or 3 or 5, is 1 itself. This is not composite, so it is not a parent.
101 - 1 = 100
That leaves 100 parent numbers. OA =(C)
Answer: (C) c) 100
Question: 0.003 * 0.5 = ?
(A) 0.00015
(B) 0.0015
(C) 0.015
(D) 0.15
(E) None of these
Rationale: Explanation:
3 * 5 = 15. Sum of decimal places = 4.
0.003 * 0.5 = 0.0015 = 0.0015
ANSWER B
Answer: (B) 0.0015
Question: What is the next number: 3, 18, 258, __
(A) 2928
(B) 3638
(C) 4098
(D) 4418
(E) 5378
Rationale: 4^0 + 2 = 3
4^2 + 2 = 18
4^4 + 2 = 258
4^6 + 2 = 4098
The answer is C.
Answer: (C) 4098
Question: What is remainder of the division (1525*1527*1529)/12?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: remainder will be number/ 100 here as the divisor is two digit number = 12.
hence checking for the last two digits = 5*7*9 = 15
Thus remainder = 3.
Answer : D
Answer: (D) 3
Question: Andrew found $10 while cleaning his car. He found 15 quarters, 22 dimes, 5 pennies and 4 dollar bills. What % of the total amount he found were made up of coins?
(A) 95 %
(B) 90 %
(C) 85 %
(D) 70 %
(E) 60 %
Rationale: Number of runs made by running = (15 x 0.25 + 22 x .10 + 5 x 0.01)
= (15 x 0.25) + (22 x .10) + (5 x 0.01)
= 6
Now, we need to calculate 6 is what percent of 10.
=> 6/10 * 100 = 60 %
E
Answer: (E) 60 %
Question: One water pump can fill half of a certain empty tank in 8 hours. Another pump can fill half of the same tank in 8.5 hours. Working together, how long will it take these two pumps to fill the entire tank?
(A) 8 7/13
(B) 1 5/8
(C) 3 1/4
(D) 8 8/33
(E) 3 1/2
Rationale: One pump can fill a tank in 8 hours and another in 8.5 hours
so the rate at which both can half fill the tank is (1/8+1/8.5) => 33/136
Thus half of the tank can be filled in 136/33
so for filling the complete tank =>136/33*2 = 272/33 = 8 8/33
ANSWER:D
Answer: (D) 8 8/33
Question: What is the measure of the radius of the circle inscribed in a triangle whose sides measure 8, 15 and 27 units?
(A) 8.5 units
(B) 6 units
(C) 3 units
(D) 5 units
(E) 2 units
Rationale: Sides are 8, 15 and 27...thus it is right angle triangle Since 27^2 = 8^2 + 15^2
therefore, area = 1/2 * 15 * 8 = 60
We have to find in-radius
Therefore, area of triangle = S*r ....where S=semi-perimeter and r= in-radius
Now S=semi-perimeter = 27+15+8 /2 = 30
Thus , 60 =30*r
and hence r=in-radius= 2
Option E
Answer: (E) 2 units
Question: By selling a house for Rs.45000, it was found that 1/8 of the outlay was gained, what ought the selling to price to have been in order to have lost 5 p.c?
(A) 38002
(B) 38000
(C) 38028
(D) 38289
(E) 380787
Rationale: CP + CP/8 = 45000
CP = 40000
SP = 40000*(95/100) = 38000
Answer: B
Answer: (B) 38000
Question: The C.I. on a certain sum for 2 years Rs.41 and the simple interest is Rs.40. What is the rate percent?
(A) 3%
(B) 5%
(C) 6%
(D) 2%
(E) 7%
Rationale: SI = 20 + 20
CI = 20 + 21
20 ---- 1
100 ---- ? => 5%
Answer:B
Answer: (B) 5%
Question: If x + 1/x = 2 then find x2 + 1/x2
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: If x+1/x= p
==> x^2+1/x^2=p^2-2
Ans= 2^2-2=2
ANSWER:B
Answer: (B) 2
Question: The average of numbers 0.34204, 0.34203, 0.34202 and 0.34201 is ?
(A) 0.34202
(B) 0.34204
(C) 0.342022
(D) 0.342025
(E) None
Rationale: Answer
Average = (0.34204 + 0.34203 + 0.34202 + 0.34201)/ 4
=1.3681/ 4
=0.342025
Correct Option: D
Answer: (D) 0.342025
Question: Mary got a weekly raise of $384. If she gets paid every other week, write an integer describing how the raise will affect her paycheck.
(A) 384
(B) 374
(C) 364
(D) 394
(E) 354
Rationale: Let the 1st paycheck be x (integer).
Mary got a weekly raise of $ 384.
So after completing the 1st week she will get $ (x+384).
Similarly after completing the 2nd week she will get $ (x + 384) + $ 384.
= $ (x + 384 + 384)
= $ (x + 768)
So in this way end of every week her salary will increase by (A)$ 384.
Answer: (A) 384
Question: A letter lock consists of three rings each marked with six different letters. The number of distinct unsuccessful attempts to open the lock is at the most ?
