mathewhe/aqua_rat huggingface dataset:
Question: If Rs.450 amount to Rs.540 in 4 years, what will it amount to in 6 years at the same rate % per annum?
(A) 288
(B) 327
(C) 585
(D) 972
(E) 271
Rationale: 90 = (450*4*R)/100
R = 5%
I = (450*6*5)/100 = 135
450 + 135 = 585
Answer: C
Answer: (C) 585
Question: A sum fetched total simple interest of 4016.25 at the rate of 13 p.c.p.a. in 5 years. What is the sum?
(A) 6178.85
(B) 8032.5
(C) 4462.5
(D) 8900
(E) None of these
Rationale: Let the sums be P.
Now, 65% of P = 4016.25
or, P = 6178.85
Answer A
Answer: (A) 6178.85
Question: There are 100 freshmen at a particular college, all of whom must take at least one of the three core classes: Art, Biology, and Calculus. Of these freshmen, 21 take only Biology, 10 take only Calculus, 5 take all three classes, and 20 take Art and exactly one of the other two core classes. If the number of freshmen who take only Art is 3 times the number of freshmen who take every core class except Art, how many freshmen take Art?
(A) 25
(B) 32
(C) 36
(D) 58
(E) 61
Rationale: Make a venn diagram to get a clear picture. Look at the diagram:
Each letter represents only one color. b represents the people who take only Art. d represents people who take only Art and Bio etc.
d + f = 20 (People who take Art and one other class)
b = 3e (people who take only Art is 3 times the people who take Bio and Calculus)
21 + 10 + 5 + b + d + e + f = 100 (Total people)
b + b/3 = 44
b = 33
Number of freshmen who take Art = 33 + 20 + 5 = 58
Answer D
Answer: (D) 58
Question: If 1/2 of a pencil is blue, 1/8 of the remaining is red and the remaining 3/8 is white, what is the total length of the pencil?
(A) 5
(B) 3
(C) 1
(D) 4
(E) 2
Rationale: Blue is 1/2 but can also be written as 4/8Red is 1/8White is 3/84/8+1/8+3/8= 8/8=1Answer is C) 1
Answer: (C) 1
Question: Look at this series: 7, 10, 8, 11, 9, 12, 10, 13, 11, 14, ... What number should come next?
(A) 10
(B) 11
(C) 12
(D) 13
(E) 14
Rationale: This is a simple alternating addition and subtraction series. In the first pattern, 3 is added; in the second, 2 is subtracted.
The answer is C.
Answer: (C) 12
Question: In a party attended by 13 persons, each clinch their glass with every other. How many glass clinches?
(A) 51
(B) 52
(C) 78
(D) 54
(E) 55
Rationale: Total no. of person = 11
Total no. of glass clinches = n(n-1)/2
=13*12/2
= 78
ANSWER:C
Answer: (C) 78
Question: Two persons start running simultaneously around a circular track of length 200 m from the same point at speeds of 6 km/hr and 12 km/hr. When will they meet for the first time any where on the track if they are moving in opposite directions?
(A) 28 sec
(B) 37 sec
(C) 17 sec
(D) 60 sec
(E) 27 sec
Rationale: Time taken to meet for the first time anywhere on the track
= length of the track / relative speed
= 200 / (6+ 12)5/18 = 300* 18 / 18 * 5 = 60 seconds.
Answer : D
Answer: (D) 60 sec
Question: 4 shepherds were watching over the flocks and they were commenting on how many sheep they each had. If ram had 3 more sheep than he would have one less than rahul. wheras akar has the same number as the other 3 shepherds put togeher. If john had 3 less sheep he would have exactly trile the number of ram. If they were evenly distributed if they would each have 11 seep how many sheep did ram have?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: akar has=ram+rahul+john
after evenly distribution each has 11. so, total no. is 44
so, akar has=22 & ram+rahul+john=22 also ram=rahul-4 & john-3=3*ram solving these we get the sol.
ANSWER:B
Answer: (B) 3
Question: Reduce
368/575 to the lowest terms.
