Evaluating The Efficacy And Safety Of Donepezil Hydrochloride (HCl) (Aricept) In Treating Cognitive Dysfunction Exhibited By Children With Down Syndrome

Inclusion Criteria: * Ages 10 to 17 years old, weight more than or equal to 20 kg * Male and female * Vineland-II Adaptive Behavior Scales (VABS-II)/Parent/Caregiver Rating Form (PCRF) standard composite score greater than (\>) 55 * Diagnosis of DS (trisomy 21) documented by chromosomal analysis (karyotyping). If such documentation is not available at screening, karyotyping will be performed with the screening labs and must be documented prior to baseline visit. * Naïve to approved or unapproved cholinesterase inhibitors is preferred however, prior use of these medications is allowed, provided that the medication was discontinued at least 3 months prior to screening and that it was not discontinued for lack of tolerability or efficacy or for the sole purpose of enrolling the subject in the study. * Subjects residing in the community * Must be expected to complete all procedures scheduled during the Screening and Baseline visits including all efficacy and safety parameters. * Must speak English and be verbal and able to be understood most of the time and must not use other forms of communication, signs, symbol boards or devices to supplement his/her communication ability * Must have a parent or other reliable caregiver who agrees to accompany the subject to all clinic visits, provide information about the subject as required by the protocol, and ensure compliance with the medication schedule * a Parent or Caregiver must be a constant and reliable informant with sufficient contact with the subject to have detailed knowledge of the subject's adaptive behavior in order to be able to complete the VABS-II/PCRF accurately. The same individual should complete the form at every visit. * Should be in good general health with no medical conditions that are considered both clinically significant and unstable * Clinical laboratory values within normal limits or abnormalities considered not clinically significant by the investigator and sponsor * Stable Type I (insulin-dependent) or Type II diabetes are eligible provided they are monitored regularly prior to and during the study to ensure adequate glucose control (fasting blood glucose \<140 milligram per deciliter (mg/dl) and glycosylated hemoglobin \[hemoglobin A1c\] \<8 percent (%) at screening). * Thyroid disease also may be included in the study provided they are euthyroid and stable on treatment for at least 3 months prior to screening. * History of seizure disorder is allowed provided that subjects are on stable treatment for at least 3 months and have not had a seizure within the past 6 months. * Independent in ambulation or ambulatory aided (example, walker or cane, wheelchair), vision and hearing (eyeglasses and/or hearing aid permissible) sufficient for achieving VABS-II/PCRF composite standard scores \>55 and for cooperating with examinations and the Test of Verbal Expression and Reasoning (TOVER). Exclusion Criteria: * Ages \<10 or \>17 years * Active or clinically significant conditions affecting absorption, distribution or metabolism of the study medication (example, inflammatory bowel disease, gastric or duodenal ulcers or severe lactose intolerance) * Known hypersensitivity to piperidine derivatives or cholinesterase inhibitors * Currently receiving cholinesterase inhibitors or who have received them in the 3 months prior to screening or with prior use \>3 months prior to screening who stopped for lack of efficacy or tolerability * No reliable parent or caregiver, or participants, or caregivers who are unwilling or unable to complete any of the outcome measures and fulfill the requirements of this study * Clinically significant obstructive pulmonary disease or asthma untreated or not controlled by treatment within 3 months prior to screening * Recent (less than or equal to 2 years) hematologic/oncologic disorders (mild anemia allowed) * Evidence of active, clinically significant, and unstable gastrointestinal, renal, hepatic, endocrine or cardiovascular system disease * Current Diagnostic and Statistical Manual IV Text Revision (DSM-IV-TR) diagnosis of Major Depressive Disorder (MDD) or any current primary psychiatric diagnosis other than DS (as per DSM-IV) * Any condition which would make the subject or the caregiver, in the opinion of the investigator, unsuitable for the study * Unsuitability which includes female subjects who have begun menstruation and are thus of child-bearing potential, who may be sexually active and who are not practicing an effective means of birth control.