divelab/Sys2Bench huggingface dataset:
Question: The difference between the squares of two consecutive odd integers
is a square<1000 whose root equals the combined sum of the digits
of the two integers. What is the sum of the digits T of the larger integer?
Options:
A)T=2
B)T=5
C)T=8
D)10
E)11
Rationale: Really hard. But let's start with few concepts:
1. Square of an odd integer will be odd.
2. Difference of odd and odd will be even.
3. Any odd integer can be expressed as difference of two squares.
4. An even integer can be expressed as difference of two squares only if that even integer is a multiple of 4.
Assume two odd integers to be (2x-1) and (2x+1).
Difference of their squares = (2x+1)^2 - (2x-1)^2
= 4x^2 + 1 + 4x - (4x^2 + 1 - 4x)
= 4x^2 + 1 + 4x - 4x^2 - 1 + 4x
= 8x
Now root of 8x needs to be an integer such that it is equal to the sum of the digits of the two odd integers.
8 = 2^3, so x needs to be such that itcompletesa perfect square.
If we find x, we can find the value of 2x+1 (larger integer) and then sum of its digits.
Let's check the options, starting with c.
For sum to be 8, few possibilities are: 17, 35, 53, 71
If we take 17, the pair is 15 and 17, meaning x = 8.
8x = 64
root of 64 = 4 but 4 is not equal to 1+5+1+7.
Reject.
If we take 35, the pair is 33 and 35, meaning x = 17.
8x = 8*17
Reject since perfect square is not possible.
If we take 53, the pair is 51 and 53, meaning x = 26.
8x = 8*26
Reject since perfect square is not possible.
If we take 71, the pair is 69 and 71, meaning x = 35.
8x = 8*35
Reject since perfect square is not possible.
I tried each option and the possibilities and then got lost.
Then, it occurred to me that I was only checking 2-digit integers. What about 3-digits?
Starting with option a, only 2-digit odd integer whose sum is 2 is 101.
If we take 101, the pair is 99 and 101, meaning x = 50.
8x = 8*50 = 400
root of 400 = 20 which is indeed equal to 9+9+1+1.
Answer (A).
Answer: A
Question: On dividing a number by 7, we get 3 as quotient and 0 as remainder. On dividing the same number by 3, what will be the remainder?
Options:
A)1
B)2
C)3
D)0
E)4
Rationale: Number = 7 * 3 + 0 = 21
3) 21 (7
21
--------
0
Required number = 0.
ANSWER:D
Answer: D
Question: Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30º and 45º respectively. If the lighthouse is 100 m high, the distance between the two ships is:
Options:
A)173 m
B)200 m
C)273 m
D)300 m
E)None of these
Rationale: xplanation:
Let AB be the lighthouse and C and D be the positions of the ships.
Then, AB = 100 m, <ACB = 30º and <ADB = 45º.
AB/AC=tan30
Answer: C
Answer: C
Question: If 12 men and 16 boys can do a piece of work in 7 days and 13 men together will 24 boys can do it in 4 days. Compare the daily work done by a man with that of a boy.
Options:
A)1:4
B)1:2
C)1:3
D)2:1
E)4:1
Rationale: 12M + 16B ----- 7 days
13M + 24B ------- 4 days
84M + 112B = 52M + 96B
32M = 16B => 2M = B
M: B = 1:2
ANSWER:B
Answer: B
Question: What is the minimum value of z for which z^2 + z - 3/4 > 0 is not true?
Options:
A)-5/2
B)-3/2
C)-1/2
D)1/4
E)1/2
Rationale: z^+z-3/4=(z+1/2)^2-1
It>0 is not true means it has to be less or equal to 0.
(z+1/2)^2-1<=0
(z+1/2)^2<=1
-1<=z+1/2<=1
-3/2<=z<=1/2
The minimum value of z is thus -3/2.
ANSWER:B
Answer: B
Question: If the tens digit x and the units digit y of a positive integer n are reversed, the resulting integer is 36 more than n. What is y in terms of x ?
