Quant- Number properties Flashcards
If x is a positive number, is x an even integer?
(1) 3x is an even integer.
(2) 5x is an even integer.
Statement 1 : 3x is an even integer
Here x can either be an even integer such as 2, 4, 6…. or it can be a fraction such as 2/3, 4/3….. So x can be an even integer or a fraction. Insufficient.
Statement 2 : 5x is an even integer
Here again x can be an even integer such as 2, 4, 6…. or it can be a fraction such as 2/5, 4/5…. So x again can either be an even integer or a fraction. Insufficient.
Now instead of recycling the values it makes sense to use a mathematical operation (or mathematical operations) between the two statements.
Let us multiply the first statement by 2, since 3x = even integer ; 3x * 2 = even integer * 2 —–> 6x = even integer
Statement 2 says that 5x is an even integer and by multiplying statement 1 by 2 we have 6x to be an even integer. Subtracting the two we get
6x - 5x = even integer - even integer —–> x = even integer. Sufficient
What is the highest power of 12 that divides 54!?
(A) 25 (B) 26 (C) 19 (D) 50 (E) 31
There are 25 powers of 2^2 in 54!, and 4 turns out to be the limiting factor not 3.
Since the largest factor of any number is the number itself, the largest factor of the sum of y and z is 24.
An “Armstrong number” is an n-digit number that is equal to the sum of the nth powers of its individual digits. For example, 153 is an Armstrong number because it has 3 digits and 1^3 + 5^3 + 3^3 = 153. What is the digit k in the Armstrong number 1,6k4 ?
A. 2 B. 3 C. 4 D. 5 E. 6
Think of last digit
If b is the product of three consecutive positive integers c, c + 1, and c + 2, is b a multiple of 24 ?
b is a multiple of 8.
c is odd.
aNS = A
If the lengths of the legs of a right triangle are integers, what is the area of the triangular region?
- The length of one leg is 3/4 the length of the other.
- The length of the hypotenuse is 5.
ANS = B
Is –3 ≤ x ≤ 3 ?
x 2 + y 2 = 9
x 2 + y ≤ 9
ans = a
If x, y, and d are integers and d is odd, are both x and y divisible by d ?
x + y is divisible by d.
x – y is divisible by d.
ans = C
If x < y < z and y-x > 5, where x is an even integer and y and z are odd integers, what is the least possible value of z - x?
A. 6 B. 7 C. 8 D. 9 E. 10
Think about it this way: x < y < z
Difference between y and x is more than 5 so it is at least 6. But x is even and y is odd so their difference would be odd. Hence the diff between them will be at least 7.
Now z is greater than y by at least 2 (since z is odd too), hence diff between x and z is at least 9.
Think about it this way: x < y < z
Difference between y and x is more than 5 so it is at least 6. But x is even and y is odd so their difference would be odd. Hence the diff between them will be at least 7.
Now z is greater than y by at least 2 (since z is odd too), hence diff between x and z is at least 9.
ANS = D
https://gmatclub.com/forum/each-entry-in-the-multiplication-table-above-is-an-integer-that-is-eit-305983.html
Exactly 3 deposits have been made in a savings account and the amounts of the deposits are 3 consecutive integer multiples of $7. If the sum of the deposits is between $120 and $170, what is the amount of each of the deposits?
(1) The amount of one of the deposits is $49.
(2) The amount of one of the deposits is $63.
consecutive integer multiples of $7. The sum of the deposits is between $120 and $170
STRATEGY: For questions like this in which we have a limited number of possible cases, I like to invest a little bit of time up front to list of all of those possible cases. This will typically make things much easier when analyzing the two statements.
Also, when I scan the answer choices, I see that two of the three deposits are $49 and $63. This will help me list the various cases
Since the sum of the deposits is between $120 and $170, the possible cases are:
case i: $49, $56, and $63 (sum = $168) [ since $168 is very close to the upper limit of $170, I can see that the remaining cases must start with smaller values than $49]
case ii: $42, $49, and $56 (sum = $147)
case iii: $35, $42, and $49 (sum = $126)
case iv: $28, $35 and $42 (sum = $105) TOO small
Target question: What is the amount of each of the deposits?
Statement 1: The amount of one of the deposits is $49.
Check the three possible cases . . . i, ii and iii all apply, which means we can’t answer the target question with certainty
Statement 1 is NOT SUFFICIENT
Statement 2: The amount of one of the deposits is $63.
Check the three possible cases . . . case i is the only one that satisfies statement 2, which means the three deposits are $49, $56, and $63
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer: B