(A) 30/25
(B) 28/29
(C) 27/29
(D) 16/25
(E) 17/28
Rationale: Explanation:
We can do it easily by in two steps
Step1: We get the HCF of 368 and 575 which is 23
Step2: Divide both by 23, we will get the answer 16/25
Option D
Answer: (D) 16/25
Question: A man can row 30 km downstream and 20 km upstream in 4 hours. He can row 45 km downstream and 40 km upstream in 7 hours. Find the speed of man in still water?
A. 15 kmph B. 10 kmph
(A) 12.9 kmph
(B) 28.8 kmph
(C) 28.9 kmph
(D) 12.5 kmph
(E) 29.9 kmph
Rationale: Let the speed of the man in still water be a kmph and let the speed of the stream be b kmph.
Now 30/(a + b) + 20/(a - b) = 4 and 45/(a + b) + 40/(a - b) = 7
Solving the equation, the speed of man in still water is 12.5 kmph.
Answer:D
Answer: (D) 12.5 kmph
Question: What is the two-digit number?
I. Sum of the digits is 7.
II. Difference between the number and the number obtained by interchanging the digits is 9.
III. Digit in the ten's place is bigger than the digit in the unit's place by 1.
(A) I and II
(B) II and III
(C) I and III only
(D) All
(E) I and II as well as I and III
Rationale: Answer: Option E
Explanation:
Let the tens and units digit be x and y respectively.
I. x + y = 7.
II. (10x + y) - (10y + x) = 9 x - y = 1.
III. x - y = 1.
Thus, I and II as well as I and III give the answer.
Correct answer is (E).
Answer: (E) I and II as well as I and III
Question: A man started driving at a constant speed, from the site of a blast, the moment he heard the blast. He heard a second blast after a time of 30 mins and 15 seconds. If the second blast occurred exactly 30 mins after the first, how many meters was he from the site when he heard the second blast? ( speed of sound = 330 m/s)
(A) 1650
(B) 2750
(C) 3850
(D) 4950
(E) 6050
Rationale: The distance the sound traveled to the man is 15*330 = 4950 meters
The answer is D.
Answer: (D) 4950
Question: Distance between A and B is 36 miles. Two men started walking from A and B at the same time towards each other. The person who started from A traveled uniformly with average speed 2 mph. While the other man traveled with varying speeds as follows: In first hour his speed was 1 mph, in the second hour it was 1.25 mph, in the third hour it was 1.5 mph, and so on. Where will they meet each other?
(A)  12 miles away from A
(B)  12 miles away from B
(C)  after 6 hours from start
(D)  after 12 hours from start
(E)  midway between A and B
Rationale: Since the question asks where A and B will meet each other, we know the answer will involve distance and location.
In such questions, look for a symmetrical situation to find a rough estimate or range. For example, in many work-rate questions, it helps if you figure out the situation in which the rate of both people is the same.
Here the average speed of A (assuming guy who starts from A is A) is 2 mph and distance is 36 miles. So this means that A would take a total of 36/2 = 18 hours to cover the distance from A to B. So, if B's speed were also 2, both A and B would travel for 9 hours to meet in the middle.
B has uniform speed per hour so its average will be the simple average of all speeds: 1, 1.25, 1.5, 1.75, 2, 2.25, 2.5...
and 2 is actually right in the middle of the 9 speeds, implying both A and B have the same average speed.
The correct answer is (E).
Answer: (E)  midway between A and B
Question: If the personal income tax rate is lowered from 42% to 32%, what is the differential savings for a tax payer having an annual income before tax to the tune of $42400?
(A) $3500
(B) $5000
(C) $4240
(D) $7000
(E) $10000
Rationale: Saving = (42-32)% of 42400 = 4240.
Answer:C
Answer: (C) $4240
Question: The number 523hbc is divisible by 7,8,9. Then what is the value of h*b*c
(A) 504
(B) 532
(C) 210
(D) 180
(E) 280
Rationale: LCM of 7, 8 and 9 is 504, thus 523hbc must be divisible by 504.
