divelab/Sys2Bench huggingface dataset:
Question: An association of mathematics teachers has 1,260 members. Only 445 of these members cast votes in the election for president of the association. What percent of the total membership voted for the winning candidate if the winning candidate received 60 percent of the votes cast?
Options:
A)75%
B)58%
C)42%
D)34%
E)22%
Rationale: Total umber of members = 1260
Number of members that cast votes = 445
Since , winning candidate received 60 percent of the votes cast
Number of votes for winning candidate = (60/100)*445 = 267
Percent of total membership that voted for winning candidate = (267/1260)*100 = 21.19%
Answer E
Answer: E
Question: The value of 99^(95/99) x 99 is:
Options:
A)9989
B)9896
C)9890
D)9809
E)9810
Rationale: (100 – 4/99) x 99 = 9900 – 4
= 9896.
ANSWER:B
Answer: B
Question: A man can row his boat with the stream at 6 km/h and against the stream in 4 km/h. The man's rate is?
Options:
A)1 kmph
B)6 kmph
C)8 kmph
D)9 kmph
E)3 kmph
Rationale: DS = 6
US = 4
S = ?
S = (6 - 4)/2 = 1 kmph
Answer: A
Answer: A
Question: A company has a hierarchical system where for every 10 workers, there is one team lead, and for every 3 teams leads, there is one supervisor. If the company has 13 supervisors, how many workers does it have?
Options:
A)140
B)321
C)390
D)500
E)130
Rationale: Some students may initially answer 130 to this question, especially if answering similar problems. However, that would be incorrect, as this is not a straight-forward ratio of 1:3:10.
The ratio of supervisors to team leads is 1:3, and the ratio of team leads to workers is 1:10. Therefore, the ratio of supervisors to workers is 1:30.
Therefore, 13*30=390
Answer: C)
Answer: C
Question: A car covers a distance of 180 km in 10 hrs. What is its speed in mps.
Options:
A)40 m/s
B)5 m/s
C)20 m/s
D)15 m/s
E)16 m/s
Rationale: Explanation:
Distance = Speed x Time
Speed = (180/10) = 18 kmph
Spees in mps = 18 x 5/18 = 1 x 5 = 5 mps.
Answer: Option B
Answer: B
Question: A fraction bears the same ratio to 1/27 as 3/7 does to 5/9. The fraction is?
Options:
A)1/23
B)1/35
C)1/25
D)1/13
E)1/15
Rationale: Let the fraction be x. Then,
x:1/27 = 3/7 : 5/9
x × 5/9 = 1/27 × 3/7
x × 5/9 = 1/9 × 1/7
x × 5/9 = 1/63
x × 5 = 9/63
5x = 1/7 = 1/35
B
Answer: B
Question: If the tens digit of positive integer x is 5 and the tens digit of positive integer y is 5, how many possible values of the tens digit of 2(x+y) can there be?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: We only need to consider the tens and ones digits of x and y, and the last two digits can be represented as 50 + p and 50 + q respectively.
2(50+p+50+q)= 200 + 2(p + q)
2(p+q) can range from 0 up to a maximum value of 36 when p=q=9.
Then the tens and ones digits of 2(x+y) can range from 00 up to 36.
There can be 4 possibilities for the tens digit.
The answer is C.
Answer: C
Question: A began business with 1000 and is joined afterwards by B with 6000. When did B join, if the profits at the end of the year are divided equally?
Options:
A)8 months
B)9 months
C)10 months
D)2 months
E)None of these
Rationale: Let B join after x months of the start of the business so that B’s money is invested for (12 – x) months.
∴ Profit ratio is 12 × 1000 : (12 – x) × 6000
or 12 : 6(12 – x)
Since profit is equally divided so
12 = 6(12 – x) or x = 2. Thus B joined after 8 months.
Answer D
Answer: D
Question: The length of a rectangle is increased by 25% and its breadth is decreased by 20%. What is the effect on its area?
