mathewhe/aqua_rat huggingface dataset:
Question: If 70% of a number exceeds 28% of it by 39.9, then find the number?
(A) 65
(B) 67
(C) 100
(D) 95
(E) 33
Rationale: Use the elimination method to find the correct option.
Of all the options only 95 fits
70% of 95 = 66.5
28% of 95 = 26.6
66.5 - 26.6 = 39.9
Required number is 95.
ANSWER:D
Answer: (D) 95
Question: Find the ratio in which rice at Rs. 7.30 a kg be mixed with rice at Rs. 5.70 a kg to produce a mixture worth Rs. 6.30 a kg
(A) 2:0
(B) 2:3
(C) 3:5
(D) 2:2
(E) 2:8
Rationale: By the rule of alligation:
Cost of 1 kg rice of 1st kind Cost of 1 kg rice of 2nd kind
Required ratio = 60 : 100 = 3 : 5
Answer: C
Answer: (C) 3:5
Question: If S + A < S - A < A - S, which of the following is correct?
(A) A < S < 0.
(B) S < A < 0.
(C) S < 0 < A.
(D) 0 < B < A.
(E) B > A > 0.
Rationale: Check first inequality
S + A < S - A
A<-A
A is -ve
Check another equality
S - A < A - S
-2A<-2S
A>S
Combining both 0>A>S
Option B fits only
Ans B
Answer: (B) S < A < 0.
Question: A man took loan from a bank at the rate of 12% p.a. simple interest. After 3 years he had to pay Dollar 5400 interest only for the period. The principal amount borrowed by him was:
(A) Dollar 2000
(B) Dollar 10,000
(C) Dollar 15,000
(D) Dollar 20,000
(E) None of these
Rationale: Explanation: Principal = Dollar (100 x 5400)/(12x3) = Dollar 15000.
Answer: Option C
Answer: (C) Dollar 15,000
Question: In a certain province in India there are 15 cities. If a single road segment connects only two cities, how many road segments are required in order to connect the cities so that each city is connected to all other cities with a single road segment?
(A) 30
(B) 105
(C) 330
(D) 14!
(E) 15!
Rationale: Method-1:
India has Total Cities = 15 and each city should be connected with every other city
So Total Roads required to connect 1st City with other 14 cities = 14
Now 1st City is connected with all other cities so,
So Total Roads required to connect 2nd City with 13 cities (Other than 1st) = 13
Now 1st and 2nd Cities are connected with all other cities so,
So Total Roads required to connect 3rd City with 12 cities (Other than 1st, and 2nd) = 12
......and so on...
Total Roads required = 14 + 13 + 12 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 105=B
Answer: (B) 105
Question: There are 6 orators A, B, C, D, E, F. In how many ways can the arrangements be made so that A always comes before B and B always comes before C.
(A) 6! / 3!
(B) 8! / 6!
(C) 5! x 3!
(D) 8! / (5! x 3!)
(E) 8! / (5! x 4!)
Rationale: Select any three places for A, B and C. They need no arrangement amongst themselves as A would always come before B and B would always come before C.
The remaining 3 people have to be arranged in 3 places.
Thus, 6C3 x 3! = 6! / 3!
ANSWER:A
Answer: (A) 6! / 3!
Question: Which of the following is non-negative?
(A) (a-0.9)(a-1)
(B) (a+1)(a-1)
(C) (a+0.7)(a+1)
(D) (a-0.7)(a-0.7)
(E) a(a+1)
Rationale: 5-sec approach:
D. (a-0.7)(a-0.7) = (a-0.7)^2. The square of a number is always non-negative.
Answer: D.
Answer: (D) (a-0.7)(a-0.7)
Question: In a group of 3 boys and 2 girls can be formed out of a total of 4 boys and4 girls?
(A) 20
(B) 22
(C) 24
(D) 26
(E) 29
Rationale: Solution: Total number of ways = (select 3 boys from group of 4 boys) * (2 girls from group of 4 girls)
=> (4c3) * (4c2) = 24
C
Answer: (C) 24
Question: What will come in place of the x in the following Number series? 5,28,57,88,125
(A) 122
(B) 324
(C) 166
(D) 175
(E) 178
Rationale: 28=23+5
57=29+28
88=31+57
125=37+88
166=41+125
=166
C
Answer: (C) 166
Question: A sun is divided among X, Y and Z in such a way that for each 2 rupees X gets, Y gets 1 rupee 50 paisa and Z gets 1 rupee 20 paisa. If the share of X is RS. 125, what is the total amount?