523hbc=523000+hbc
523000 divided by 504 gives a remainder of 352.
Hence, 352hbc=k*504.
k=1 hbc=152 --> h*b*c=10
k=2 hbc=656 --> h*b*c=180
As hbc is three digit number k can not be more than 2.
Two answers? Well only one is listed in answer choices, so D.
Answer: D.
Answer: (D) 180
Question: Find the area of the quadrilateral of one of its diagonals is 30 cm and its off sets 9 cm and 6 cm?
(A) 225 cm2
(B) 150 cm2
(C) 127 cm2
(D) 177 cm2
(E) 187 cm2
Rationale: 1/2 * 30(9 + 6)
= 225 cm2
Answer: A
Answer: (A) 225 cm2
Question: In the xy-plane, the point (3, 1) is the center of a circle. The point (3, -2) lies inside the circle and the point (-2, 1) lies outside the circle. If the radius r of the circle is an integer, then r =
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: An easy way to solve this question will be just to mark the points on the coordinate plane.
You'll see that the distance between the center (3, 1) and the point inside the circle (3, -2) is 3 units
(both points are on x=3 line so the distance will simply be 1-(-2)=3)
So the radius must be more than 3 units.
The distance between the center (3,1) and the point outside the circle (-2,1) is 5 units
(both points are on y=1 line so the distance will simply be 3-(-2)=5)
So the radius must be less than 5 units, which implies 3 < r < 5, thus as r is an integer then r=4.
Answer: C.
Answer: (C) 4
Question: How long does a train 165 meters long running at the rate of 90 kmph take to cross a bridge 660 meters in length?
(A) 28
(B) 27
(C) 33
(D) 18
(E) 12
Rationale: T = (660 + 165)/90 * 18/5
T = 33
Answer: C
Answer: (C) 33
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) 26
(C) 28
(D) 69
(E) 17
Rationale: 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: A reduction of 44% in the price of bananas would enable a man to obtain 64 more for Rs.40, what is reduced price per dozen?
(A) 2.3
(B) 8.3
(C) 7.3
(D) 3.3
(E) 1.3
Rationale: Explanation:
40*(44/100) = 17.6 --- 64
? --- 12 => Rs.3.30
Answer: D
Answer: (D) 3.3
Question: Sum of the squares of 3 no. is 52 and the sum of their products taken two at a time is 72. Find the sum?
(A) 18
(B) 21
(C) 13
(D) 16
(E) 14
Rationale: (a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 52 + 2* 72
a + b + c = âˆš196 = 14
Answer E
Answer: (E) 14
Question: X and Y are integers, X is even and negative, Y is odd and positive. Which of the following could be false?
1. (X + Y) is an even number.
2. Y^(X + Y) is not an integer.
3. X^Y is a positive number.
(A) 2 only.
(B) 3 only.
(C) 1 and 3 only.
(D) 2 and 3 only.
(E) 1, 2 and 3.
Rationale: Statement I is not TRUE
Statement II is TRUE
Statement III is not TRUE
Answer : A
Answer: (A) 2 only.
Question: How many times digit 5 is used while writing numbers from 100 to 1000?
(A) 648
(B) 300
(C) 252
(D) 225
(E) 290
Rationale: There are 100 numbers which begin with 600
Next, In every 10 numbers such as 100 to 110, 110 to 120, 120 to 130 5 comes at least once. Number of such intervals = End limit - First no. / interval. Our range of numbers is 100 - 1000
1000 - 100 = 900/10 = 90
Number of 10s interval in this is 90. So 90 '6s'
So far we have calculated 190.
The total now comes to 280. The nearest to which is 290. Hence E.