Options:
A)Remains same
B)5% decrease
C)7% decrease
D)2% decrease
E)3% decrease
Rationale: 100 * 100 = 10000
125 * 80 = 10000
No change
A
Answer: A
Question: A box contains either blue or red flags. The total number of flags in the box is an even number. A group of children are asked to pick up two flags each. If all the flags are used up in the process such that 60% of the children have blue flags, and 65% have red flags, what percentage of children have flags of both the colors?
Options:
A)5%
B)10%
C)15%
D)20%
E)25%
Rationale: Solution: let the total number of flags be 100(even number)
let the total number of 'blue' flags alone be 'a'
let the total number of 'red' flags alone be 'b'
let the total number of 'both' flags be 'c'
We have given,
total number of blue flags = 60% = 60 = a+c
total number of red flags=65%=65=b+c
total number of flags = a+b+c=100 (since all the flags have been utilized)
So, substituting for c in the third equation, we have,
60-c+c+65-c=100
c=25
Option E.
Answer: E
Question: Which of the following is equivalent to the pair of inequalities x + 7 > 10 and x - 1 <= 5 ?
Options:
A) 2 < x < 16
B) 2 <= x < 4
C) 3 < x <= 6
D) 4 < x <= 8
E) 4 <= x <= 16
Rationale: Solution:
Let’s isolate x in both inequalities, starting with x + 7 > 10.
x + 7 > 10
x > 3
Next we isolate x in the inequality x – 1  5.
x – 1 <= 5
x <= 6
Bringing these two inequalities together we know:
3 < x <= 6
The answer is C.
Answer: C
Question: Ramu bought an old car for Rs. 40000. He spent Rs. 13000 on repairs and sold it for Rs. 64900. What is his profit percent?
Options:
A)20
B)22.5
C)18
D)99
E)88
Rationale: Total CP = Rs. 40000 + Rs. 13000 = Rs. 53000 and SP = Rs. 64900
Profit(%) = (64900 - 53000)/53000 * 100 = 22.5%
Answer: B
Answer: B
Question: A room has equal number of men and women. Eight women left the room, leaving twice as many men as women in the room . What was the total number of men and women present in the room initially?
Options:
A)32
B)34
C)28
D)30
E)36
Rationale: Explanation :
Assume that initial number of men = initial number of women = x
2(x-8) = x
=> 2x - 16 = x
=> x = 16
Total number of men and women = 2x = 2 × 16 = 32
Answer : A
Answer: A
Question: Selling an kite for Rs. 30, a shop keeper gains 40%. During a clearance sale, the shopkeeper allows a discount of 10% on the marked price. His gain percent during the sale is?
Options:
A)8%
B)10%
C)11%
D)15%
E)26%
Rationale: Explanation:
Marked price = Rs. 30
C.P. = 100/140 * 30 = Rs. 21.42
Sale price = 90% of Rs. 30 = Rs. 27
Required gain % = 5.57/21.42 * 100 = 26%.
Answer: E
Answer: E
Question: On June 1 a bicycle dealer noted that the number of bicycles in stock had decreased by 4 for each of the past 5 months. If the stock continues to decrease at the same rate for the rest of the year, how many fewer bicycles will be in stock on december 1 than were in stock on January 1?
Options:
A) 8
B) 12
C) 20
D) 44
E) 36
Rationale: Jan 1 = C
Feb 1 = C - 4
March 1 = C - 8
April 1 = C - 12
May 1 = C - 16
June 1 = C - 20
July 1 = C - 24
Aug 1 = C - 28
Sept 1 = C - 32
Oct 1 = C - 36
Nov 1 = C - 40
Dec 1 = C - 44
Difference between stock on December 1 than were in stock on January 1 will be -
C - ( C - 44 )= 44
Hence answer will be (D)
Answer: D
Question: A certain country had a total annual expenditure of $1.2x10^12. If the population of the country was 240 million last year, what was the per capita expenditure?