(A) 283.75
(B) 193.75
(C) 293.75
(D) 290.75
(E) 313.75
Rationale: x:y:z = 200:150:120
20:15:12
20 --- 125
47 --- ? => 293.75
Answer: C
Answer: (C) 293.75
Question: The average temperature for Monday, Tuesday, Wednesday and Thursday was 48 degrees and for Tuesday, Wednesday, Thursday and Friday was 46 degrees. If the temperature on Monday was 42 degrees. Find the temperature on Friday?
(A) 227
(B) 268
(C) 127
(D) 150
(E) 187
Rationale: M + Tu + W + Th = 4 * 48 = 192
Tu + W + Th + F = 4 * 46 = 184
M = 42
Tu + W + Th = 192 -42 = 150
F = 184 – 150 = 34
Answer: D
Answer: (D) 150
Question: A hollow cube of size 5 cm is taken, with a thickness of 1 cm. It is made of smaller cubes of size 1 cm. If 4 faces of the outer surface of the cube are painted, totally how many faces of the smaller cubes remain unpainted?
(A) 488
(B) 269
(C) 299
(D) 266
(E) 261
Rationale: The Hallow cube volume = n3−(n−2)2n3−(n−2)2, Here n is the number of small cubes lie on the big cube edge.
Now n = 5 so Hallow cube volume = 53−(5−2)2=125−27=9853−(5−2)2=125−27=98
So 98 small cubes required to make a hallow cube of size 5 cm. Now total surfaces = 6 x 98 = 588
Now if the bigger cube is painted 4 sides, total 4 x 25 small faces got paint. So remaining small faces which does not have paint after cutting is 588 - 100 = 488
Answer:A
Answer: (A) 488
Question: A group of n students can be divided into equal groups of 4 with 1 student left over or equal groups of 7 with 2 students left over. What is the sum of the two smallest possible values of n?
(A) 42.
(B) 46.
(C) 50.
(D) 54.
(E) 58.
Rationale: n = 4k+1 = 7j+2
Let's start at 1 = 4(0)+1 and keep adding 4 until we find a number in the form 7j+2.
1, 5, 9 = 7(1)+ 2
The next such number is 9 + 4*7 = 37.
9+37 = 46
The answer is B.
Answer: (B) 46.
Question: If −y ≥ x, and −x < −4, then which of the following must be true?
(A) y = −4
(B) y > −4
(C) −y > 4
(D) y ≤ −4
(E) y ≥ −4
Rationale: −y ≥ x, and −x < −4
y <= -x < -4
As '-x' is less than '-4' and Y is less than or equal to '-x'
we have y < -4 which is similar to -y > 4.
C) -y >4
Answer: (C) −y > 4
Question: The average of six numbers is 3.95. The average of two of them is 3.4, while the average of the other two is 3.85. What is the average of the remaining two numbers ?
(A) 4.7
(B) 4.6
(C) 4.2
(D) 4.1
(E) 4.9
Rationale: Explanation:
Sum of the remaining two numbers = (3.95 * 6) - [(3.4 * 2) + (3.85 * 2)]
= 23.70 - (6.8 + 7.7) = 23.70 - 14.5 = 9.20.
Required average = (9.2 / 2) = 4.6.
Answer: B) 4.6
Answer: (B) 4.6
Question: what is the least number. which should be added to 0.0355 to make it a perfect square?
(A) 0.0005
(B) 0.0016
(C) 0.0056
(D) 0.0066
(E) 0.0006
Rationale: 0.0355+0.0006=0.0361
(0.19)^2
ANSWER:E
Answer: (E) 0.0006
Question: A man can row 7 ½ kmph in still water.if in a river running at 1.5 km/hr an hour,it takes him 50 minutes to row to a place and back,how far off is the place?
