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# If c and d are both integers, c>d, and -3c>19, then the largest value

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If c and d are both integers, c>d, and -3c>19, then the largest value  [#permalink]

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17 Jul 2015, 05:19
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65% (hard)

Question Stats:

48% (00:59) correct 52% (00:46) wrong based on 141 sessions

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If c and d are both integers, c>d, and -3c>19, then the largest value of d would be?

A. -5
B. -6
C. -7
D. -8
E. -10

Source: EmpowerGMAT
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Current Student
Joined: 20 Mar 2014
Posts: 2643
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
If c and d are both integers, c>d, and -3c>19, then the largest value  [#permalink]

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17 Jul 2015, 05:34
1
Engr2012 wrote:
If c and d are both integers, c>d, and -3c>19, then the largest value of d would be?

A. -5
B. -6
C. -7
D. -8
E. -10

Source: EmpowerGMAT

Given: c and d are both integers and -3c>19.

Whenever we talk about "greatest" values, only an inequality of the form $$a<X$$ or $$a\leq{Y}$$ will give the maximum value of a as either X-1 or Y (for 'a' $$\in$$ integer).

Now, -3c>19 ----> 3c<-19 ---> c<-6.33 ---> the maximum value of c is -7 (as c MUST be an integer, given).

As d<c and d is an integer , thus d<-7 ---> d = -8 as the maximum value. D is the correct answer.
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Re: If c and d are both integers, c>d, and -3c>19, then the largest value  [#permalink]

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18 Jul 2015, 06:25
1
Engr2012 wrote:
If c and d are both integers, c>d, and -3c>19, then the largest value of d would be?

A. -5
B. -6
C. -7
D. -8
E. -10

Source: EmpowerGMAT

Given : d < c

CONCEPT: For largest value of d, the value of c must be greatest

-3c > 19
i.e. 3c < -19
i.e. c < -19/3
i.e. c < -6.33
i.e. Largest Integer possible value of c which is less than -6.33 is -7
$$c_{max.} = -7$$

and since d < c
therefore Largest possible Integer Value of d is less than -7 i.e. -8

$$d_{max.} = -8$$

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Re: If c and d are both integers, c>d, and -3c>19, then the largest value  [#permalink]

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18 Jul 2015, 11:07
I am having trouble understanding why the maximum of D is -8. What about -10? If C>D, then D could be any number less than -7, so, the largest in the 5 answer choices is -10....?
Current Student
Joined: 20 Mar 2014
Posts: 2643
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
If c and d are both integers, c>d, and -3c>19, then the largest value  [#permalink]

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18 Jul 2015, 11:15
1
immanl wrote:
I am having trouble understanding why the maximum of D is -8. What about -10? If C>D, then D could be any number less than -7, so, the largest in the 5 answer choices is -10....?

No, your thinking is incorrect. When we know that c>d and c<-6.33, the largest value of c can be -7 while if c=-7, then largest value of d < -7 will be -8. For negative numbers, -7 > -8 and -8> -10 .

You are right in saying that d can take any value less than -7 ---> d could be -8, -9, -10 .... and out of all these values, -8 is the greatest.

Look at the numbers on the number line. For any 2 numbers, the ones on the right are greater than the ones on the left:

.......-11 -10 -9 -8 -7 -6 -5 ..... 0 1 2 3 4 5 6 ... (-11< -10, -10< -8, 4< 5 etc).

So, as per the question if d<c and c = -7 , then d's largest 'possible' value has to be -8.

-10 is smaller than -8.

Hope this helps.
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Posts: 2139
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Re: If c and d are both integers, c>d, and -3c>19, then the largest value  [#permalink]

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18 Jul 2015, 21:32
immanl wrote:
I am having trouble understanding why the maximum of D is -8. What about -10? If C>D, then D could be any number less than -7, so, the largest in the 5 answer choices is -10....?

-10 is LESS than -8

therefore -8 is the biggest value of d

Any value towards the left on the Number line is smaller than the value to the right of the number

Please refer the picture attached to see the numbers on the Number line
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Re: If c and d are both integers, c>d, and -3c>19, then the largest value  [#permalink]

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19 Jul 2015, 08:37
Engr2012 wrote:
immanl wrote:
I am having trouble understanding why the maximum of D is -8. What about -10? If C>D, then D could be any number less than -7, so, the largest in the 5 answer choices is -10....?

No, your thinking is incorrect. When we know that c>d and c<-6.33, the largest value of c can be -7 while if c=-7, then largest value of d < -7 will be -8. For negative numbers, -7 > -8 and -8> -10 .

You are right in saying that d can take any value less than -7 ---> d could be -8, -9, -10 .... and out of all these values, -8 is the greatest.

Look at the numbers on the number line. For any 2 numbers, the ones on the right are greater than the ones on the left:

.......-11 -10 -9 -8 -7 -6 -5 ..... 0 1 2 3 4 5 6 ... (-11< -10, -10< -8, 4< 5 etc).

So, as per the question if d<c and c = -7 , then d's largest 'possible' value has to be -8.

-10 is smaller than -8.

Hope this helps.

Thank you! I dont know what i was thinking!
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Re: If c and d are both integers, c>d, and -3c>19, then the largest value  [#permalink]

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05 Feb 2018, 10:22
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