Options:
A)$500
B)$1000
C)$2000
D)$3000
E)$5000
Rationale: Explanation:
In scientific notation 240 million is 2.4x10^8. So the per capita expenditure was:
($1.2x10^12)/(2.4x10^8)=($1.2)/(2.4)x10^12-8=$0.5x10^4=$5000
Answer: Option E
Answer: E
Question: If you are given $4, and the amount doubles every day, how much money will you have after 8 days?
Options:
A)$256
B)$512
C)$1024
D)$65536
E)$4096
Rationale: 4^8=65536
The answer is D.
Answer: D
Question: Fill in the blanks:
3 3 5 4 4 ? 5
Options:
A)2
B)7
C)8
D)3
E)1
Rationale: D
3
Number of letters in one, two, three, four, five, six, seven and so on.
Answer: D
Question: A reduction of 50% in the price of oil enables a house wife to obtain 5kgs more for Rs.800, what is the reduced price for kg?
Options:
A)s.42
B)s.46
C)s.40
D)s.80
E)s.34
Rationale: 800*(50/100) = 400 ---- 5
? ---- 1 => Rs.80
Answer: D
Answer: D
Question: How many digits are used to number a book containg 300 pages.
Options:
A)694
B)792
C)698
D)784
E)789
Rationale: Explanation:
Number of digits in 1 digit numbers = 1 to 9 = 9
Number of digits in 2 digit numbers = 10 to 99 = 90 (2) = 180
Number of digits in 3 digit numbers = 100 to 300 = 201 (3) = 603
Total = 792
Answer: Option B
Answer: B
Question: A towel, when bleached, was found to have lost 20% of its length and 10% of its breadth. The percentage of decrease in area is
Options:
A)28%
B)30%
C)32%
D)38%
E)40%
Rationale: Let original length = x and original breadth = y.
Decrease in area
= xy - 80 x x 90 y
100 100
= xy - 18 xy
25
= 7 xy.
25
Decrease % = 7 xy x 1 x 100 % = 28%.
25 xy
A)
Answer: A
Question: A train travels at the rate of 10 miles/hr for the first hour of a trip, at 20 miles/hr for the second hour, at 30 miles/hr for the third hour and so on. How many hours will it take the train to complete a 210-mile journey? Assume that the train makes no intermediate stops.
Options:
A)6
B)6.5
C)7
D)7.5
E)5
Rationale: A train travels at the rate of 10 miles/hr for the first hour of a trip, at 20 miles/hr for the second hour, at 30 miles/hr for the third hour and so on. How many hours will it take the train to complete a 210-mile journey? Assume that the train makes no intermediate stops.
I think the easiest way to solve this problem would be simply to count the number of miles it travels per hour (and in total)
Hour miles/hour Total miles
1 10 10
2 20 30
3 30 60
4 40 100
5 50 150
6 60 210
It takes a total of nine hours to cover the 210 mile distance.
ANSWER: A 6
Answer: A
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?
Options:
A)27
B)29
C)24
D)28
E)12
Rationale: 2c = 1/4 + 1/6 – 1/3 = 1/12
c = 1/24 => 24 days
Answer: C
Answer: C
Question: find two integers, neither of which ends in a zero, and whose product is exactly 1,000,000
Options:
A)64 and 15,625
B)60 and 15,625
C)64 and 15,620
D)64 and 15,635
E)64 and 16,625
Rationale: 1,000,000=10^6
=10x10x10x10x10x10
=(2x5)x(2x5)x(2x5)x(2x5)x(2x5)x(2x5)
=(2^6)x(5^6)
= 64x15625
so the numbers are 64 and 15,625
ANSWER:A
Answer: A
Question: Three friends (Caleb, Jerry and Elvis) are employees of a company. Their respective salaries are in the ratio of 3 : 4 : 6. Jerry and Elvis's salaries together is Rs. 10000. By what percent is Elvis's salary than that of Sarah?
Options:
A)500%.
B)400%.
C)300%.
D)200%.
E)100%.