Answer: (E) 290
Question: fill in ht blank:(a) the point with coordinates (0,0) is called ____ of a rectangular coordinate system,(b) to find the y-intercept of a line, we let ___ equal 0 and solve for ___; to find x- intercept , we let ____ equal 0 and solve for___
(A) (a) the point with coordinates (0,0) is called axis of a rectangular coordinate system, (b) to find the y-intercept of a line, we let x equal 0 and solve for y ; to find x- intercept , we let y equal 0 and solve for y
(B) (a) the point with coordinates (0,0) is called end of a rectangular coordinate system, (b) to find the y-intercept of a line, we let x equal 0 and solve for x ; to find x- intercept , we let y equal 0 and solve for y
(C) (a) the point with coordinates (0,0) is called origin of a rectangular coordinate system, (b) to find the y-intercept of a line, we let x equal 0 and solve for y ; to find x- intercept , we let y equal 0 and solve for x
(D) (a) the point with coordinates (0,0) is called end of a rectangular coordinate system, (b) to find the y-intercept of a line, we let x equal 0 and solve for y ; to find x- intercept , we let y equal 0 and solve for z
(E) none of the above
Rationale: (a) the point with coordinates (0,0) is called origin of a rectangular coordinate system, (b) to find the y-intercept of a line, we let x equal 0 and solve for y ; to find x- intercept , we let y equal 0 and solve for xcorrect answer (C)
Answer: (C) (a) the point with coordinates (0,0) is called origin of a rectangular coordinate system, (b) to find the y-intercept of a line, we let x equal 0 and solve for y ; to find x- intercept , we let y equal 0 and solve for x
Question: How many three letter words are formed using the letters of the word TIME?
(A) 28
(B) 21
(C) 26
(D) 24
(E) 29
Rationale: The number of letters in the given word is four.
The number of three letter words that can be formed using these four letters is ⁴P₃
= 4 * 3 * 2 = 24.
Answer: D
Answer: (D) 24
Question: Calculate the largest 6 digit number which is exactly divisible by 55?
(A) 999955
(B) 999900
(C) 999845
(D) 999790
(E) 999735
Rationale: Largest 4 digit number is 999999
After doing 999999 ÷ 55 we get remainder 44
Hence largest 4 digit number exactly divisible by 88 = 999999 - 44 = 999955
A
Answer: (A) 999955
Question: A baseball team won 45 percent of the first 80 games it played. How many of the remaining 82 games will the team have to win in order to have won exactly 50 percent of all the games it played?
(A) 36
(B) 45
(C) 50
(D) 55
(E) 81
Rationale: Number of games won by baseball team in first 80 games = .45* 80 = 36
Total number of games = 80 + 82 = 162
% of wins required in 162 = 50
Number of wins required in 162 = 81
Number of wins required in remaining 82 games = 81 - 36 = 45
Answer B
Answer: (B) 45
Question: Barbie invests $2400 in the National Bank at 5%. How much additional money must she invest at 8% so that the total annual income will be equal to 6% of her entire investment?
(A) 1250
(B) 3000
(C) 1000
(D) 3600
(E) 1200
Rationale: Let the additional invested amount for 8% interest be x;
Equation will be;
2400+0.05*2400+x+0.08x = 2400+x+0.06(2400+x)
0.05*2400+0.08x = 0.06x+0.06*2400
0.02x = 2400(0.06-0.05)
x = 2400*0.01/0.02 = 1200
Ans:E
Answer: (E) 1200
Question: The scoring system in a certain football competition goes as follows: 3 points for victory, 1 point for a draw, and 0 points for defeat. Each team plays 20 matches. If a team scored 10 points after 5 games, what is the least number of the remaining matches it has to win to reach the 45-point mark by the end of the tournament?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: To get 45 points as end of season we need another 35 points or more from remaining 15 matches:
Option A= 6*3+9*1=27
Option B=7*3 + 8*1=29
Option C=8*3+7*1=31
Option D=9*3+6*1=33
Option E=10*3+5*1=35
hence option E-10
Answer: (E) 10
Question: Two persons start running simultaneously around a circular track of length 400 m from the same point at speeds of 15 kmph and 25 kmph. When will they meet for the first time any where on the track if they are moving in the opposite direction ?