(A) 4km
(B) 2km
(C) 5km
(D) 3km
(E) 1km
Rationale: Speed downstream =(7.5+1.5)km/hr=9 km/hr;
Speed upstream=(7.5-1.5)kmph=6kmph.
Let the required distance be x km.then,
x/9+x/6=50/60.
2x+3x=(5/6*18)
5x=15
x=3.
Hence,the required distance is 3km
ANSWER D 3km
Answer: (D) 3km
Question: Which of the following is a prime number ?
(A) 33
(B) 81
(C) 93
(D) 97
(E) 99
Rationale: Clearly, 97 is a prime number.
answer -Option D
Answer: (D) 97
Question: A and B can do a piece of work in 3 days, B and C in 4 days, C and A in 6 days. How long will C take to do it?
(A) 23 days
(B) 16 days
(C) 11 days
(D) 24 days
(E) 35 days
Rationale: D
24 days
2c = ¼ + 1/6 – 1/3 = 1/12
c = 1/24 => 24 days
Answer: (D) 24 days
Question: If n is an integer, f(n) = f(n-1) - n and f(4)=15. What is the value of f(6)?
(A) 4
(B) 0
(C) 1
(D) 2
(E) 24
Rationale: Since f(n)=f(n-1)-n then: f(6)=f(5)-6 and f(5)=f(4)-5.
As given that f(4)=15 then f(5)=15-5=10 --> substitute the value of f(5) back into the first equation: f(6)=f(5)-6=10-6=4.
Answer: A.
Questions on funtions to practice:
Answer: (A) 4
Question: There are 21 students in a class. In how many different ways can a committee of 3 students be formed?
(A) 1180
(B) 1330
(C) 1540
(D) 1760
(E) 1920
Rationale: 21C3 = 21*20*19 / 6 = 1330
The answer is B.
Answer: (B) 1330
Question: Tough and Tricky questions: Exponents.
If 7^(3x-1)*3^(4y-3) = 49^x*27^y, then x + y =
(A) 3
(B) 4
(C) 2
(D) 1
(E) 5
Rationale: Here is my solution.
7^(3x-1)*3^(4y-3) = 49^x*27^y
Here RHS 49^x*27^y= 7^(2x)*3^(3y)
Equating powers on both sides-->
3x-1=2x , thus x=1 and
4y-3=3y giving y=3
So, x+y=4
Option: B
Answer: (B) 4
Question: An error 3% in excess is made while measuring the side of a square. What is the percentage of error in the calculated area of the square?
(A) 9.09%
(B) 4.02%
(C) 4%
(D) 3%
(E) 2%
Rationale: Percentage error in calculated area
=(3+3+(3Ã—3)/100)%
=9.09%
ANSWER:A
Answer: (A) 9.09%
Question: The CI on Rs 30000 at 7% per annum for a certain period is 4347.The period is ?
(A) 2
(B) 3
(C) 1
(D) 6
(E) 5
Rationale: I year 2100II year 2100+147=22472100+2247=4347So 2 YearsAnswer A
Answer: (A) 2
Question: The temperature of a certain cup of coffee 6 minutes after it was poured was 120 degrees Fahrenheit. If the temperature F of the coffee t minutes after it was poured can be determined by the formula F = 120*2^(-at) + 60, where F is in degrees Fahrenheit and a is a constant. Then the temperature of the coffee 30 minutes after it was poured was how many degrees Fahrenheit?
(A) 65
(B) 63.75
(C) 80
(D) 85
(E) 90
Rationale: First, we have to find a.
We know that after t=6 minutes the temperature F=120 degrees.
Hence:
120 = 120*(2^-6a)+60
60 = 120*(2^-6a)
60/120 = 2^-6a
1/2 = 2^-6a
2^-1 = 2^-6a
-1 = -6a
1/6 = a
Now we need to find F after t=30 minutes:
F = 120*(2^-1/6*30)+60
F = 120* (2^-5) +60
F = 120* (1/2^5) +60
F = 120*1/32 +60
F = 3.75+60 = 63.75
Answer B!
Answer: (B) 63.75
Question: A committee of 5 people is to be selected from 7 people. How many different committees are possible?
(A) 21
(B) 40
(C) 56
(D) D.168
(E) 336
Rationale: Because the order does not matter in selecting 5 people for the committee, this is a combination question.
