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

Question

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

(PS04797)

EgmatQuantExpert · Accepted Answer

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.

Answer: B

Mega1234 · Answer

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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Iakovos1995 · Answer

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.

The correct answer is B.

LevanKhukhunashvili · Answer

OG 2019? very interesting
Has "bb" already made an excel spreadsheet about it?
If yes, please give me the link

KSBGC · Answer

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.

Abhishek009 · Answer

(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

Kinshook · Answer

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

ScottTargetTestPrep · Answer

Solution:

If x = 1, y = 4^1 - 3 = 1.

If x = 2, y = 4^2 - 3 = 13.

If x = 3, y = 4^3 - 3 = 61.

If x = 4, y = 4^4 - 3 = 253.

We see that y can’t be 7 if x is a positive integer.

Answer: B

clover1987 · Answer

The simple method I used:

Q: 4^x - 3 = y

All units digit of power of 4's follow this pattern: 4, 6, 4, 6 
 (For example: 4^1 = 4 or 4^2 = 16 or 4^3 = 64)

Therefore the units digit of the answer can only be:
i) 4 - 3 =  1 
ii) 6 - 3 =  3

Therefore, out of the answer choices  ANS B  ends with 7 and is the only that does not end with 1 or 3.

ANS B is correct

GMATinsight · Answer

Answer: Option B

Video solution by  GMATinsight

https://www.youtube.com/watch?v=ifSbHbiHVdg

avigutman · Answer

Video solution from Quant Reasoning: Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1 https://www.youtube.com/watch?v=xuWLAU8Yz0M

Rohanx9 · Answer

Another way of figuring it out without calculating. 
4^x - 4 should be a multiple of 4. Therefore any answer term minus -1 (as 4^x -3 - 1 = 4^x-4) should be a multiple of 4.

Only 7 is not, as 7-1 = 6. Not a multiple of 4.

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

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GMAT Problem Solving (PS) Questions

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

Prep Toolkit

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