Options:
A)x-2
B)x-4
C)x+4
D)x-3
E)x-1
Rationale: Original Digits=xy i.e. Number=10x+y
After reversing the digits:
Digits=yx i.e. Number=10y+x
10y+x is 36 more than 10x+y
10x+y+36=10y+x
10x-x+36=10y-y
9x+36=9y
x+4=y
OR
y=x+4
Answer : C
Answer: C
Question: How many odd numbers between 10 and 900 are the squares of integers?
Options:
A)12
B)13
C)14
D)15
E)16
Rationale: The square of an odd number is an odd number:
10 < odd < 1,000
10 < odd^2 < 1,000
3.something < odd < 31.something (by taking the square root).
So, that odd number could be any odd number from 5 to 31, inclusive: 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, and 31.
13 numbers.
Answer: B.
Answer: B
Question: Assuming i have an infinite supply of coins.
What is the fewest number of coins would be required in order to make sure each and every coin touched exactly three other coins.
Options:
A)1
B)6
C)4
D)2
E)8
Rationale: C
Four
three placed flat on the table in a triangle(touching each other) and put the fourth one on top of them in the middle.
Answer: C
Question: For what value of x will the function f(x) = -3(x - 10)(x - 4) have a maximum value? Find the maximum value.
Options:
A)15
B)36
C)33
D)27
E)29
Rationale: f(x) = -3(x - 10)(x - 4) = -3x2 + 42x - 120 : expand and obtain a quadratic function
h = -b/2a = -42/-6 = 7 : h is the value of x for which f has a maximum value
f(h) = f(7) = 27 : maximum value of f.
Answer: D
Question: The true discount on a bill of Rs.8640 is Rs.1440.The banker's discount is
Options:
A)1428
B)1528
C)1628
D)1728
E)None of these
Rationale: Solution
P.W	= Rs.(8640 - 1440)
= Rs. 720
S.I on Rs. 8640	=Rs.(1440/7200 x 8640)
= Rs. 1728.
Answer D
Answer: D
Question: How many possible different bus routes are available in a metro city ? Suppose the bus route numbers consist of a natural number less than 100, followed by one of the letters U,V,W,X,Y and Z.
Options:
A)500
B)550
C)564
D)594
E)None of these
Rationale: The number can be any one of the natural numbers from 1 to 99. There are 99 choices for the number. The letter can be chosen in 6 ways. Number of possible bus routes are 99*6= 594
Answer D
Answer: D
Question: A store sells chairs and tables. If the price of 2 chairs and 1 table is 60% of the price of 1 chair and 2 tables, and the price of 1 table and 1 chair is $64, what is the price, in dollars, of 1 table? (Assume that every chair has the same price and every table has the same price.)
Options:
A)48
B)52
C)54
D)58
E)56
Rationale: LET C= CHAIR ; T =TABLE
2C+1T = 0.6 (1C + 2T) OR C( 2-0.6) = 1.2T -1T OR 1.4C = 0.2 T THEREFORE C= 0.2/1.4 T = 1/7 T
IC +1T =64 OR 1/7T + 1T =64 THEREFORE T= 64*7/8 = 56
E
Answer: E
Question: Two pipe A and B fill a tank in 6 hours and 8 hours respectively.and C empty that tank in 12 hour.if all three pipe open together in empty tank then how much time it take to fill the tank?
Options:
A)19/3
B)23/2
C)24/5
D)18
E)16
Rationale: all three pipe resultant fill tank in 1 hour=[1/6+1/8-1/12]=5/24
total time taken to fill tank=24/5 hour
answer C
Answer: C
Question: In a certain corporation, there are 300 male employees and 150 female employees. It is known that 30% of the male employees have advanced degrees and 40% of the females have advanced degrees. If one of the 450 employees is chosen at random, what is the probability this employee has an advanced degree or is female?