The number of ways to select 5 people from 7 = 7C5 = 7!/5!*2! = 21. Hence A
Answer: (A) 21
Question: The annual budget of a certain college is to be shown on a circle graph. If the size of each sector of the graph is to be proportional to the amount of the budget it represents, how many degrees of the circle should be used to represent an item that is 30 percent of the budget?
(A)  15 °
(B)  36 °
(C)  54 °
(D)  90 °
(E)  108 °
Rationale: 100 percent = 360 degrees
30 percent = 360*30/100 = 108 degrees
Answer is E.
Answer: (E)  108 °
Question: Difference of two numbers is 1860. If 7.5% of the number is 12.5% of the other number , find the number ?
(A) 2660, 1000
(B) 3660, 2000
(C) 3000, 4160
(D) 2790, 4650
(E) 4660, 3000
Rationale: Let the numbers be x and y. Then, 7.5 % of x =12.5% of y
X = 125*y/75 = 5*y/3.
Now, x-y =1860
5*y/3 –y =1860
2*y/3= 1860
y =[ (1860*3)/2] =2790.
One number = 2790, Second number =5*y/3 =4650.
Answer D.
Answer: (D) 2790, 4650
Question: What is the greatest positive integer n such that 3^n is a factor of 36^450?
(A) 100
(B) 200
(C) 300
(D) 600
(E) 900
Rationale: 36 = 3^2 * 2^2.
36^450 = 3^900 * 2^900
The answer is E.
Answer: (E) 900
Question: A and B are partners in a business. A contributes 1/4 of the capital for 15 months and B received 2/3 of the profit. For how long B's money was used ?
(A) 11 months
(B) 17 months
(C) 10 months
(D) 19 months
(E) 12 months
Rationale: Let the total profit be Rs. z. Then,
B's share = Rs. 2z/3, A's share = Rs. ( z - 2z/3 ) = Rs. z/3.
A : B = z/3 : 2z/3 = 1:2
Let the total capital be Rs, X and suppose B's money was used for x months. Then.
(1(x) / 4 * 15) / (3x) / 4 * y) = 1/2 <=> y = (15 * 2 / 3) = 10 .
Thus, B's money was used for 10 months.
Answer: C
Answer: (C) 10 months
Question: If x < y < z and y - x > 5, where x is an even integer and y and z are odd integers, what is the least possible value S of z - x?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: x<y<z
To find the least possible value for z-x; we need to find the values for z and x that can be closest to each other. If x is some even number, then what could be minimum possible odd z.
If x is some even number
y-x>5; y>x+5; minimum value for y=x+5+2=x+7[Note: x+5 is as even+odd=odd and nearest odd greater than x+5 is x+5+2]
Minimum value for z=y+2=x+7+2=x+9 [Note: z=y+2 because both z and y are odd. Difference between two odd numbers is 2]
S=z-x = x+9-x= 9
Ans:D
Answer: (D) 9
Question: A is a working partner and B is a sleeping partner in the business. A puts in Rs.15000 and B Rs.25000, A receives 10% of the profit for managing the business the rest being divided in proportion of their capitals. Out of a total profit of Rs.9600, money received by A is?
(A) Rs.3240
(B) Rs.3600
(C) Rs.3800
(D) Rs.4200
(E) Rs.5200
Rationale: 15:25 => 3:5
9600*10/100 = 960
9600 - 960 = 8640
8640*3/8 = 3240 + 960
= 4200
ANSWER:D
Answer: (D) Rs.4200
Question: What is the place value of 7 in the numeral 2734?
(A) 450
(B) 500
(C) 700
(D) 800
(E) 840
Rationale: Option 'C'
7 * 100 = 700
Answer: (C) 700
Question: A bowl was half full of water. 4 cups of water were then added to the bowl, filling the bowl to 70% of its capacity. How many cups of water are now in the bowl?
(A) 14 cups
(B) 15
(C) 16
(D) 17
(E) 18
Rationale: lets say total volume of the container = V
Initial water content is half of total volume = V/2
Then 4 cups of water were added.