(A) 144
(B) 36
(C) 124
(D) 32
(E) 38
Rationale: Time taken to meet the first time = length of track/relative speed
= 400/ (15 +25) (5/18)
= 400/40 *(18/5) = 36 sec.
ANSWER:B
Answer: (B) 36
Question: A car takes 3hrs less than a truck to cover the distance frm Bombay to pune(192 km). The speed of the truck is 16km/hr slower than car.Find the speed of the car?
(A) 40.38
(B) 38.38
(C) 41.3
(D) 48
(E) 45
Rationale: Let the speed of car = x km/hrs
then that of truck = (x-16) km/hrs
According to the given condition
[192/(x-16)]- [192/x] = 3
on solving the equation we have x = 8[(sq-root of 17) + 1] =40.38
ANSWER:A
Answer: (A) 40.38
Question: If d=1/(2^3*5^11) is expressed as a terminating decimal, how many nonzero digits will d have?
(A) One
(B) Two
(C) Three
(D) Seven
(E) Ten
Rationale: Another way to do it is :
We know x^a*y^a=(X*Y)^a
given = 1/(2^3*5^11)
= Multiply and divide by 2^8
=2^8/(2^3*2^8*5^11)
=2^8/10^11
=> non zero digits are 256=> Ans C
Answer: (C) Three
Question: What least number should be added to 1101, so that the sum is completely divisible by 24
(A) A)4
(B) B)1
(C) C)2
(D) D)3
(E) E)5
Rationale: Explanation:
(1056 / 24) gives remainder 21
21 + 3 = 24, So we need to add 3.
Answer: Option D
Answer: (D) D)3
Question: Find the value of y from (12)^3 x 6^4 ÷ 432 = y?
(A) 2456
(B) 3456
(C) 4578
(D) 4290
(E) 5184
Rationale: Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184
432 12 x 62
E
Answer: (E) 5184
Question: If the average (arithmetic mean) of 2a+16, 3a-8 is 94, what is the value of a?
(A) 25
(B) 30
(C) 28
(D) 36
(E) 42
Rationale: AM of 2a+16, 3a-8=2a+16+ 3a-8 /2= 5a+8/2
Given that 5a+8 /2 = 94
a= 36
Answer is D
Answer: (D) 36
Question: Find the value of (875 233/899) × 899
(A) 786600
(B) 786650
(C) 786700
(D) 786750
(E) 786858
Rationale: (875 233/899) × 899
(786625 + 233)/899 × 899
786858/899 × 899
786858
E
Answer: (E) 786858
Question: How many words can be formed by using all letters of the word ‘LONDON’ ?
(A) 120
(B) 320
(C) 420
(D) 620
(E) 720
Rationale: Solution
The word LONDON contains 6 different letters.
Required number of words = 6P6 = 6 ! = (6 x 5 x 4 x 3 x 2 x 1) = 720
Answer E
Answer: (E) 720
Question: Following an increase in prices, the price of a candy box was 20 pounds and the price of a can of soda was 6 pounds. If the price of a candy box was raised by 25%, and the price of a can of soda was raised by 50%. What was the price of a box of candy plus a can of soda before prices were raised?
(A) 11.
(B) 20.
(C) 13.
(D) 14.
(E) 14.5
Rationale: Price of candy before price increase= 20/1.25= 16
Price of soda before price increase= 6/1.5= 4
Total price = 16+4= 20
B is the answer
Answer: (B) 20.
Question: The rate of Interest on a sum of money is 8% p.a. for the first 3 years, 4% p.a. for the next 4 years, and 5% for the period beyond 7 years. If the S.I, Occured on the sum for the total period of 8 years is Rs. 540/-, the sum is
(A) 1,200
(B) 2,000
(C) 2,100
(D) 2,250
(E) 2,540
Rationale: Explanation:
I1 = (P x 3 x 8)/100 = 6P/25
I2 = (P x 4 x 4)/100 = 4P/25
I3 = (P x 1 x 5)/100 = P/20
6P/25 + 4P/25 + P/20 = 540
9P/20 = 540
P = 1200
Answer: Option A
Answer: (A) 1,200
Question: A mail handler needs 3 hours to sort the mail. His assistant takes 6 hours to sort the mail. How many hours will it take for both of them working together to sort the mail?
