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Seven questions for christoph! [#permalink]
26 Dec 2005, 16:44

Question 4 edited

[Question 1]

There's a square glass. To paint this glass, it costs $8 per square meter. To paint its circumference, it costs $10 per meter. If the total cost of painting the glass and the total cost of painting its circumference are the same, what is the area of this glass?

[Question 2]

Is (a+5)^4 < (b-5)^4 ?

1) a+b > 5
2) a > b

[Question 3]

John has 25 cent coins and 5 cent coins. The number of 25 cent coins are four times as many as that of 5 cent coins. What is the ratio of the total value of 25 cent coins to the total value of 5 cent coins?

[Question 4]

A set is consisted of consecutive integers. The smallest element and the largest element are even. The number of even elements in this set is 7. When you pick one out of this set, what is the probability of picking an even number?

[Question 5]

The sum of 1, 2, 6, and 24 is a multiple of a prime number. What is the sum of the prime numbers?

[Question 6]

A car runs at 80 km/hour. How many seconds does it take for this car to run 400 meters?

[Question 7]

Either 6 or 24 ornaments are put into boxes. If the total number of these ornaments are 126, what are the number of boxes with 6 ornaments and boxes with 24 ornaments?

1) There are less than 4 boxes with 6 ornaments.
2) There are more than 3 boxes with 24 ornaments. _________________

Auge um Auge, Zahn um Zahn !

Last edited by gamjatang on 26 Dec 2005, 20:01, edited 1 time in total.

Re: Seven questions for christoph! [#permalink]
26 Dec 2005, 16:54

gamjatang wrote:

[Question 1]

There's a square glass. To paint this glass, it costs $8 per square meter. To paint its circumference, it costs $10 per meter. If the total cost of painting the glass and the total cost of painting its circumference are the same, what is the area of this glass?

cost to paint area = 8a^2
cost to paint circumference = 10x4a=40a

Re: Seven questions for christoph! [#permalink]
26 Dec 2005, 17:09

gamjatang wrote:

[Question 3]. John has 25 cent coins and 5 cent coins. The number of 25 cent coins are four times as many as that of 5 cent coins. What is the ratio of the total value of 25 cent coins to the total value of 5 cent coins?

There's a square glass. To paint this glass, it costs $8 per square meter. To paint its circumference, it costs $10 per meter. If the total cost of painting the glass and the total cost of painting its circumference are the same, what is the area of this glass?

Ans: The area of glass = 25

Lets say a is the side of the square

To paint glass, $8, i.e 8a^2
To paint circumference, $1, ie 4a * 10 = 40a

Now these are equal, so 8a^2 = 40a, solving a = 5
The area = a^2 = 25 _________________

"The difference between a smart person and a wise person is that
a smart person knows what to say and
a wise person knows whether or not to say it."

Re: Seven questions for christoph! [#permalink]
26 Dec 2005, 20:03

Bhai wrote:

gamjatang wrote:

[Question 1]

There's a square glass. To paint this glass, it costs $8 per square meter. To paint its circumference, it costs $10 per meter. If the total cost of painting the glass and the total cost of painting its circumference are the same, what is the area of this glass? 8x^2 = 10.4.x; x = 5 so area = 25

[Question 2]

Is (a+5)^4 < (b-5)^4 ?

1) a+b > 5 2) a > b E Dont ask how. I messed this up royally and finally got E

[Question 3]

John has 25 cent coins and 5 cent coins. The number of 25 cent coins are four times as many as that of 5 cent coins. What is the ratio of the total value of 25 cent coins to the total value of 5 cent coins? 8*25/2*5 = 20:1

[Question 4]

A set is consisted of 7 consecutive integers. The smallest element and the largest element are even. When you pick one out of this set, what is the probability of picking an even number? 4/7

[Question 5]

The sum of 1, 2, 6, and 24 is a multiple of a prime number. What is the sum of the prime numbers? 3 + 11 = 14

[Question 6]

A car runs at 80 km/hour. How many seconds does it take for this car to run 400 meters? 400*3600/80,000 = 18 secs

[Question 7]

Either 6 or 24 ornaments are put into boxes. If the total number of these ornaments are 126, what are the number of boxes with 6 ornaments and boxes with 24 ornaments?

1) There are less than 4 boxes with 6 ornaments. 2) There are more than 3 boxes with 24 ornaments. A

Sorry for the confusion, Bhai. I edited question 4. And please double-check question2. _________________

There's a square glass. To paint this glass, it costs $8 per square meter. To paint its circumference, it costs $10 per meter. If the total cost of painting the glass and the total cost of painting its circumference are the same, what is the area of this glass?

25

Let side of square = x Cost of area painting = 8*x^2 Cost of circumfrence painting = 10 * 4x

8* x^2 = 40 x so x = 5 Area = 25

[Question 2]

Is (a+5)^4 < (b-5)^4 ?