Current water content = (V/2) + 4 cups = (70/100)V
=> V = 20 cups
=> current water content is equivalent to = V/2+ 4 cups = 20/2 + 4 = 14 cups; ANSWER:A
Answer: (A) 14 cups
Question: Last month, John rejected 0.5% of the products that he inspected and Jane rejected 1.00 percent of the products that she inspected. If total of 0.75 percent of the products produced last month were rejected, what fraction of the products did Jane inspect?
(A) 1/6
(B) 1/2
(C) 5/8
(D) 5/4
(E) 15/16
Rationale: X - fraction of products Jane inspected
(1 - X) - fraction of products John inspected
0.8(X) + 1.00(1-X) = 0.75
0.2X = 1.00 - 0.75
X = 0.25/0.2
X = 5/4
Therefore the answer is D: 5/6.
Answer: (D) 5/4
Question: What is the greatest value of n such that 17^n is a factor of 17! ?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Another way to solve this question :
We know that 18 = 2 *3^2.
Hence, we need to find total number of 3s in 18! ( As out of 3 and 2 , we will have count of 3 least)
No. of 3s = 18/3 =6/3 =2.
Add the numbers in Bold, you will get total number of 3s = 8.
Hence, total number of 2^2 = 4/2 = 2.
Hence, answer is 2. B
Answer: (B) 2
Question: What is the area of square field whose side of length 20 m?
(A) 200 sq m
(B) 186 sq m
(C) 586 sq m
(D) 287 sq m
(E) 400 sq m
Rationale: 20 * 20
= 400 sq m
Answer: E
Answer: (E) 400 sq m
Question: In the biology lab of "Jefferson" High School there are 2.16*10^6 germs, equally divided among 10,800 Petri dishes. How many germs live happily in a single dish?
(A) 100
(B) 200
(C) 500
(D) 1000
(E) 5000
Rationale: 2.16*10^6/ 10800==> 21.6*10^3/108==> 21600/108= 200
ANSWER:B
Answer: (B) 200
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) 3/8
(B) 3/2
(C) 3/5
(D) 3/9
(E) 3/1
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: A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man?
(A) 6.24 km
(B) 6 km
(C) 5.76 km
(D) 5.66 km
(E) 10 km
Rationale: M = 6
S = 1.2
DS = 7.2
US = 4.8
x/7.2 + x/4.8 = 1
x = 2.88
D = 2.88 * 2 = 5.76
ANSWER:C
Answer: (C) 5.76 km
Question: If r = 199,999 and s = 991,999, which of the following is the units digit of r^2 + s^3?
(A) 0
(B) 1
(C) 3
(D) 9
(E) 7
Rationale: Using cyclicity rule of number 9
199,999^2 will have units digit as 1
991,999^3 will have units digit as 9
Thus r2 + s3 = 1 + 9 = 0
Thus answer will be (A)
Answer: (A) 0
Question: A profit of Rs. 900 is divided between X and Y in the ratio of 1/2:1/3 . What is the difference between their profit shares ?
(A) s. 280
(B) s. 180
(C) s. 380
(D) s. 50
(E) s. 90
Rationale: A profit of Rs. 900 is divided between X and Y in the ratio of 1/2 : 1/3 or 3:2.
so profits are 540 and 360.
difference in profit share = 540-360=180
ANSWER:B
Answer: (B) s. 180
Question: A train speeds past a pole in 15 sec and a platform 100 m long in 25 sec, its length is?
(A) 155 m
(B) 150 m
(C) 187 m
(D) 177 m
(E) 186 m
Rationale: Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 15 => y
= x/15
(x + 100)/25
= x/15
=> x = 150 m.
Answer: B
Answer: (B) 150 m
Question: What will come in place of the x in the following Number series? 6, 12, 21, x , 48
(A) 33
(B) 36
(C) 45
(D) 50
(E) 52
Rationale: (A)
The pattern is + 6, + 9, + 12, +15 ………..
So the missing term is = 21 + 12 = 33
Answer: (A) 33
Question: An investor bought two shares of stock, which he sold for $48 each. If he had a profit of 20% on one of the shares and a loss of 20% on the other share, then on the sale of both shares combined, the investor had:
(A) a profit of $10
(B) a profit of $4
(C) a loss of $4
(D) a loss of $10
(E) neither a profit nor a loss
Rationale: The cost of the first stock was 48/1.2=40, so the profit from it is 8.
