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A number 4p25q is divisible by 4 and 9; where p and q are the thousand 06 Apr 2021, 06:45
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A 4p25q is divisible by 4 and 9; where p and q are the thousands and units digits, respectively. What is the minimum value of p/q ?

(A) 1/8
(B) 1/7
(C) 1/6
(D) 2/5
(E) 5/2
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C
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GMAT Focus 1: 735 Q90 V89 DI81
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A number 4p25q is divisible by 4 and 9; where p and q are the thousand 06 Apr 2021, 07:16
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Bunuel
A 4p25q is divisible by 4 and 9; where p and q are the thousands and units digits, respectively. What is the minimum value of p/q ?

(A) 1/8
(B) 1/7
(C) 1/6
(D) 2/5
(E) 5/2
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Divisibility by 4 or 2^2 depends on the last two digits.
52 and 56 are divisible by 4, so q can be 2 or 6.

Divisibility by 9 depends on the sum of all digits = 4+p+2+5+q=11+p+q
q=2: 11+p+q=13+p, so p=5.....\(\frac{p}{q}=\frac{5}{2}\)
q =6: 11+p+6=17+p, so p=1.....\(\frac{p}{q}=\frac{1}{6}\)

C
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A number 4p25q is divisible by 4 and 9; where p and q are the thousand 06 Apr 2021, 07:43
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Given: A 4p25q is divisible by 4 and 9; where p and q are the thousands and units digits, respectively.
Asked: What is the minimum value of p/q ?

Since last 2 digits should be divisible by 4, max value of q = 6
Since sum of digits should be divisible by 9, min value of p = 1
Minimum value of p/q = 1/6

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A number 4p25q is divisible by 4 and 9; where p and q are the thousand 06 Apr 2021, 08:03
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Bunuel
A 4p25q is divisible by 4 and 9; where p and q are the thousands and units digits, respectively. What is the minimum value of p/q ?

(A) 1/8
(B) 1/7
(C) 1/6
(D) 2/5
(E) 5/2
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Possible values of are \(q = 2\) & \(6\)

For, minimum value of p/q maximumizing the value of q and minimizing the value of p

1. If \(q = 2\) , p must be 5 Thus, \(\frac{p}{q} = \frac{5}{2}\)
2. If \(q = 6\) , p must be 1 Thus, \(\frac{p}{q} = \frac{1}{6}\), Answer must be (C)
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A number 4p25q is divisible by 4 and 9; where p and q are the thousand 08 Apr 2021, 04:32
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For p/q to be minimum,

p should me min and q should be maximum

4p25q
First lets check the divisibility of 4
q can be 2 0r 6
But we need max value of q , so will take 6

For divisibility by 9

sum of digits should be divisible by 9

4+2+5+q(which we have taken alraedy as 6)= 17

min value of 1 is required , so p is 1

p/q = 1/6
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A number 4p25q is divisible by 4 and 9; where p and q are the thousand 11 Nov 2024, 13:14
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