Rationale: Explanation:
Let the salaries be 3x, 4x and 6x respectively.
Then,4x + 6x = 10000 => x = 1000.
Caleb's salary = Rs. 3000, , Jerry's salary = Rs. 4000, and and Elvis's salary Rs. 6000.
Excess of Elvis's salary over Caleb's=[ (3000 /3000) x 100] = 100%.
Answer: E
Answer: E
Question: P is four times as fast as Q and working together, they can complete a work in 16 days. In how many days can Q alone complete the work?
Options:
A)20 days
B)15 days
C)16 days
D)25 days
E)18 days
Rationale: P = 4Q
P + Q = 4Q + Q = 5Q
These 5Q people can do the work in 16 days, which means Q can do the work in 80 days.
Hence, P can do the work in 20 days.
ANSWER:A
Answer: A
Question: A man's speed with the current is 8km/hr and the speed of the current is 20km/hr. The current's speed against the man is:
Options:
A)3 km/hr
B)4 km/hr
C)5 km/hr
D)7 km/hr
E)9 km/hr
Rationale: Man's rate in still water = (20 - 8) km/hr = 12 km/hr.
Current's rate against the current = (12 - 8) km/hr = 4 km/hr
B
Answer: B
Question: If one-seventh of a number exceeds its eleventh part by 100 then the number is…
Options:
A)770
B)870
C)1825
D)1925
E)925
Rationale: let no be :x
1/7x-1/11x=100
4x/77=100
x=7700/4=1925
ANSWER:D
Answer: D
Question: By selling an article at 80% of its marked price, a merchant makes a loss of 12%. What % profit will the merchant make if the article is sold at 95% of its marked price?
Options:
A)5% profit
B)1% loss
C)10% profit
D)5.5% profit
E)4.5% profit
Rationale: Explanatory Answer
Approach: Assume cost to be $100
Let the marked price be S and the cost price of the article be $100.
When the article is sold at 80% of its marked price, it is sold at 0.8S.
Selling the article at 0.8S results in a loss of 12% of the cost.
Therefore, the loss incurred when selling at 0.8S = 12% of 100 = $12.
Hence, when selling at 80% of the marked price, the article is sold at 100 - 12 = $88.
i.e., 0.8S = $88.
or S = 88/0.8 = $110.
If the merchant sells at 95% of the marked price, he will sell the article at 95% of $110 = $104.5
The profit made = 104.5 - 100 = $4.5.
% Profit = profit/cost price=4.5/100 = 4.5%
Choice E
Answer: E
Question: In a class there are 22 boys and 20 girls. In how many ways can a boy and a girl be selected?
Options:
A)288
B)500
C)440
D)266
E)255
Rationale: We can select one boy from 22 boys in 22 ways.
We select one girl from 20 girls in 20 ways
We select a boy and girl in 22 * 20 ways i.e.,
= 440 ways.
Answer: C
Answer: C
Question: The length of a room is 5.5 m and width is 3.75 m. What is the cost of paying the floor by slabs at the rate of $500 per sq. metre.
Options:
A)$10312.50
B)$13512.50
C)$16512.50
D)$14512.50
E)$18512.50
Rationale: Area =5.5×3.75 sq. metre.
Cost for 1 sq. metre. = $500
Hence, total cost
=5.5×3.75×500= $10312.50
A
Answer: A
Question: The greatest common factor of positive integers m and n is 11. What is the greatest common factor of (2m^2, 2n^2)?
Options:
A)2
B)11
C)22
D)121
E)242
Rationale: m = 11j and n = 11k, where the greatest common factor of j and k is 1.
2m^2 = 2*11*11*j^2 and 2n^2 = 2*11*11*k^2
The greatest common factor of 2m^2 and 2n^2 is 2*11*11 = 242
The answer is E.
Answer: E
Question: The smallest number which when divided by 20, 25, 35 and 40 leaves a remainder of 14, 19, 29 and 34 respectively is?