The cost of the second stock was 48/0.8=60, so loss from it is 12.
Overall the loss is $4.
The answer is C.
Answer: (C) a loss of $4
Question: How many times are the hands of a clock at right angle in a day?
(A) 22
(B) 24
(C) 44
(D) 46
(E) 48
Rationale: In 12 hours, they are at right angles 22 times.
In 24 hours, they are at right angles 44 times. Answer: Option C
Answer: (C) 44
Question: What is the remainder when (63)(65) is divided by 8?
(A) 1
(B) 2
(C) 4
(D) 5
(E) 7
Rationale: (63)(65) = (64-1)(64+1) = 64^2 - 1 which is 1 less than a multiple of 8.
Then the remainder will be 7.
The answer is E.
Answer: (E) 7
Question: Tara bought 19 cartons of ice cream and 4 cartons of yoghurt. Each carton of ice cream cost $7 and each carton of yoghurt cost $1. How much more did Tara spend on ice cream than on yoghurt?
(A) $144
(B) $130
(C) $80
(D) $110
(E) $129
Rationale: Step 1: Find the cost of the ice cream.
19 × $7 = $133
Step 2: Find the cost of the yoghurt.
4 × $1 = $4
Step 3: Find how much more the ice cream cost than the yoghurt.
$133 – $4 = $129
Tara spent $129 more on ice cream.
Answer is E.
Answer: (E) $129
Question: If k and w are the dimensions of a rectangle that has area 21, and if k and w are integers such that k > w, what is the total number of possible values of k?
(A)  Two
(B)  Three
(C)  Four
(D)  Five
(E)  Six
Rationale: kw=21=21*1=7*3--> k can take 2 values,
Answer: A
Answer: (A)  Two
Question: Find the invalid no.from the following series 2,3,12,37,86,166,288
(A) 2
(B) 3
(C) 166
(D) 37
(E) 86
Rationale: 3-2=1
12-3=9
37-12=25
86-37=49
166-86=80(this must be 81=167-86=81)
so wrong number in the sequence is 166
difference between two sucessive numbers sequence would be
1,9,25,49,81,121(square of 1,3,5,7,9,11)
C
Answer: (C) 166
Question: An empty fuel tank with a capacity of 200 gallons was filled partially with fuel A and then to capacity with fuel B. Fuel A contains 12% ethanol by volume and fuel B contains 16% ethanol by volume. If the full fuel tank contains 20 gallons of ethanol, how many gallons of fuel A were added?
(A) 300
(B) 150
(C) 100
(D) 80
(E) 50
Rationale: Say there are A gallons of fuel A in the tank, then there would be 200-A gallons of fuel B.
The amount of ethanol in A gallons of fuel A is 0.12A;
The amount of ethanol in 200-A gallons of fuel B is 0.16(200-A);
Since the total amount of ethanol is 20 gallons then 0.12A+0.16(200-A)=20 --> A=300.
Answer: A.
Answer: (A) 300
Question: When 2/9 of the votes on a certain resolution have been counted, 3/4 of those counted are in favor of the resolution. What fraction e of the remaining votes must be against the resolution so that the total count will result in a vote of 2 to 1 against the resolution?
(A) 11/14
(B) 13/18
(C) 4/7
(D) 3/7
(E) 3/14
Rationale: If we use variable for total votes there will be too many fractions to manipulate with, so pick some smart #: let set total # of votes is 18.
2/9 of the votes on a certain resolution have been counted--> 4 counted and 18-4=14 votes left to be counted;
3/4 of those counted are in favor of the resolution--> 3 in favor and 1 against;
Ratio of those who voted against to those who voted for to be 2 to 1 there should be total of 18*2/3=12 people who voted against, so in the remaining 14 votes there should be 12-1=11 people who voted against. Thus e=11/14 of the remaining votes must be against.
Answer: A.
