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# If x is a positive integer and 4^x – 3 = y, which of the following CAN

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Math Expert
Joined: 02 Sep 2009
Posts: 58340
If x is a positive integer and 4^x – 3 = y, which of the following CAN  [#permalink]

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22 Jun 2018, 00:14
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Question Stats:

94% (00:55) correct 6% (01:02) wrong based on 912 sessions

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If x is a positive integer and $$4^x – 3 = y$$, which of the following CANNOT be a value of y ?

A. 1

B. 7

C. 13

D. 61

E. 253

NEW question from GMAT® Official Guide 2019

(PS04797)

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Posts: 3074
Re: If x is a positive integer and 4^x – 3 = y, which of the following CAN  [#permalink]

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22 Jun 2018, 03:31
8
3

Solution

Given:
• x is a positive integer
• $$4^x – 3 = y$$

To find:
• From the given options, which one cannot be the value of y

Approach and Working:

Apart from checking with the options, there is one more way of figuring out the correct answer
From the given expression $$4^x – 3 = y$$,
• $$4^x = y + 3$$

Now, for any value of x, $$4^x$$ will always end with either 4 of 6
• Hence, y must be ending with either 1 or 3

From the given options, only option B is not ending with either 1 or 3

Hence, the correct answer is option B.

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##### General Discussion
Intern
Joined: 08 Jul 2017
Posts: 15
Location: Greece
GPA: 3.31
Re: If x is a positive integer and 4^x – 3 = y, which of the following CAN  [#permalink]

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22 Jun 2018, 00:26
If x=1: 4^1 - 3 = 1
If x=2: 4^2 - 3 = 13
If x=3: 4^3 - 3 = 61
If x=4: 4^4 - 3 = 253

The only value that y cannot take is 7.

Senior Manager
Joined: 13 Feb 2018
Posts: 451
GMAT 1: 640 Q48 V28
Re: If x is a positive integer and 4^x – 3 = y, which of the following CAN  [#permalink]

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22 Jun 2018, 01:29
OG 2019? very interesting
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Joined: 03 Aug 2014
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Re: If x is a positive integer and 4^x – 3 = y, which of the following CAN  [#permalink]

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22 Jun 2018, 02:15
1
1
4x-3 = y => 4x = y+3

This implies that y+3 should be a multiple of 4. Quickly scanning the options reveal that for option B, 7+3 = 10 is not a multiple of 4.

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GPA: 3.68
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If x is a positive integer and 4^x – 3 = y, which of the following CAN  [#permalink]

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22 Jun 2018, 02:16
Bunuel wrote:
If x is a positive integer and $$4^x – 3 = y$$, which of the following CANNOT be a value of y ?

A. 1

B. 7

C. 13

D. 61

E. 253

NEW question from GMAT® Official Guide 2019

(PS04797)

Note:

x = positive integer

Given,

$$4^x$$-3=y

we are asked to find out which can't be the value of y. No specific value of x is given.

Trail and error is the way to get the correct answer. Assume the value of x = 1 , 2 , 3 , 4. All the option matches except B.

$$4^1$$-3=1
$$4^2$$-3=13
$$4^3$$-3=61
$$4^4$$-3=253

Thus , B is the correct answer.
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Re: If x is a positive integer and 4^x – 3 = y, which of the following CAN  [#permalink]

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20 Aug 2019, 07:52
Bunuel wrote:
If x is a positive integer and $$4^x – 3 = y$$, which of the following CANNOT be a value of y ?

A. 1

B. 7

C. 13

D. 61

E. 253

NEW question from GMAT® Official Guide 2019

(PS04797)

(A) $$4^1 - 3 = 1$$ ; Possible
(C) $$4^2 - 3 = 13$$ ; Possible
(D) $$4^3 - 3 = 61$$ ; Possible
(E) $$4^4 - 3 = 253$$ ; Possible

Thus, Answer must be (B) 7
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Joined: 03 Jun 2019
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Re: If x is a positive integer and 4^x – 3 = y, which of the following CAN  [#permalink]

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15 Sep 2019, 03:08
Bunuel wrote:
If x is a positive integer and $$4^x – 3 = y$$, which of the following CANNOT be a value of y ?

A. 1

B. 7

C. 13

D. 61

E. 253

NEW question from GMAT® Official Guide 2019

(PS04797)

Given: x is a positive integer and $$4^x – 3 = y$$

Asked: Which of the following CANNOT be a value of y ?

$$4^x – 3 = y$$

A. 1
4^x - 3 = 1
4^x = 4
x =1

B. 7
4^x - 3 = 7
4^x = 10
x is not an integer

C. 13
4^x - 3 = 13
4^x = 16
x = 2

D. 61
4^x = 61+3 = 64
x = 3

E. 253
4^x = 253+3 = 256
x = 4

IMO B
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Re: If x is a positive integer and 4^x – 3 = y, which of the following CAN   [#permalink] 15 Sep 2019, 03:08
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