(A) 177
(B) 199
(C) 215
(D) 168
(E) 167
Rationale: Since each ring consists of six different letters, the total number of attempts possible with the three rings is
= 6 * 6 * 6 = 216. Of these attempts, one of them is a successful attempt.
Maximum number of unsuccessful attempts
= 216 - 1
= 215.
Answer: C
Answer: (C) 215
Question: A company has 2 directors and 5 managers. How many different committees with 5 people can be chosen having at least 1 director?
(A) 500
(B) 720
(C) 4500
(D) 20
(E) 55
Rationale: atleast one means exactly one and more than one.
different committees with 5 people can be chosen having at least 1 director is
(2c1*5c4) + (2c2*5c3) = 20;
Hence D.
Answer: (D) 20
Question: What should come in place of the question mark in the following questions?
?⁄24 = 72⁄√?
(A) 12
(B) 16
(C) 114
(D) 144
(E) None of these
Rationale: ? × √? = 24 × 72 Squaring both the sides,
(?2 × ? ) = ?3 = (8 × (3) × (8 × 3) × (8 × 9) × (8 × 9)
= 2(3)8(3)9(3)
∴ ? = 2 × 8 × 9 = 144
Answer D
Answer: (D) 144
Question: A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 165 m long?
(A) 40
(B) 99
(C) 88
(D) 77
(E) 42
Rationale: :
Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 360 + 165 = 525 m
Required time = 525 * 2/25 = 42 sec
Answer:E
Answer: (E) 42
Question: The line K represented by which of the following equation does not intersect with the line represented by y = 3x^2+5x+1
(A) y = 2x^2+5x+1
(B) y = x^2+5x+2
(C) y = 3x^2+5x+2
(D) y = 3x^2+7x+2
(E) y = x^2+7x+1
Rationale: concept of slope for linesparabolas are different. Bunuel, please correct if I am wrong. Also please help to solve this problem if its a GMAT type question.
The general form of parabolic equ. is y^2= 4ax which implies the axis is x or x^2 = 4ay where axis is y.
We have a similar form as x^2 = 4ay.
here the vertex is origin.
So if we have same values of x and y but constant term changes then we will have parallel parabolas.
This is same as for straight line K which are parallel for different values of constant term c
ax + by +c1 = 0 and ax +by+ c2 =0
We have quadratic equations. These equations when drawn give parabolas, not lines. The question is: which of the following parabolas does not intersect with the parabola represented by y=3x^2+5x+1.C
Answer: (C) y = 3x^2+5x+2
Question: A town's oldest inhabitant is x years older than the sum of the ages of the Lee triplets. If the oldest inhabitants is now J years old, how old will one of the triplets E be in 20 years?
J-X-40/3 is my answers.
J = X + L + L + L is the initial situation
After 20 years
J + 20 = X + L + L + L + 60 ...20 years for each triplet so 60 years totally.
J - X - 40/ 3 = L is my answer.
What wrong am i doing ? Since the age asked is after 20 years i also consider adding 20 years to J .
(A) (J - 50)/3
(B) 3(J + 20)/x
(C) (J + x - 50)/3
(D) (J - x + 60)/3
(E) (J + x - 20)/3
Rationale: here it goes:
Oldest inhabitant = sum of age of triplets + X
J = 3L + X so L = (J - X)/3
After 20 years = L + 20
E= (J - X)/3 + 20
= (J - X + 60)/3=D
Answer: (D) (J - x + 60)/3
Question: Circular gears P and Q start rotating at the same time at constant speeds. Gear P makes 10 revolutions per minute and Gear Q makes 40 revolutions per minute. How many seconds after the gears start rotating will gear Q have made exactly 5 more revolutions than gear P?
(A) 6
(B) 8
(C) 10
(D) 12
(E) 15
Rationale: Gear Q makes 30 more revolutions each 60 seconds.
The time to make 5 = 30/6 more revolutions is 60/6 = 10 seconds.
The answer is C.
Answer: (C) 10
Question: If n is an integer greater than 5, which of the following must be divisible by 3?
(A) 1. n (n+1) (n-4)
(B) 2. n (n+2) (n-1)
(C) 3. n (n+3) (n-5)
(D) 4. n (n+4) (n-2)
(E) 5. n (n+5) (n-6)
Rationale: We need to find out the number which is divisible by three,
In every 3 consecutive integers, there must contain 1 multiple of 3.
So n+4 and n+1 are same if we need to find out the 3's multiple. replace all the numbers which are more than or equal to three
1. n (n+1) (n-4) = > n(n+1)(n-1) = > (n-1)n(n+1)
2. n (n+2) (n-1) = > n(n+2)(n-1) = > (n-1)n(n+1)
3. n (n+3) (n-5) = > n(n+0)(n-2) = > (n-2)n(n)
4. n (n+4) (n-2) = > n(n+1)(n-2) = > (n-2)n(n+1)
5. n (n+5) (n-6) = > n(n+2)(n-0) = > (n)n(n+2)
from the above onlyoption Ais product of consecutive three numbers.
E
Answer: (E) 5. n (n+5) (n-6)