Answer: (A) 11/14
Question: Of 60 children, 30 are happy, 10 are sad, and 20 are neither happy nor sad. There are 18 boys and 42 girls. If there are 6 happy boys and 4 sad girls, how many boys are neither happy nor sad?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 10
Rationale: Venn diagrams are useful for multiple values of a single variable e.g. State of mind - happy/sad/neither. When you have two or more variables such as here where you have gender - boy/girl too, it becomes unwieldy. In this case, either use the table or logic.
Table method is shown above; here is how you will use logic:
There are 6 happy boys.
There are 4 sad girls but total 10 sad children. So rest 6 sad children must be sad boys.
We have 6 happy boys and 6 sad boys. Total we have 18 boys. So 18 - 6 - 6 = 6 boys must be neither happy nor sad.
Answer (C)
Answer: (C) 6
Question: A man can row 4.5 km/hr in still water and he finds that it takes him twice as long to row up as to row down the river. Find the rate of the stream.
(A) 2
(B) 2.5
(C) 1.5
(D) 1
(E) 3
Rationale: Speed - x
upward speed (4.5-x)
downward = 4.5+x
distance => y
time rowing upwards = 2 * time rowing upwards
y/4.5-x = 2*y/4.5+x
x =1.5 km/hr
ANSWER C
Answer: (C) 1.5
Question: Which of the following is closest to (7!-6!)/(7!+6!)?
(A) 0.75
(B) 1.25
(C) 0.92
(D) 0.86
(E) 1
Rationale: (7!-6!)/(7!+6!)
6! (7-1)/6! (7+1)
6/8 = 3/4 = 0.75
A is the answer
Answer: (A) 0.75
Question: Sum of 3 consecutive even no.'s is 26 more than the 1st no. of the series. Find the middle no.?
(A) 10
(B) 12
(C) 14
(D) 17
(E) 18
Rationale: Let the numbers be x, x+2 and x+4 then
x + x+2 + x+4 = x+26
3x + 6 = x + 26
2x = 20
\inline \therefore x = 10
\inline \therefore Middle number = x + 2 = 10+2 = 12
B
Answer: (B) 12
Question: One year ago the ratio between Laxman's and Gopal's salary was 3:4. The ratio's of their individual salaries between last year's and this year's salaries are 4:5 and 2:3 respectively. At present the total of their salary is Rs.4290. The salary of Laxman now is :
(A) Rs.1040
(B) Rs.1650
(C) Rs.2560
(D) Rs.3120
(E) None
Rationale: Explanation:
Let the salaries of Laxman and Gopal one yer before be 12x and 16x.
Given that laxman's last year and present year salary are in the ratio 4 : 5 so his present salary = 5/4(12x) = 15x
Also Gopal's last year and present year salary are in the ratio 2 : 3 so his present salary = 3/2(16x) = 24x
But given that sum of the salaries 15x + 24x = 39x = 4290 ⇒⇒ x = 110
Laxman's present salary = 15x = 15 x 110 = 1650
Correct Option: B
Answer: (B) Rs.1650
Question: The distance between 2 cities A and B is 1000km. A train starts from A at 9 a.m. and travels towards B at 100 km/hr. Another starts from B at 10 a.m. and travels towards A at 150 km/hr. At what time do they meet?
(A) 11am.
(B) 12p.m.
(C) 3pm.
(D) 2p.m.
(E) 1p.m.
Rationale: Suppose they meet x hrs after 9 a.m.
Distance moved by first in x hrs + Distance moved by second in (x-1)hrs = 1000
100x + 150 (x-1) = 1000
x = 4.60 = 5 hrs
They meet at 9+5 = 2 p.m.
Answer is D
Answer: (D) 2p.m.
Question: To mail a package, the rate is 10 cents for the first pound and 5 cents for each additional pound. Two packages weighing 3 pounds and 5 pounds, respectively can be mailed seperately or combined as one package. Which method is cheaper and how much money is saved?
(A) Combined, with a saving of 5 cents
(B) Combined, with a saving of 10 cents
(C) Combined, with a saving of 15 cents
(D) Separately, with a saving of 5 cents
(E) Separately, with a saving of 10 cents
Rationale: 3 pounds cost = 10+2*5 = 20
5 pounds cost = 10+4*5 = 30
Total = 50
8 pounds cost = 10+ 7*5 =45
Answer : A
Answer: (A) Combined, with a saving of 5 cents