Options:
A)1994
B)1494
C)1349
D)1496
E)1500
Rationale: LCM = 1400
1400 - 6 = 1394
ANSWER:C
Answer: C
Question: When you multiply a number by 5 and
then subtract 5, the result is the same as
if you first subtracted 7 from the same
number and then multiplied by 11. What
is the number?
Options:
A)A)23
B)B)13
C)C)12
D)D)31
E)E)10
Rationale: Let x equal the number and then change the words into an equation and solve for x:
5x – 5 = 11(x – 7)
5x – 5 = 11x – 77
72 = 6x
12 = x
correct answer C)12
Answer: C
Question: If x = a!, which of these following values of a is the least possible value (in this list) for which the last 6 digits of the integer x will all be zero?
Options:
A)18
B)24
C)29
D)34
E)38
Rationale: 2*5 will give one 0 at the end. We need 2^6*5^6 to get 6 zeroes at the end.
There are many 2's, so we need to find the first 6 appearances of 5.
These multiples of 5 are: 5, 10, 15, 20, 5*5...which gives us 6.
To have at least 6 zeroes at the end, a => 25.
The answer is C.
Answer: C
Question: The no. of girls in a class are seven times the no. of boys, which value cannever be the of total students?
Options:
A)3
B)4
C)8
D)9
E)12
Rationale: Let the boys are X, then girls are 7X, total = X+7X = 8X
So it should be multiple of 8, 30 is not a multiple of 8.
C
Answer: C
Question: What number should replace the question mark?
105, 87, ?, 52, 35
Options:
A)49
B)37
C)70
D)55
E)83
Rationale: C
70
The sequence progresses -18, -17, -18, -17.
Answer: C
Question: Bob wants to run a mile in the same time as his sister. If Bob’s time for a mile is currently 10 minutes and his sister’s time is currently 8 minutes 48 seconds, by what percent does Bob need to improve his time in order run a mile in the same time as his sister?
Options:
A) 3%
B) 5%
C) 8%x
D) 10%
E) 12%
Rationale: Bob's time = 600 secs.
His sis' time = 528 secs.
Percent increase needed = (600-528/600) * 100 = 72/600 * 100 = 12%. Ans (E).
Answer: E
Question: A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is?
Options:
A)11
B)50
C)99
D)88
E)61
Rationale: Speed of the train relative to man = 125/10 = 25/2 m/sec.
= 25/2 * 18/5 = 45 km/hr
Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr.
x - 5 = 45 => x = 50 km/hr.
Answer: B
Answer: B
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 ?
Options:
A)4.2
B)4.6
C)4.3
D)4.1
E)4.0
Rationale: Sum of the remaining two number
= (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
Answer: B
Question: Three numbers are randomly selected, with replacement, from the set of integers {0, 1, 2, 3, 4, 5, 6, 7}. If the first number selected is w, the second number selected is x, and the third number is y, what is the probability that w < x < y ?
Options:
A)5/32
B)7/64
C)9/64
D)53/512
E)81/512
Rationale: The number of ways to select w, x, and y is: 8*8*8=512
The number of ways to choose three different numbers from the set is 8C3=56.
There are six permutations for each group of three different numbers, but only one permutation satisfies w < x < y.
P(w < x < y) = 56/512 = 7/64
The answer is B.
Answer: B
Question: If x and y are integers such that x^2= 3y and xy = 36, then x – y = ?
Options:
A)-30
B)-20
C)-5
D)5
E)0
Rationale: here x and y are integers .
x^2=3y,xy =36.
substitute (x^2)/3=y in xy => x^3=36*3=>x^3=108.
here x^3 is positive ,
x is also positive.
x=6 then y=6.
x-y=0
so option E is correct
Answer: E
Question: The table below shows the enrollment in various classes at a certain college.
Class | Number of Students
Biology | 60
Physics | 35
Calculus | 40
Although no student is enrolled in all three classes, 15 are enrolled in both Biology and Physics, 10 are enrolled in both Biology and Calculus, and 12 are enrolled in both Physics and Calculus. How many different students are in the three classes?