Options:
A)2/3
B)3/5
C)3/10
D)8/15
E)11/30
Rationale: P(female) = 150/450 = 1/3
P(male with advanced degree) = 0.3*300/450 = 90/450 = 1/5
The sum of the probabilities is 8/15
The answer is D.
Answer: D
Question: If the average of ten numbers is 60, then which of the following could be the standard deviation of the ten numbers?
I. 0
II. 10
III. 60
Options:
A)I
B)II
C)III
D)I&II
E)all three options
Rationale: We know that we have 10 numbers (and they could be ANY values - including negatives and non-integers) and we know that the average of those numbers is 10. This is meant to say that there are an INFINITE number of possible sets of 10 numbers that fit this prompt.
IF all ten numbers were the same (meaning that we had ten 10s), then the SD would be 0. The more 'spread out' those ten numbers get, the higher the SD becomes. Since there's no limit to the 'spread', then there's no limit to what the SD could be either. Thus, it could be 10 or 20 or any other number.
E
Answer: E
Question: Car T and Car Y traveled the same 80-mile route. If Car T took 2 hours and Car Y traveled at an average speed that was 50 percent faster than the average speed of Car T, how many hours did it take Car Y to travel the route?
Options:
A) 2/3
B) 1
C) 4/3
D) 8/5
E) 3
Rationale: The speed of car T is (distance)/(time) = 80/2 = 40 miles per hour.
The speed of car Y = 3/2*40 = 60 miles per hour --> (time) = (distance)/(speed) = 80/60 = 4/3 hours.
Answer: C.
Or: to cover the same distance at 3/2 as fast rate 2/3 as much time is needed --> (time)*2/3 = 2*2/3 = 4/3 hours.
Answer: C.
Answer: C
Question: If a4 +(1/a4)=119 then a power 3-(1/a3)
Options:
A)22
B)36
C)27
D)18
E)19
Rationale: Explanation:
Given that a4+1a4=119a4+1a4=119 , adding 2 on both sides, we get : (a2+1a2)2=121(a2+1a2)2=121
⇒a2+1a2=11⇒a2+1a2=11
Again, by subtracting 2 on both sides, we have, ⇒(a−1a)2=9⇒(a−1a)2=9
⇒a−1a=3⇒a−1a=3
Now, ⇒a3−1a3⇒a3−1a3 = (a−1a)(a2+1a2+1)(a−1a)(a2+1a2+1) = 12×3 = 36
Answer:B
Answer: B
Question: What is the greatest prime factor of 4^17 - 2^29?
Options:
A)2
B)3
C)5
D)7
E)31
Rationale: I'm happy to help with this.
We know 4 = 2^2, so 4^17 = (2^2)^17 = 2^(2*17) = 2^34
That takes advantage of a law of exponents that says (a^n)^m = a^(n*m)
So, 4^17 - 2^29 = 2^34 - 2^29 = 2^(29 + 5) - 2^29 = (2^29)*(2*6) - 2^29 = (2^6 - 1) *(2^29)
= (32 - 1)*(2^29) = 31*(2^29)
The prime factors of 31 are 31, so the largest prime factor is 31, answer choice D.
Here's a blog you may find helpful.
http://magoosh.com/gmat/2012/gmat-math-factors/
Does all that make sense? Please let me know if you have any further questions.
Mike
Wow. I am floored by how great of an explanation you provided. Posts like that make me really think that doing thousands of practice problems with good explanations beats out reading books on math every day of the week.
E
Answer: E
Question: The average of five numbers is 27. If one number is excluded, the average becomes 25. The excluded number is?
Options:
A)35
B)25
C)40
D)52
E)16
Rationale: Excluded number = 27*5-25*4 = 135-100 = 35
Answer is A
Answer: A
Question: In an electric circuit, two resistors with resistances x and y are connected in parallel. If R is the combined resistance of these two resistors, then the reciprocal of R is equal to the sum of the reciprocals of x and y. What is R if x is 5 Ohms and y is 6 Ohms?