(A) 3
(B) 2
(C) 1
(D) 2 1/2
(E) 1 1/5
Rationale: Work hrs=AB/(A+B)= 18/9 =2
Answer is B
Answer: (B) 2
Question: Three pipes, A, B, & C are attached to a tank. A & B can fill it in 20 & 30 minutes respectively while C can empty it in 15 minutes. If A, B & C are kept open successively for 0.5 minute each, how soon will the tank be filled?
(A) 1 hour 30 min
(B) 4 hours
(C) 3 hours
(D) 5 hours
(E) 6 hours
Rationale: in three minute 1/20+1/30-1/15=1/60 part is filled
1.5 min--------1/60 parts
x min--------- 1 part(full)
x=90 min =1 hour 30 min
ANSWER:A
Answer: (A) 1 hour 30 min
Question: If the value of a piece of property decreases by 10% while the new tax rate on the property represent 110% of the original tax rate, what is the effect on the taxes?
(A) taxes increase by 10%
(B) taxes increase by 1%
(C) there is no change in taxes
(D) taxes decrease by 1%
(E) taxes decrease by 10%
Rationale: Consider the value of property = 100, Original tax rate 10%, hence tax value = 100*10% = 10.
Decreased value of property = 90, New tax rate = 110% of 10 = 11%, hence tax value = 90*11% = 9.9
10-9.9 = decrease by 1%.
Answer D.
Answer: (D) taxes decrease by 1%
Question: ABCD is a parallelogram on xy rectangular coordinate plane, three of the four vertices of parallelogram are (5,15) , (5,55) and (-5,15). Which can be the coordinate of fourth vertex?
(A) (15,55)
(B) (5,15)
(C) (-5,-25)
(D) (-5,10)
(E) (15,25)
Rationale: A(-5, 15)
B(5, 15)
C(5, 55)
X(-5, 55): 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, 55): Parallelogram=ACZB, where AC||ZB, AC=ZB, CZ||AB, CZ=AB
Ans:A
Answer: (A) (15,55)
Question: Solution A is 20% salt and Solution B is 80% salt. If you have 30 ounces of solution A and 60 ounces of solution B, in what ratio could you mix Solution A with Solution B to produce 50 ounces of a 50% salt solution?
(A) 6:4
(B) 6:14
(C) 4:4
(D) 4:6
(E) 3:7
Rationale: let:
x = ounces taken from solution A (20% salt)
y = ounces taken from solution B (80% salt)
to prepare 50 ounce 50% salt.
first equation is simple:
x + y = 50
to get another equation so as to be able to solve, compute salt contents.
20% of x + 80% of y = 50% of 50 or
x/5 + 4/5 * y = 25 or
x+4y = 125
solve two equations to get:
x = 25
y = 25
so solutions has to mix in
1:1 oops 4:4
ANSWER:C
Answer: (C) 4:4
Question: Three years ago, the average age of A and B was 18 years. With C joining them, the average age becomes 22 years. How old is C now?
(A) 20 years
(B) 24 years
(C) 27 years
(D) 30 years
(E) None
Rationale: Sol.
Present age of ( A + B) = ( 18 × 2 + 3 × 2) years = 42 years.
Present age of ( A + B + C) = (22 × 3) years = 66 years.
Therefore C’s age = (66 – 42) years
= 24 years.
Answer B
Answer: (B) 24 years
Question: A thief steals at a car at 2.30 p.m. and drives it at 60 km/hr. The theft is discovered at 3 p.m. and the owner sets off in another car at 75 km/hr. When will he overtake the thief?
(A) 2
(B) 78
(C) 5
(D) 6
(E) 7
Rationale: Suppose the thief is overtaken x hrs after 2.30 p.m.
