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GMAT 1: 690 Q50 V34

Re: when x is separated by 10, the quotient is y v a remainder that 4. If x<#permalink>04 Jun 2020, 22:04
When x is divided by 10, the quotient is y v a remainder the 4. If x and y space both confident integers, what is the remainder when x is split by 5?(A) 0(B) 1(C) 2(D) 3(E) 4
Given: as soon as x is separated by 10, the quotient is y v a remainder of 4.Asked: If x and y room both positive integers, what is the remainder as soon as x is split by 5?When x is split by 10, the quotient is y with a remainder of 4.x = 10y + 4x = 5(2y) + 4IMO E_________________
When x is separated by 10, the quotient is y through a remainder the 4. If x<#permalink>04 Jun 2020, 22:29
I typically pick numbers:14/10= 1. + R the 424/10=2 + R the 414/5 R is 4 24/5 R is 4.
posted from GMAT ToolKitI think that as soon as a number is split by 10 the reminder after separating by 5 will be the same
When x is split by 10, the quotient is y through a remainder of 4. If x<#permalink>07 Jun 2020, 08:06
When x is separated by 10, the quotient is y through a remainder of 4. If x and also y space both hopeful integers, what is the remainder as soon as x is divided by 5?(A) 0(B) 1(C) 2(D) 3(E) 4

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APPROACH #1: test a feasible value that xWhen it involves remainders, we have actually a nice home that says: If N split by D pipeline remainder R, then the feasible values of N are R, R+D, R+2D, R+3D,. . . Etc. for example, if k divided by 5 leaves a remainder of 1, climate the possible values the k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . Etc. So, native the given information, the feasible values that x are: 4, 14, 24, 34, 44, 54,....If friend divide any of these feasible x-values by 5, you"ll always get a remainder of 4.Answer: EAPPROACH #2: usage algebraThere"s a nice dominion that says, "If N split by D equates to Q through remainder R, then N = DQ + R"For example, since 17 split by 5 equates to 3 v remainder 2, climate we deserve to write 17 = (5)(3) + 2Likewise, due to the fact that 53 divided by 10 equals 5 through remainder 3, climate we can write 53 = (10)(5) + 3From the given information we can write: x = 10y + 4We can rewrite this as: x = (5)(2x) + 4We know that (5)(2x) is a many of 5, which means (5)(2x) + 4 is 4 more THAN a many of 5So, as soon as we division (5)(2x) + 4 by 5, the remainder will be 4Answer: ERELATED video clip _________________