Options:
A)7/30
B)11/30
C)11/15
D)30/11
E)15/11
Rationale: 1/R = 1/x + 1/y
1/R = 1/5+1/6 = 11/30
R = 30/11
The answer is D.
Answer: D
Question: probability Like between 100 and 999 how many no have the probability that they does not contain 7 ?
Options:
A)646/900
B)648/900
C)649/900
D)658/900
E)642/900
Rationale: There are 900 numbers between 100 and 999.
those that contain 7 are.....
107, 117, 127, ........ -- 10 of these
207, 217, 227, ........ -- 10 of these too
307, 317, 327, .......
....
9*10 numbers that end in 7.
170, 171, 172, 173, 174, 175, 176, (NOT 177 WE ALREADY COUNTED IT), 178, 179 -- 9 of these
270, 271, 272, 273, 274, 275, 276, (NOT 277 WE ALREADY COUNTED IT), 278, 279 -- 9 of these
...
and so on
so 9*9 numbers that have a middle digit of 7
and finally
700, 701, 702, 703, 704.................., but NOT
(707, 717, 727,....) or (770, 771, 772, 773, ....)
So that's (100 - 10 - 9) = 81 numbers that start with 7.
We had 900 numbers.
N = 900 - 90 - 81 - 81 = 648
So the probability is 648/900 = 0.72
ANSWER:B
Answer: B
Question: What is the average (arithmetic mean) of all multiples of 10 from 10 to 200 inclusive?
Options:
A)190
B)105
C)200
D)205
E)210
Rationale: This question can be solved with the Average Formula and 'bunching.'
We're asked for the average of all of the multiples of 10 from 10 to 200, inclusive.
To start, we can figure out the total number of terms rather easily:
1(10) = 10
2(10) = 20
...
20(10) = 200
So we know that there are 40 total numbers.
We can now figure out the SUM of those numbers with 'bunching':
10 + 200 = 210
20 + 190 = 210
30 + 180 = 210
Etc.
Since there are 20 total terms, this pattern will create 10 'pairs' of 210.
Thus, since the average = (Sum of terms)/(Number of terms), we have...
(10)(210)/(20) =105
Answer : B
Answer: B
Question: 10 business executives and 3 chairmen meet at a conference. If each business executive shakes the hand of every other business executive and every chairman once, and each chairman shakes the hand of each of the business executives but not the other chairmen, how many handshakes would take place?
Options:
A)144
B)131
C)115
D)90
E)75
Rationale: there are 10 business exec and in each handshake 2 business execs are involved.
hence 10C2=45
Also, each of 10 exec will shake hand with every 3 other chairmen for total of 30 handshake.
total=45+30=75
ANS: E
Answer: E
Question: The arithmetic mean of the scores of a group of students in a test was 52. The brightest 20% of them secured a mean score of 80 and the dullest 25% a mean score of 31. The mean score of remaining 55% is?
Options:
A)57.6
B)51.6
C)51.4
D)51.1
E)51.1
Rationale: Let the required means score be x. Then,
20 * 80 + 25 * 31 + 55 * x = 52 * 100
= 1600 + 775 + 55x = 5200
= 55x = 2825
= x = 565/11 = 51.4.
Answer: C
Answer: C
Question: A train travels from Albany to Syracuse, a distance of 120 miles, at the average rate of 40 miles per hour. The train then travels back to Albany from Syracuse. The total travelling time of the train is 5 hours and 24 minutes. What was the average rate of speed of the train on the return trip to Albany?
Options:
A)45
B)20
C)30
D)40
E)50
Rationale: 40*T =120 THEREFORE T = 120/40 =3
ON RETURN SPEED * ( 5.4 -3) =120 THEREFORE T = 120/2.4 =50
E
Answer: E
Question: A certain school principal must choose 5 students to attend a field trip out of a group of 11 students. In addition, out of the 5 chosen students, the principal must select a note-taker and a treasurer. How many different ways are there for the principal to select the 5 students and then select the treasurer and the note-taker?