Then, distance covered by the owner in (x - 1/2) hrs.
60x = 75(x - 1/2) => x = 5/2 hrs.
So, the thief is overtaken at 5 p.m.
Answer: C
Answer: (C) 5
Question: The ratio between the length and the breadth of a rectangular park is 3:2. If a man cycling along theboundary of the park at the speed of 12 km/hr completes one round in 8 min, then the area of the park is?
(A) 163600 m
(B) 178600 m
(C) 153600 m
(D) 163600 m
(E) 173600 m
Rationale: Perimeter = Distance covered in 8 min. = 12000 x 8 m = 1600 m.
60
Let length = 3x metres and breadth = 2x metres.
Then, 2(3x + 2x) = 1600 or x = 160.
Length = 480 m and Breadth = 320 m.
Area = (480 x 320) m2 = 153600 m
C
Answer: (C) 153600 m
Question: If a company allocates 10 percent of its budget to advertising, 10 percent to capital improvements, and 55 percent to salaries, what fraction of its budget remains for other allocations?
(A) 4/5
(B) 1/4
(C) 3/10
(D) 1/5
(E) 1/10
Rationale: 10 + 10 + 55 = 75% 100 - 75 = 25% to all others
B
Answer: (B) 1/4
Question: If the price of sugar rises from Rs. 10 per kg to Rs. 11 per kg, a person, to have no increase in the expenditure on sugar, will have to reduce his consumption of sugar by
(A) 9%
(B) 20%
(C) 25%
(D) 30%
(E) none
Rationale: Sol.
Let the original consumption = 100 kg and new consumption = x kg.
So, 100 x 10 = x × 11 = x = 91 kg.
∴ Reduction in consumption = 9%.
Answer A
Answer: (A) 9%
Question: A father said to his son, "I was as old as you are at present at the time of your birth." If the father's age is 40 years now, the son's age five years back was?
(A) 16 years
(B) 15 years
(C) 18 years
(D) 19 years
(E) 25 years
Rationale: Let the son's present age be x years.
Then, (40 - x) = x
2x = 40 => x = 20
Son's age 5 years back = (20 - 5)
= 15 years.
Answer: B
Answer: (B) 15 years
Question: If q and r are both odd numbers N, which of the following must also be odd?
(A) q – r
(B) (q + r)^2
(C) q(q + r)
(D) (qr)^2
(E) q/r
Rationale: We're told that q and r are both ODD numbers N. We're asked which of the following must also be odd.
IF...
q = 1
r = 3
Answer A) q – r = 1-3 = -2 NOT odd
Answer B) (q + r)^2 = (1+3)^2 = 16 NOT odd
Answer C) q(q + r) = (1)(4) = 4 NOT odd
Answer D) (qr)^2 = (3)^2 = 9 This IS ODD
Answer E) q/r = 1/3 NOT odd
Final Answer:
D
Answer: (D) (qr)^2
Question: A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes. How long will it take to go 5 km in stationary water?
(A) 40 minutes
(B) 1 hour
(C) 1 hour 15 min
(D) 1 hour 30 min
(E) none
Rationale: Solution
Rate downstream	= (1 / 10 x 60)km/hr
= 6 km / hr.
Rate upstream	= 2 km/hr.
Speed in still water	= 1 / 2(6 + 2)km/hr
= 4 km.
Required time	= (5 / 4) km/hr
= 1x 1/4 km/hr
= 1 hr 15 min.
Answer C
Answer: (C) 1 hour 15 min
Question: If f(x)= 5x^3- 2x+8 and h(y)= 4y-4, then h(f(x)) =
(A) 11x^2+4x+4
(B) 11x^2-12x+44
(C) 8x^3-8x+32
(D) 30x^3+4x+4
(E) 20x^3-8x+28
Rationale: h(f(x)) = 4(f(x)) -4 = 4(5x^3- 2x+8) - 4 = 20x^3-8x+28 =>E
Answer: (E) 20x^3-8x+28