Options:
A)51
B)88
C)90
D)98
E)162
Rationale: No. of total students = no of students of biology + no of students of physics but not biology + no of students of calculus but not biology and physics
No. of total students = 60 + (35-15) + (40-10-12) = 60+20+18 = 98
Hence, Answer will be D.
Answer: D
Question: For all positive integers n and m, the function A(n) equals the following product:
(1 + 1/2 + 1/2^2)(1 + 1/3 + 3^2)(1 + 1/7 + 7^2)…(1 + 1/p_n + 1/p_n^2), where p_n is the nth smallest prime number, while B(m) equals the sum of the reciprocals of all the positive integers from 1 through m, inclusive. The largest reciprocal of an integer in the sum that B(25) represents that is NOT present in the distributed expansion of A(5) is
Options:
A)1/4
B)1/5
C)1/6
D)1/7
E)1/8
Rationale: For all positive integers n and m,
A(n) = (1 + 1/2 + 1/2^2)(1 + 1/3 + 3^2)(1 + 1/5 + 5^2)…(1 + 1/p_n + 1/p_n^2), where p_n is the nth smallest prime number,
note:i think there's a typo in the above function, A(n) could be (1 + 1/2 + 1/2^2)(1 + 1/3 +1/3^2)(1 + 1/5 +1/5^2)…(1 + 1/p_n + 1/p_n^2)
B(m) = sum of the reciprocals of all the positive integers from 1 through m, inclusive.
A(5), here 5 represents the 5th smallest prime number; the 5th smallest prime number is 11 {2, 3, 5, 7, 11, ...}
A(5) = (1 + 1/2 + 1/2^2)(1 + 1/3 + 3^2)(1 + 1/5 + 5^2)(1 + 1/7 + 1/7^2)(1 + 1/11 + 11^2)
The distributed expansion of A(5) = 1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 +1/7 + 1/9+ 1/10 + 1/11 +1/12 + 1/14+ ...
missing numbers are 1/8, 1/13, 1/16, ....
B(25) = (1 + 1/2 + 1/3 + 1/4 + ... + 1/16 + 1/17 + ... + 1/25)
here the largest reciprocal is 1 and the reciprocals are arranged in descending order based on their values
The largest reciprocal that present in B(25) but not in A(5) is 1/5
Answer B
Answer: B
Question: The function f is defined by subtracting 25 from the square of a number and the function d is defined as the square root of one-half of a number. If d(f(x))=10, then which of the following is a possible value of x?
Options:
A)-15
B)-5
C)0
D)5
E)25
Rationale: f(x) = x^2-25
d(x) = sqrt(x/2) not sqrt(x)/2, because the question clearly says its square root of (half of the number).
d(f(x)) = 10
d(x^2-25) =10
sqrt((x^2-25)/2) = 10
=> (x^2-25)/2 = 100
=>x^2 = 225
=> x = 15 or -15
Answer is A.
Answer: A
Question: The difference between two no is 9 and the product of the two is 14. What is the square of their sum?
Options:
A)237
B)260
C)177
D)197
E)137
Rationale: We know that (a+b)2=(a−b)2+4ab(a+b)2=(a−b)2+4ab
Substituting a - b = 9, and ab = 14, (a+b)2=(9)2+4(14)=137(a+b)2=(9)2+4(14)=137
Answer:E
Answer: E
Question: At what price must an article costing Rs.47.50 be marked in order that after deducting 5% from the list price. It may be sold at a profit of 25% on the cost price?
Options:
A)62.5
B)62.8
C)62.1
D)62.2
E)62.7
Rationale: CP = 47.50
SP = 47.50*(125/100) = 59.375
MP*(95/100) = 59.375
MP = 62.5
Answer:A
Answer: A
Question: The arithmetic mean and standard deviation of a certain normal distribution are 16.5 and 1.5, respectively. What value is exactly 2 standard deviations less than the mean?