Options:
A)1,260
B)2,520
C)9,240
D)6,020
E)10,080
Rationale: 5 students can be selected out of 11 students in 11C5 ways.
out of the remaining 5 students,Note taker can be chosen in 5 ways.
Finally only 4 students remain from which we can choose a treasurer in 4 ways.
Total number of ways = 462 * 5 *4 = 9240
correct answer - C
Answer: C
Question: How much water should be added to 12 liters of a 20%-solution of alcohol to reduce the concentration of alcohol in the solution by 75% ?
Options:
A)28 liters
B)27 liters
C)30 liters
D)32 liters
E)35 liters
Rationale: Let x ltr water to be added
2ltr alcohol to be represented as (20(1-3/4(new soln.=12+x)))
2=5%*(12+x)-------->x=28
Ans A
Answer: A
Question: In the rectangular coordinate system, points (4, 0) and (– 4, 0) both lie on circle C. What is the maximum possible value of the radius of C
Options:
A)2
B)4
C)8
D)16
E)None of the above
Rationale: It takes 3 distinct points to define a circle. Only 2 are given here.
The two points essentially identify a single chord of the circle C. Since no other information is provided, however, the radius of the circle can essentially be anything. All this information tell us is that the radius isgreater 4
B
Answer: B
Question: If n is the smallest integer such that 54 times n is the square of an integer, what is the value of n?
Options:
A) 2
B) 1
C) 6
D) 12
E) 24
Rationale: 54 can written as = 2 * 3 * 3 * 3 --> 2^1 * 3^3 ---(1)
so for 54 * n to be a square of an integer, the integer should have even powers to the prime numbers it composed of.
here 2 already has even power -> So n has to be 2 to make the power of 1 in (1) even
Option B is correct
Answer: B
Question: In how many different number of ways 5 men and 2 women can sit on a shopa which can accommodate persons?
Options:
A)160
B)170
C)190
D)210
E)230
Rationale: 7p3 = 7 × 6 × 5 = 210
Option 'D'
Answer: D
Question: If the annual rate of simple interest increases from 10% to 12 1/2 %, a man's yearly income increases by Rs. 1250. His principal in Rs. is?
Options:
A)32778
B)50000
C)27798
D)27799
E)27601
Rationale: Let the sum be Rs. x. Then,
(x * 25/2 * 1/100) - (x * 10 * 1)/100 = 1250
25x - 20x = 250000
x = 50000.Answer:B
Answer: B
Question: A publishing company advertisd the job opening.The response was good. One hundred people applied for the post. The company wanted someone expert in both physics and chemistry. Out of which 10 did not had any specalization.70 of them had got physics training and 82 got training in chemistry.how many applicants had got training in both
physics and chemistry?
Options:
A)60
B)61
C)62
D)63
E)64
Rationale: (100-10)=90-82=8,70-8=62
ANSWER:C
Answer: C
Question: 20 litres of a mixture contains milk and water in the ratio 3:1. How much milk must be added to this mixture to have a mixture containing milk and water in the ratio 4 :1 ?
Options:
A)2
B)5
C)6
D)7
E)8
Rationale: Quantity of milk in the given mixture = \inline \frac{20\times 3}{4}=15 lts
Quantity of water in this mixture = 20 - 15 = 5 lts
Let x litres of milk be added to given mixture to have the requisite ratio of milk and water
Then
\inline \Rightarrow 15 + x =20
\inline \therefore x = 5
\inline \therefore Milk to be added = 5 litres
Answer:B
Answer: B
Question: The present population of a town is 260. Population increase rate is 10% p.a. Find the population of town after 1 years?
Options:
A)100
B)120
C)200
D)226
E)286
Rationale: P = 260
R = 10%
Required population of town = P*(1 + R/100)^T
= 260*(1 + 10/100)
= 260*(11/10)
= 286
Answer is E
Answer: E
Question: A man can row downstream at 24 kmph and upstream at 10 kmph. Find the speed of the man in still water and the speed of stream respectively?
