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X is a multiple of 5.what is the value of X? (1) 1237 < X < 1242.5

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If X is a multiple of 5,what is the value of X?
(1) 1237 < X < 1242.5
(2) 3711 < 3X < 3727.5

[Reveal] Spoiler:
This is unofficial question. I marked E for this. The pdf document says the answer is D.

On dividing statement (2) by 3, we get statement 1. Hence, both statements are same.

Way pdf solved it:
Only one integer multiple i.e. 1240 is present between this range. so this is sufficient => Ans = D

Way I solved it:
X is a multiple of 5 => X can be 1240 or 1240.5 or 1237.5, etc as all of them are multiple of 5, not necessary integral multiple! Ans = E

My Doubt - Am I going wrong somewhere i.e. It is very much necessary that a multiple of an integer (in this case, 5) has to be an integer (in this case, 1240)?
Or Is this question a poor quality question i.e a multiple of an integer (in this case, 5) need not be an integer (in this case, 1237.5 or 1238.995 or ...)?

Thanks!

For a display, identical cubic boxes are stacked in square layers

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For a display, identical cubic boxes are stacked in square layers. Each layer consists of cubic boxes arranged in rows that form a square, and each layer has 1 fewer row and 1 fewer box in each remaining row than the layer directly below it. If the bottom layer has 21 boxes and the top layer has only 1 box, how many boxes are in the display?

A. 236
B. 260
C. 269
D. 276
E. 285

If [x] denotes the latest integer greater than or equal..

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If [x] denotes the latest integer greater than or equal and [x/2] = 0, which of the following could be the value of x?

A. -2
B. -3/2
C. 1/2
D. 1
E. 2

Is the integer M a negative number...?

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Is the integer m a negative number?

1. m^5 - m < 0

(second part I got it right)


Answer said that 1) was sufficient, but I disagree.

For whatever negative m you pick, it will be true that m^5 - m < 0. I'm fine with it.

But what if m = -1 ?
In this case, the result would be 0 < 0, so 1) would not be sufficient.

Any tips? I really cannot see my error, it seems obvious to me that if m = -1, we would have -1+1=0.


Source: Optimus Prep test. Difficulty: Difficult

In a work force, the employees are either managers or directors

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In a work force, the employees are either managers or directors. What is the percentage of directors?

(1) The average salary for manager is $5,000 less than the total average salary.
(2) The average salary for directors is $15,000 more than the total average salary.

If x=-1 and n is the sum of the first 100 prime numbers, what is the

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If x=-1 and n is the sum of the first 100 prime numbers, what is the value of \(x^n+x^n^+^1+x^n^+^2\)?

A. -2 B. -1 C. 0 D. 1 E. 2

In the x-y plane, what is the slope of line K?

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In the x-y plane, what is the slope of line K?

1) Line K intersects with line equation y=-3x
1) Line K is parallel to line equation y=2x

An air-powered rifle was shot at a target. What was the average speed

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An air-powered rifle was shot at a target. What was the average speed of the bullet?

(1) The target is 800 meters away
(2) The bullet reached the target in 3 seconds.

If it takes Josh 18 minutes to do 54 math problems and he continues

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If it takes Josh 18 minutes to do 54 math problems and he continues working at the same rate, how long will it take him to do 81 problems?

A. 18 minutes
B. 27 minutes
C. 36 minutes
D. 54 minutes
E. 1 hour 21 minutes

If Jake washes x cars in 18 minutes, which of the following expresses

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If Jake washes x cars in 18 minutes, which of the following expresses the number of minutes it would take him to wash 3x + 3 cars?

A. 6x + 3
B. 54x + x/6
C. 54(x + 1)/x
D. (x + 1)/6
E. 54 + (x + 1)/2

A boy's club, which is trying to raise money by having a car wash, can

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A boy's club, which is trying to raise money by having a car wash, can wash 100 cars if they work for 8 hours, without a break. A girl's club is also going to have a car wash, if the members of the girl's club wash 5 cars per hour, how many more cars per hour does the boy's club wash?

A. 1.15
B. 1.25
C. 3.5
D. 6.25
E. 7.5

If $2.00 were invested at 4% annual interest at the end of 8 years the

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If $2.00 were invested at 4% annual interest at the end of 8 years the total value of investment would be

A. 8(2.04)
B. 2(8)(1.04)
C. 2(8)(1.4)
D. 2 + 8(0.04)
E. 2 + 2(8)(0.04)

Do the official DS Qs use the "no" answer as unique and sufficient?

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Hi everyone!

A question on DS here.

Is y > 0?

(1) x^2 y^2 = 0

(2) x^2 + y^2 = 0

The answer is B, because the statement gives a NO answer.

My question: do the real questions have the "definitively NO" as a possible outcome? Or should we always aim for the "absolutely YES" answer?

There are many prep companies that have these def-NO questions and since we get a unique NO answer it's sufficient, but I have never seen an OG question "aiming" for a def-NO answer. They all seem to be tuned to be proven "True, YES" and not proven "NO"

Do I make myself clear here?

Cheers!

If a, b, c, d, and e are integers and the expression

How much money must be invested at 10% annual interest, compounded sem

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How much money must be invested at 10% annual interest, compounded semi-annually, in order to earn $51.25 in interest income by the end of the year?

A. $1,025.00
B. $512.50
C. $500.00
D. $256.25
E. $42.00

If x dollars were invested at 10% annual interest, which of the follow

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If x dollars were invested at 10% annual interest, which of the following, in terms of x, is the profit the investment will yield, in dollars, after a year?

A. 0.1x
B. 0.9x
C. x
D. 1.1x
E. 1.2x

If $2,000 were invested at 10% annual interest, how much profit would

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If $2,000 were invested at 10% annual interest, how much profit would the investment yield, in dollars, after a year?

A. $0.2
B. $2
C. $20
D. $200
E. $2,200

How much money would have to be invested in an account, which yields 3

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How much money would have to be invested in an account, which yields 3% annual interest, for a period of a year in order to earn a total investment value of $721?

A. $554.62
B. $700.00
C. $721.00
D. $742.63
E. $937.30

What is the largest value of non negative integer N for which 10N is a

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What is the largest value of non negative integer N for which \(10^N\) is a factor of 50!?

A. 5
B. 6
C. 12
D. 15
E. 20

If x is not equal y, is

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