Options:
A)10.5
B)11
C)11.5
D)12
E)13.5
Rationale: The value which isexactlytwo SD less than the mean is:mean-2*SD=16.5-2*1.5=13.5.
Answer: E.
Answer: E
Question: A sales executive was given a target to get annual bonus. He already reached 1/2 of his last year's target. If the target was reduced by 5% this year, what percentage target of the last year's target does he need to reach to get bonus?
Options:
A)9/20
B)6/12
C)7/5
D)10/20
E)3/6
Rationale: We have 1/2 and 5% that is 1/20
If we assume the last year's target to be 20
This year's target is 5% less of last year=19
The target reached this year 1/2*20=10
Remaining is 19-10=9
Required 9/20
Answer (A)
Answer: A
Question: Molly's age in 18 years will be four times her age three years ago. What is Molly's present age?
Options:
A)6
B)8
C)10
D)12
E)14
Rationale: Let x be Molly's present age.
x + 18 = 4(x-3)
x = 10
The answer is C.
Answer: C
Question: Some pens are divided among A, B, C and D. A gets twice the number of pens that B gets. C gets the same number of pens as D gets. If A gets 25 pens more than D and the ratio of the number of pens that B and C get is 2:3, then find the number of pens that D gets?
Options:
A)16
B)76
C)75
D)88
E)52
Rationale: Let the number of pens that A, B, C and D get be a, b, c and d respectively.
a:b = 2:1
a = c + 25
b:c = 2:3
a:b:c:d = 4:2:3:3
a, d get 4p, 3p pens
=> 4p - 3p = 25 => p = 25
=> D gets 3p = 3 * 25 = 75 pens.
AnswerC
Answer: C
Question: There are two circles of different radii. The are of a square is 784 sq cm and its side is twice the radius of the larger circle. The radius of the larger circle is seven - third that of the smaller circle. Find the circumference of the smaller circle.
Options:
A)18
B)99
C)12
D)07
E)11
Rationale: Let the radii of the larger and the smaller circles be l cm and s cm respectively. Let the side of the square be a cm.
a2 = 784 = (4)(196) = (22).(142)
a = (2)(14) = 28
a = 2l, l = a/2 = 14
l = (7/3)s
Therefore s = (3/7)(l) = 6 Circumference of the smaller circle = 2∏s = 12∏ cm.
Answer: C
Answer: C
Question: Andrea invested a certain sum of money in a bank that paid simple interest. The amount grew to $340 at the end of 2 years. She waited for another 4 years and got a final amount of $420. What was the principal amount that she invested at the beginning?
Options:
A)$350
B)$300
C)$400
D)$375
E)$360
Rationale: What shall be the rate of interest.? Does that is not required for the calculation?
Not really!
Keep in mind that the interest earned each year will be the same in Simple Interest.
At the end of 2 years, Amount = $340
At the end of 6 years, Amount = $420
This means she earned an interest of $80 in 4 years. Or $20 in each year.
We know that the interest earned each year will be the same.
Therefore she must have earned $40 in 2 years.
Hence Principal Amount = $340 - $40 = $300 Option B
Answer: B
Question: Find the area of a parallelogram with base 24 cm and height 16 cm.
Options:
A)298 cm2
B)288 cm2
C)187 cm2
D)384 cm2
E)177 cm2
Rationale: Area of a parallelogram = base * height
= 24 * 16
= 384 cm2
Answer: D
Answer: D
Question: A “palindromic integer” is an integer that remains the same when its digits are reversed. So, for example, 43334 and 516615 are both examples of palindromic integers. How many 6-digit palindromic integers are both even and greater than 500,000?
Options:
A)160
B)200
C)240
D)300
E)480
Rationale: The first digit and last digit are the same so the 2 possibilities are 6 or 8.
The second and third digits can be any number from 0 to 9.
The total number of palindromic integers is 2*10*10 = 200
The answer is B.
Answer: B