Options:
A)2, 7
B)7, 4
C)8, 7
D)4, 7
E)17, 7
Rationale: Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively.
Given x + y = 24 --- (1)
and x - y = 10 --- (2)
From (1) & (2) 2x = 34 => x = 17, y = 7
Answer:E
Answer: E
Question: A cube of side 4 meter length is cut into small cubes of side 25 cm each. How many such small cubes can be obtained?
Options:
A)4069
B)6048
C)1000
D)4096
E)4060
Rationale: Along one edge, the number of small cubes that can be cut
= 400/25=16
Along each edge 16 cubes can be cut. (Along length, breadth and height). Total number of small cubes that can be cut
= 16 * 16 * 16= 4096
Answer:D
Answer: D
Question: The mass of 1 cubic meter of a substance is 300 kg under certain conditions. What is the volume in cubic centimeters of 1 gram of this substance under these conditions? (1 kg =1,000 grams and 1 cubic meter = 1,000,000 cubic centimeters)
Options:
A)3.33
B)3.34
C)3.53
D)5.32
E)3.92
Rationale: 300 kg - 1 cubic meter;
300,000 g - 1 cubic meter;
300,000 g - 1,000,000 cubic centimeters;
1 g - 1,000,000/300,000 = 10/3 = 3.33 cubic centimeters.
Answer: A.
Answer: A
Question: A train running at the speed of 90 km/hr crosses a pole in 6 seconds. Find the length of the train.
Options:
A)150 meter
B)100 meter
C)105 meter
D)120 meter
E)130 meter
Rationale: Speed = 90*(5/18) m/sec = 25 m/sec
Length of Train (Distance) = Speed * Time
(25) * 6 = 150 meter
Answer:A
Answer: A
Question: The bacteria have the probability of split into 3 and probability to die is 1/3rd of the total bacteria. Let the probability is P. Some of them survived with probability 1/5.Then which among the following relation is true?
Options:
A)P=1/3+1/5*3
B)P=1/3+1/5*4
C)P=1/3+1/5*2
D)P=1/8*(1/8-3)
E)P=1/5*(1/4-3)
Rationale: The bacteria have the probability of split into 3 and probability to die is 1/3rd of the total bacteria. Let the probability is P. Some of them survived with probability 1/5.Then which among the following relation is true?
a)P=1/3+1/5*3 b)P=1/5*(1/8-3)
P=1/3+1/5*3 is true.
ANSWER:A
Answer: A
Question: What is the sum of all possible solutions to |x - 3|^2 + |x - 3| = 20 ?
Options:
A)-1
B)6
C)7
D)12
E)14
Rationale: First of all |x - 3|^2 = (x - 3)^2, so we have: (x - 3)^2 + |x - 3| = 20.
When x < 3, x - 3 is negative, thus |x - 3| = -(x - 3). In this case we'll have (x - 3)^2 - (x - 3) = 20 --> x = -1 or x = 8. Discard x = 8 because it's not in the range we consider (< 3).
When x >= 3, x - 3 is non-negative, thus |x - 3| = x - 3. In this case we'll have (x - 3)^2 + (x - 3) = 20 --> x = -2 or x = 7. Discard x = -2 because it's not in the range we consider (>= 3).
Thus there are two solutions: x = -1 and x = 7 --> the sum = 6.
Answer: B.
Answer: B
Question: A fair coin is tossed 4 times. What is the probability of getting at least 2 tails?
Options:
A)1/16
B)1/2
C)3/16
D)11/16
E)3/8
Rationale: Let's find the probability of the opposite event and subtract this value from 1.
The opposite event would be getting zero tails (so all heads) or 1 tail.
P(HHHH)=(12)4=116P(HHHH)=(12)4=116.
P(THHH)=4!3!∗(12)4=416P(THHH)=4!3!∗(12)4=416, we are multiplying by 4!3!4!3! since THHH scenario can occur in number of ways: THHH, HTHH , HHTH, or HHHT (notice that 4!3!4!3! basically gives number of arrangements of 4 letters THHH out of which 3 H's are identcal).