1) a+b > 5
2) a > b

C

St 1: Let a = 5 and b = 4 then stem eq is FALSE Let a = 10 and b = -4 then stem eq is FALSE Let a = -4 and b = 10 then stem eq is TRUE

so INSUFF

St2: Let a = 4 and b = 3 then stem eq is FALSE Let a = -3 and b = -4 then stem eq is TRUE

So INSUFF

Combined St1 and St2: Take same examples and its always FALSE So SUFF [Question 3]

John has 25 cent coins and 5 cent coins. The number of 25 cent coins are four times as many as that of 5 cent coins. What is the ratio of the total value of 25 cent coins to the total value of 5 cent coins?

20:1

25 cents coins = x 5 cents coins = y

x= 4y

Total value of 25 cents coins = 25x Total value of 5 cents coins = 5y Ratio = 25x/5y = (25 * 4y)/y = 20:1

[Question 4]

A set is consisted of consecutive integers. The smallest element and the largest element are even. The number of even elements in this set is 7. When you pick one out of this set, what is the probability of picking an even number?

7/13

When first and last elements are even in a series of consecutive integers then there will be 6 odd integers in the whole series. So prob = 7/13

[Question 5]

The sum of 1, 2, 6, and 24 is a multiple of a prime number. What is the sum of the prime numbers?

3+11 = 14 [Question 6]

A car runs at 80 km/hour. How many seconds does it take for this car to run 400 meters?

(3600 * 400)/80000 = 18

[Question 7]

Either 6 or 24 ornaments are put into boxes. If the total number of these ornaments are 126, what are the number of boxes with 6 ornaments and boxes with 24 ornaments?

1) There are less than 4 boxes with 6 ornaments.
2) There are more than 3 boxes with 24 ornaments.

A

Eq from stem is

6x + 24y =126

St1: When x < 4 then x is either 1,2 or 3. Only x = 1 leads to integer value of y in above equation . So x =1 and y = 5. So SUFF

St2: When y > 3 then y is either 4 or 5 (greater values will not fit in above equation). y = 4 leads x = 5 and y = 5 leads x = 1. So INSUFF. _________________

There's a square glass. To paint this glass, it costs $8 per square meter. To paint its circumference, it costs $10 per meter. If the total cost of painting the glass and the total cost of painting its circumference are the same, what is the area of this glass?

25

Let side of square = x Cost of area painting = 8*x^2 Cost of circumfrence painting = 10 * 4x

8* x^2 = 40 x so x = 5 Area = 25

[Question 2]

Is (a+5)^4 < (b-5)^4 ?

1) a+b > 5 2) a > b

C

St 1: Let a = 5 and b = 4 then stem eq is FALSE Let a = 10 and b = -4 then stem eq is FALSE Let a = -4 and b = 10 then stem eq is TRUE

so INSUFF

St2: Let a = 4 and b = 3 then stem eq is FALSE Let a = -3 and b = -4 then stem eq is TRUE

So INSUFF

Combined St1 and St2: Take same examples and its always FALSE So SUFF [Question 3]

John has 25 cent coins and 5 cent coins. The number of 25 cent coins are four times as many as that of 5 cent coins. What is the ratio of the total value of 25 cent coins to the total value of 5 cent coins?

20:1

25 cents coins = x 5 cents coins = y

x= 4y

Total value of 25 cents coins = 25x Total value of 5 cents coins = 5y Ratio = 25x/5y = (25 * 4y)/y = 20:1

[Question 4]

A set is consisted of consecutive integers. The smallest element and the largest element are even. The number of even elements in this set is 7. When you pick one out of this set, what is the probability of picking an even number?

7/13

When first and last elements are even in a series of consecutive integers then there will be 6 odd integers in the whole series. So prob = 7/13

[Question 5]

The sum of 1, 2, 6, and 24 is a multiple of a prime number. What is the sum of the prime numbers?

3+11 = 14 [Question 6]

A car runs at 80 km/hour. How many seconds does it take for this car to run 400 meters?

(3600 * 400)/80000 = 18

[Question 7]

Either 6 or 24 ornaments are put into boxes. If the total number of these ornaments are 126, what are the number of boxes with 6 ornaments and boxes with 24 ornaments?

1) There are less than 4 boxes with 6 ornaments. 2) There are more than 3 boxes with 24 ornaments.

A

Eq from stem is

6x + 24y =126

St1: When x < 4 then x is either 1,2 or 3. Only x = 1 leads to integer value of y in above equation . So x =1 and y = 5. So SUFF

St2: When y > 3 then y is either 4 or 5 (greater values will not fit in above equation). y = 4 leads x = 5 and y = 5 leads x = 1. So INSUFF.

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