P(T≥2)=1−(116+416)=1116P(T≥2)=1−(116+416)=1116.
Answer: D.
Answer: D
Question: A train running at the speed of 80 km/hr crosses a pole in 9 sec. What is the length of the train?
Options:
A)298 m
B)200 m
C)208 m
D)988 m
E)299 m
Rationale: Speed = 80 * 5/18 = 200/9 m/sec
Length of the train = speed * time = 200/9 * 9
= 200 m
Answer:B
Answer: B
Question: A certain business produced x rakes each month form November through February and shipped x/2 rakes at the beginning of each month from March through October. The business paid no storage costs for the rakes from November through February, but it paid storage costs of $0.30 per rake each month from March through October for the rakes that had not been shipped. In terms of x, what was the total storage cost, in dollars, that the business paid for the rakes for the 12 months form November through October?
Options:
A)0.40x
B)4.20x
C)1.40x
D)1.60x
E)3.20x
Rationale: because we have a total of 4X
Also from Mar- Oct the rakes will be deducted by 1/8 X
so
In Apr they pay for the storage 0.3 * 4X * 7/8
In May they pay for the storage 0.3 * 4X * 6/8
In Jun they pay for the storage 0.3 * 4X * 5/8
In Jul they pay for the storage 0.3 * 4X * 4/8
In Aug they pay for the storage 0.3 * 4X * 3/8
In Sep they pay for the storage 03 * 4X * 2/8
In Oct they pay for the storage 0.3 * 4X * 1/8
total = 0.3 * 4X * 1/8 * [ 1+2+3+4+5+6+7]
= 0.3 * X/2 * (28)
= 4.2X
(B)
Answer: B
Question: The sum of the present ages of two persons A and B is 60. If the age of A is twice that of B, find the sum of their ages 7 years hence?
Options:
A)22
B)77
C)74
D)98
E)71
Rationale: A + B = 60, A = 2B
2B + B = 60 => B = 20 then A = 40.
7 years, their ages will be 47 and 27.
Sum of their ages = 47 + 27 = 74.
Answer: C
Answer: C
Question: A certain sum of money at simple interest amounted Rs.890 in 10 years at 3% per annum, find the sum?
Options:
A)681.61
B)682.61
C)683.61
D)684.61
E)685.61
Rationale: 890 = P [1 + (10*3)/100]
P = 684.61
Answer: D
Answer: D
Question: 1,000^2 + 1,001^2 =
Options:
A)6,030,053
B)6,002,001
C)6,030,055
D)6,030,056
E)6,030,057
Rationale: Interesting problem.
I think key is to notice that all the given answer choices differs in last two digits. Therefore, our entire focus should be to figure out how the given terms contribute to last two digits of total.
1000^2 -> 00
1001^1 -> 01
Total -> *1
Answer B.
Answer: B
Question: A man spends Rs. 1600 per month on an average for the first three months, Rs 1550 for next four months and Rs. 1800 per month for the last five months and saves Rs . 5200 a year. What is his average monthly income?
Options:
A)2000
B)2100
C)2200
D)2300
E)2400
Rationale: Explanation:
Total expenditure for the first 3 months = 3 × 1600 = 4800
Total expenditure for 4 months = 4 × 1550 = 6200
Total expenditure for 5 months = 5 × 1800 = 9000
Total expenditure and saving (which is income for one year)
= 4800 + 6200 + 9000 + 5200 = Rs. 25200
So, Average monthly income = 25200/12 = Rs. 2100
Answer B
Answer: B
Question: In the Biotechnology class of 2000, there were E graduates. 32 of the graduates found a job, 45 continued on to their second degree and 13 did both. If only 9 people didn't do both, What is E equal to?
Options:
A)69.
B)71.
C)73.
D)75.
E)76.
Rationale: Total = 32 +45 -13 +9 = 73 .... My first post on the forum... I hope I am correct
C is correct choice.
Answer: C